Mathematics Books

Book SynopsisBased on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry''s history to illustrate how crucial proof writing is to the job of a mathematician.Table of ContentsPreface. Acknowledgments. PART I FOUNDATIONS. 1 The First Geometers. 2 Thales. 3 Plato and Aristotle. PART II THE GOLDEN AGE. 4 Pythagoras. 5 Euclid. 6 Archimedes. PART III ENLIGHTENMENT. 7 François Viète. 8 René Descartes. 9 Gérard Desargues. PART IV A STRANGE NEW WORLD. 10 Giovanni Saccheri. 11 Johann Lambert. 12 Nicolai Lobachevski and János Bolyai. PART V NEW DIRECTIONS. 13 Bernhard Riemann. 14 Jean-Victor Poncelet. 15 Felix Klein. References. Index.

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Book SynopsisAn accessible and multidisciplinaryintroduction to cellular automata As the applicability of cellular automata broadens and technology advances, there is a need for a concise, yet thorough, resource that lays the foundation of key cellularautomata rules and applications. In recent years, Stephen Wolfram''s A New Kind of Science has brought the modeling power that lies in cellular automata to the attentionof the scientific world, and now, Cellular Automata: A Discrete View of the World presents all the depth, analysis, and applicability of the classic Wolfram text in a straightforward, introductory manner. This book offers an introduction to cellular automata as a constructive method for modeling complex systems where patterns of self-organization arising from simple rules are revealed in phenomena that exist across a wide array of subject areas, including mathematics, physics, economics, and the social sciences. The book begins with a preliminary introduction to cellular autTrade Review"The book is well produced and a good introduction to its subject." (Computing Reviews, January 30, 2009) "An interesting read and worth browsing by somebody interested in getting a general background on CA. The examples are many and varied, and the numerous citations--both to electronic and printed media--are very helpful." (Computing Reviews, November 11, 2008) "An interesting read and worth browsing by somebody interested in getting a general background on CA. The examples are many and varied, and the numerous citations--both to electronic and printed media--are very helpful." (Computing Reviews, Nov 2008) "Schiff suppresses most mathematical details, rendering his book highly accessible, informative, and entertaining, but leaving open niches for a textbook treatment with exercises or an advanced monograph with proofs." (CHOICE, October 2008) "This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical ground." (Mathematical Reviews, 2008m) "Schiff suppresses most mathematical details, rendering his book highly accessible, informative, and entertaining, but leaving open niches for a textbook treatment with exercises or an advanced monograph with proofs." (CHOICE Oct 2008) "This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical ground." (Mathematical Reviews 2008)Table of ContentsPreface. 1. Preliminaries. 2. Dynamical Systems. 3. One-Dimensional Cellular Automata. 4. Two-Dimensional Automata. 5. Applications. 6. Complexity. Appendix A. References. Index.

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Book SynopsisPraise for Modeling for Insight Most books on modeling are either too theoretical or too focused on the mechanics of programming. Powell and Batt''s emphasis on using simple spreadsheet models to gain business insight (which is, after all, the name of the game) is what makes this book stand head and shoulders above the rest. This clear and practical book deserves a place on the shelf of every business analyst. Jonathan Koomey, PhD, Lawrence Berkeley National Laboratory and Stanford University, author of Turning Numbers into Knowledge: Mastering the Art of Problem Solving Most business analysts are familiar with using spreadsheets to organize data and build routine models. However, analysts often struggle when faced with examining new and ill-structured problems. Modeling for Insight is a one-of-a-kind guide to building effective spreadsheet models and using them to generate insights. With its hands-on approach, this book provides readers witTrade Review"Most books on modeling are either too theoretical or too focused on the mechanics of programming. Powell and Batt's emphasis on using simple spreadsheet models to gain business insight (which is, after all, the name of the game) is what makes this book stand head and shoulders above the rest. This clear and practical book deserves a place on the shelf of every business analyst." (Jonathan Koomey, PhD, Lawrence Berkeley National Laboratory and Stanford University, author Turning Numbers into Knowledge: Mastering the Art of Problem Solving)Table of ContentsPREFACE xiii USING THIS BOOK xix ACKNOWLEDGMENTS xxiii ACKNOWLEDGMENTS FOR CASES xxv ABOUT THE AUTHORS xxvii PART I 1 1. Introduction 3 1.0 Models and Modeling 3 1.1 Well-Structured versus Ill-Structured Problems 4 1.2 Modeling versus Problem Solving 5 1.3 Modeling for Insight 6 1.4 Novice Modelers and Expert Modelers 7 1.5 Craft Skills in Modeling 8 1.6 A Structured Modeling Process 9 1.7 Modeling Tools 9 1.8 Summary 10 2. Foundations of Modeling for Insight 11 2.0 Introduction 11 2.1 The Modeling Process 11 2.2 Tools for Modeling 19 2.3 Presentation Skills 26 2.4 Summary 34 3. Spreadsheet Engineering 36 3.0 Why Use Spreadsheets? 36 3.1 Spreadsheet Engineering 37 3.2 Summary 49 PART II 51 4. A First Example—The Red Cross Problem 53 4.0 Introduction 53 4.1 The Red Cross Problem 53 4.2 Bringing Blood Quality into the Analysis 69 4.3 Improving and Iterating 78 4.4 Summary 79 5. Retirement Planning Problem 80 5.0 Introduction 80 5.1 Retirement Planning (A) 80 5.2 Retirement Planning (B) 99 5.3 Retirement Planning (C) 107 5.4 Presentation of Results 112 5.5 Summary 122 6. Technology Option 122 6.0 Introduction 122 6.1 Technology Option (A) 122 6.2 Technology Option (B) 131 6.3 Additional Refi nements 138 6.4 Presentation of Results 147 6.5 Summary 152 PART III 155 7. MediDevice 157 7.0 Introduction 157 7.1 MediDevice Case (A) 157 7.2 Revising the Model 172 7.3 MediDevice Case (B) 178 7.4 Presentation of Results 184 7.5 Summary 190 8. Draft Commercials 194 8.0 Introduction 194 8.1 Draft Commercials Case 194 8.2 Frame the Problem 196 8.3 Diagram the Problem 198 8.4 M1 Model and Analysis 200 8.5 M2 Model and Analysis 205 8.6 M3 Model and Analysis 207 8.7 M4 Model and Analysis 216 8.8 Presentation of Results 222 8.9 Summary 232 9. New England College Skiway 233 9.0 Introduction 233 9.1 New England College Skiway Case 233 9.2 Frame the Problem 234 9.3 Diagram the Problem 237 9.4 M1 Model and Analysis 239 9.5 Analyzing Mountain Capacity 246 9.6 M2 Model and Analysis 250 9.7 M3 Model and Analysis 256 9.8 Considering Uncertainty 273 9.9 Presentation of Results 274 9.10 Summary 283 10. National Leasing, Inc. 285 10.0 Introduction 285 10.1 National Leasing Case 286 10.2 Frame the Problem 289 10.3 Diagram the Problem 291 10.4 M1 Model and Analysis 293 10.5 M2 Model and Analysis 304 10.6 M3 Model and Analysis 313 10.7 M4 Model and Analysis 319 10.8 Presentation of Results 324 10.9 Summary 333 11. Pharma X and Pharma Y 334 11.0 Introduction 334 11.1 The Pharma X and Pharma Y Case 334 11.2 Frame the Problem 338 11.3 Diagram the Problem 339 11.4 Expected Value or Simulation? 340 11.5 M1 Model and Analysis 341 11.6 M2 Model and Analysis 354 11.7 M3 Model and Analysis 366 11.8 Presentation of Results 372 11.9 Summary 380 12. Invivo Diagnostics, Inc. 381 12.0 Introduction 381 12.1 Invivo Diagnostics Case 381 12.2 Frame and Diagram the Problem 384 12.3 M1 Model and Analysis 388 12.4 M2 Model and Analysis 394 12.5 M3 Model and Analysis 406 12.6 M4 Model and Analysis 426 12.7 Presentation of Results 434 12.8 Summary 443 Appendix A: Guide to Solver 445 Appendix B: Guide to Crystal Ball 451 Appendix C: Guide to the Sensitivity Toolkit 456 INDEX 464

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Book SynopsisPraise for the Second Edition This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere. ?IIE Transactions Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a methods approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical prTable of ContentsPreface xvii Acknowledgments xxi 1 Introduction 1 1.1 Why Multivariate Analysis? 1 1.2 Prerequisites 3 1.3 Objectives 3 1.4 Basic Types of Data And Analysis 4 2 Matrix Algebra 7 2.1 Introduction 7 2.2 Notation and Basic Definitions 8 2.3 Operations 11 2.4 Partitioned Matrices 22 2.5 Rank 23 2.6 Inverse 25 2.7 Positive Definite Matrices 26 2.8 Determinants 28 2.9 Trace 31 2.10 Orthogonal Vectors and Matrices 31 2.11 Eigenvalues and Eigenvectors 32 2.12 Kronecker and VEC Notation 37 Problems 39 3 Characterizing and Displaying Multivariate Data 47 3.1 Mean and Variance of a Univariate Random Variable 47 3.2 Covariance and Correlation Of Bivariate Random Variables 49 3.3 Scatter Plots of Bivariate Samples 55 3.4 Graphical Displays for Multivariate Samples 56 3.5 Dynamic Graphics 58 3.6 Mean Vectors 63 3.7 Covariance Matrices 66 3.8 Correlation Matrices 69 3.9 Mean Vectors and Covariance Matrices for Subsets of Variables 71 3.9.1 Two Subsets 71 3.9.2 Three or More Subsets 73 3.10 Linear Combinations of Variables 75 3.10.1 Sample Properties 75 3.10.2 Population Properties 81 3.11 Measures of Overall Variability 81 3.12 Estimation of Missing Values 82 3.13 Distance Between Vectors 84 Problems 85 4 The Multivariate Normal Distribution 91 4.1 Multivariate Normal Density Function 91 4.2 Properties of Multivariate Normal Random Variables 94 4.3 Estimation in the Multivariate Normal 99 4.4 Assessing Multivariate Normality 101 4.5 Transformations to Normality 108 4.6 Outliers 111 Problems 117 5 Tests on One or Two Mean Vectors 125 5.1 Multivariate Versus Univariate Tests 125 5.2 Tests on µ With ??Known 126 5.3 Tests on µ When ??is Unknown 130 5.4 Comparing two Mean Vectors 134 5.5 Tests on Individual Variables Conditional on Rejection of H0 by the T2-test 139 5.6 Computation of T2 143 5.7 Paired Observations Test 145 5.8 Test for Additional Information 149 5.9 Profile Analysis 152 Profile Analysis 154 Problems 161 6 Multivariate Analysis of Variance 169 6.1 One-way Models 169 6.2 Comparison of the Four Manova Test Statistics 189 6.3 Contrasts 191 6.4 Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test 195 6.5 Two-Way Classification 198 6.6 Other Models 207 6.7 Checking on the Assumptions 210 6.8 Profile Analysis 211 6.9 Repeated Measures Designs 215 6.10 Growth Curves 232 6.11 Tests on a Subvector 241 Problems 244 7 Tests on Covariance Matrices 259 7.1 Introduction 259 7.2 Testing a Specified Pattern for ∑ 259 7.3 Tests Comparing Covariance Matrices 265 7.4 Tests of Independence 269 Problems 276 8 Discriminant Analysis: Description of Group Separation 281 8.1 Introduction 281 8.2 The Discriminant Function for two Groups 282 8.3 Relationship Between two-group Discriminant Analysis and Multiple Regression 286 8.4 Discriminant Analysis for Several Groups 288 8.5 Standardized Discriminant Functions 292 8.6 Tests of Significance 294 8.7 Interpretation of Discriminant Functions 298 8.8 Scatter Plots 301 8.9 Stepwise Selection of Variables 303 Problems 306 9 Classification Analysis: Allocation of Observations to Groups309 9.1 Introduction 309 9.2 Classification into two Groups 310 9.3 Classification into Several Groups 314 9.4 Estimating Misclassification Rates 318 9.5 Improved Estimates of Error Rates 320 9.6 Subset Selection 322 9.7 Nonparametric Procedures 326 Problems 336 10 Multivariate Regression 339 10.1 Introduction 339 10.2 Multiple Regression: Fixed X’s 340 10.3 Multiple Regression: Random X’s 354 10.4 Multivariate Multiple Regression: Estimation 354 10.5 Multivariate Multiple Regression: Hypothesis Tests 364 10.6 Multivariate Multiple Regression: Prediction 370 10.7 Measures of Association Between the Y’s and the X’s 372 10.8 Subset Selection 374 10.9 Multivariate Regression: Random X’s 380 Problems 381 11 Canonical Correlation 385 11.1 Introduction 385 11.2 Canonical Correlations and Canonical Variates 385 11.3 Properties of Canonical Correlations 390 11.4 Tests of Significance 391 11.5 Interpretation 395 11.6 Relationships of Canonical Correlation Analysis to Other Multivariate Problems 402 12 Principal Component Analysis 405 12.1 Introduction 405 12.2 Geometric and Algebraic Bases of Principal Components 406 12.3 Principal Components and Perpendicular Regression 412 12.4 Plotting of Principal Components 414 12.5 Principal Components from the Correlation Matrix 419 12.6 Deciding How Many Components to Retain 423 12.7 Information in the Last Few Principal Components 427 12.8 Interpretation of Principal Components 427 12.9 Selection of Variables 430 Problems 432 13 Exploratory Factor Analysis 435 13.1 Introduction 435 13.2 Orthogonal Factor Model 437 13.3 Estimation of Loadings and Communalities 442 13.4 Choosing the Number of Factors, m 453 13.5 Rotation 457 13.6 Factor Scores 466 13.7 Validity of the Factor Analysis Model 470 13.8 Relationship of Factor Analysis to Principal Component Analysis 475 Problems 476 14 Confirmatory Factor Analysis 479 14.1 Introduction 479 14.2 Model Specification and Identification 480 14.3 Parameter Estimation and Model Assessment 487 14.4 Inference for Model Parameters 492 14.5 Factor Scores 495 Problems 496 15 Cluster Analysis 501 15.1 Introduction 501 15.2 Measures of Similarity or Dissimilarity 502 15.3 Hierarchical Clustering 505 15.4 Nonhierarchical Methods 531 15.5 Choosing the Number of Clusters 544 15.6 Cluster Validity 546 15.7 Clustering Variables 547 Problems 548 16 Graphical Procedures 555 16.1 Multidimensional Scaling 555 16.2 Correspondence Analysis 565 16.3 Biplots 580 Problems 588 Appendix A: Tables 597 Appendix B: Answers and Hints to Problems 637 Appendix C: Data Sets and SAS Files 727 References 729 Index 747

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Book SynopsisAn accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation Table of ContentsPreface. Acknowledgments. List of Worked-Out Example Problems. 1 Equations Representing Physical Quantities. 1.1 Systems of Units. 1.2 Conversion of Units. 1.3 Dimensional Checks and the Use of Symbolic Parameters. 1.4 Arguments of Transcendental Functions. 1.5 Dimensional Checks to Generalize Equations. 1.6 Other Types of Units. 1.7 Simplifying Intermediate Calculations. Exercises. 2 A Few Pitfalls and a Few Useful Tricks. 2.1 A Few Instructive Pitfalls. 2.2 A Few Useful Tricks. 2.3 A Few “Advanced” Tricks. Exercises. 3 Limiting and Special Cases. 3.1 Special Cases to Simplify and Check Algebra. 3.2 Special Cases and Heuristic Arguments. 3.3 Limiting Cases of a Differential Equation. 3.4 Transition Points. Exercises. 4 Diagrams, Graphs, and Symmetry. 4.1 Introduction. 4.2 Diagrams for Equations. 4.3 Graphical Solutions. 4.4 Symmetry to Simplify Equations. Exercises. 5 Estimation and Approximation. 5.1 Powers of Two for Estimation. 5.2 Fermi Questions. 5.3 Estimates Based on Simple Physics. 5.4 Approximating Definite Integrals. 5.5 Perturbation Analysis. 5.6 Isolating Important Variables. Exercises. 6 Introduction to Dimensional Analysis and Scaling. 6.1 Dimensional Analysis: An Introduction. 6.2 Dimensional Analysis: A Systematic Approach. 6.3 Introduction to Scaling. Exercises. 7 Generalizing Equations. 7.1 Binomial Expressions. 7.2 Motivating a General Expression. 7.3 Recurring Themes. 7.4 General yet Simple: Euler’s Identity. 7.5 When to Try to Generalize. Exercises. 8 Several Instructive Examples. 8.1 Choice of Coordinate System. 8.2 Solution Has Unexpected Properties. 8.3 Solutions in Search of Problems. 8.4 Learning from Remarkable Results. Exercises. Index.

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Book SynopsisA valuable guide on creativity and critical thinking to improve reasoning and decision-making skills Critical thinking skills are essential in virtually any field of study or practice where individuals need to communicate ideas, make decisions, and analyze and solve problems. An Introduction to Critical Thinking and Creativity: Think More, Think Better outlines the necessary tools for readers to become critical as well as creative thinkers. By gaining a practical and solid foundation in the basic principles that underlie critical thinking and creativity, readers will become equipped to think in a more systematic, logical, and imaginative manner. Creativity is needed to generate new ideas to solve problems, and critical thinking evaluates and improves an idea. These concepts are uniquely introduced as a unified whole due to their dependence on each other. Each chapter introduces relevant theories in conjunction with real-life examples and findings Table of ContentsPreface ix 1 Introduction 1 2 Thinking and writing clearly 11 3 Definitions 21 4 Necessary and sufficient conditions 33 5 Linguistic pitfalls 41 6 Truth 53 7 Basic logic 59 8 Identifying arguments 69 9 Valid and sound arguments 75 10 Inductive reasoning 87 11 Argument mapping 95 12 Argument analysis 107 13 Scientific reasoning 113 14 Mill's methods 125 15 Reasoning about causation 133 16 Diagrams of causal processes 141 17 Statistics and probability 145 18 Thinking about values 159 19 Fallacies 173 20 Cognitive biases 185 21 Analogical reasoning 195 22 Making rational decisions 201 23 What is creativity? 215 24 Creative thinking habits 223 Solutions to exercises 233 Bibliography 256 Index 261

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Book SynopsisThis introductory textbook on nonlinear partial differential equations is technique oriented with an emphasis on applications and is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises.Trade Review"This book is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs." (Mathematical Reviews, 2009c)Table of ContentsPreface xi 1. Introduction to Partial Differential Equations 1 1.1 Partial Differential Equations 2 1.1.1 Equations and Solutions 2 1.1.2 Classification 5 1.1.3 Linear versus Nonlinear 8 1.1.4 Linear Equations 11 1.2 Conservation Laws 20 1.2.1 One Dimension 20 1.2.2 Higher Dimensions 23 1.3 Constitutive Relations 25 1.4 Initial and Boundary Value Problems 35 1.5 Waves 45 1.5.1 Traveling Waves 45 1.5.2 Plane Waves 50 1.5.3 Plane Waves and Transforms 52 1.5.4 Nonlinear Dispersion 54 2. First-Order Equations and Characteristics 61 2.1 Linear First-Order Equations 62 2.1.1 Advection Equation 62 2.1.2 Variable Coefficients 64 2.2 Nonlinear Equations 68 2.3 Quasilinear Equations 72 2.3.1 The General Solution 76 2.4 Propagation of Singularities 81 2.5 General First-Order Equation 86 2.5.1 Complete Integral 91 2.6 A Uniqueness Result 94 2.7 Models in Biology 96 2.7.1 Age Structure 96 2.7.2 Structured Predator-Prey Model 101 2.7.3 Chemotherapy 103 2.7.4 Mass Structure 105 2.7.5 Size-Dependent Predation 106 3. Weak Solutions to Hyperbolic Equations 113 3.1 Discontinuous Solutions 114 3.2 Jump Conditions 116 3.2.1 Rarefaction Waves 118 3.2.2 Shock Propagation 119 3.3 Shock Formation 125 3.4 Applications 131 3.4.1 Traffic Flow 132 3.4.2 Plug Flow Chemical Reactors 136 3.5 Weak Solutions: A Formal Approach 140 3.6 Asymptotic Behavior of Shocks 148 3.6.1 Equal-Area Principle 148 3.6.2 Shock Fitting 152 3.6.3 Asymptotic Behavior 154 4. Hyperbolic Systems 159 4.1 Shallow-Water Waves: Gas Dynamics 160 4.1.1 Shallow-Water Waves160 4.1.2 Small-Amplitude Approximation 163 4.1.3 Gas Dynamics 164 4.2 Hyperbolic Systems and Characteristics 169 4.2.1 Classification 170 4.3 The Riemann Method 179 4.3.1 Jump Conditions for Systems 179 4.3.2 Breaking Dam Problem 181 4.3.3 Receding Wall Problem 183 4.3.4 Formation of a Bore 187 4.3.5 Gas Dynamics 190 4.4 Hodographs and Wavefronts 192 4.4.1 Hodograph Transformation 192 4.4.2 Wavefront Expansions 193 4.5 Weakly Nonlinear Approximations 201 4.5.1 Derivation of Burgers‘ Equation 202 5. Diffusion Processes 209 5.1 Diffusion and Random Motion 210 5.2 Similarity Methods 217 5.3 Nonlinear Diffusion Models 224 5.4 Reaction-Diffusion: Fisher’s Equation 234 5.4.1 Traveling Wave Solutions 235 5.4.2 Perturbation Solution 238 5.4.3 Stability of Traveling Waves 240 5.4.4 Nagumo‘s Equation 242 5.5 Advection-Diffusion: Burgers’ Equation 245 5.5.1 Traveling Wave Solution 246 5.5.2 Initial Value Problem 247 5.6 Asymptotic Solution to Burgers’ Equation 250 5.6.1 Evolution of a Point Source 252 Appendix: Dynamical Systems 257 6. Reaction-Diffusion Systems 267 6.1 Reaction-Diffusion Models 268 6.1.1 Predator-Prey Model 270 6.1.2 Combustion 271 6.1.3 Chemotaxis 274 6.2 Waveling IJ1Bve Solutions 277 6.2.1 Model for the Spread of a Disease 278 6.2.2 Contaminant Transport in Groundwater 284 6.3 Existence of Solutions 292 6.3.1 Fixed-Point Iteration 293 6.3.2 Semilinear Equations 297 6.3.3 Normed Linear Spaces 300 6.3.4 General Existence Theorem 303 6.4 Maximum Principles and Comparison Theorems 309 6.4.1 Maximum Principles 309 6.4.2 Comparison Theorems 314 6.5 Energy Estimates and Asymptotic Behavior 317 6.5.1 Calculus Inequalities 318 6.5.2 Energy Estimates 320 6.5.3 Invariant Sets 326 6.6 Pattern Formation 333 7. Equilibrium Models 345 7.1 Elliptic Models 346 7.2 Theoretical Results 352 7.2.1 Maximum Principle 353 7.2.2 Existence Theorem 355 7.3 Eigenvalue Problems 358 7.3.1 Linear Eigenvalue Problems 358 7.3.2 Nonlinear Eigenvalue Problems 361 7.4 Stability and Bifurcation 364 7.4.1 Ordinary Differential Equations 364 7.4.2 Partial Differential Equations 368 References 387 Index 395

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Book SynopsisA modern, comprehensive treatment of latent class and latent transition analysis for categorical data On a daily basis, researchers in the social, behavioral, and health sciences collect information and fit statistical models to the gathered empirical data with the goal of making significant advances in these fields. In many cases, it can be useful to identify latent, or unobserved, subgroups in a population, where individuals'' subgroup membership is inferred from their responses on a set of observed variables. Latent Class and Latent Transition Analysis provides a comprehensive and unified introduction to this topic through one-of-a-kind, step-by-step presentations and coverage of theoretical, technical, and practical issues in categorical latent variable modeling for both cross-sectional and longitudinal data. The book begins with an introduction to latent class and latent transition analysis for categorical data. Subsequent chapters delve into more in-depthTable of ContentsList of Figures. List of Tables. Acknowledgments. Acronyms. Part I Fundamentals. 1. General Introduction. 1.1 Overview. 1.2 Conceptual foundation and brief history of the latent class model. 1.3 Why select a categorical latent variable approach? 1.4 Scope of this book. 1.5 Empirical example of LCA: Adolescent delinquency. 1.6 Empirical example of LTA: Adolescent delinquency. 1.7 About this book. 1.8 The examples in this book. 1.9 Software. 1.10 Additional resources: The book’s web site. 1.11 Suggested supplemental readings. 1.12 Points to remember. 1.13 What’s next. 2. The latent class model. 2.1 Overview. 2.2 Empirical example: Pubertal development. 2.3 The role of item-response probabilities to label the latent classes in the pubertal development example. 2.4 Empirical example: Health risk behaviors. 2.5 LCA: Model and notation. 2.6 Suggested supplemental readings. 2.7 Points to remember. 2.8 What’s next. 3. The relation between the latent variable and its indicators. 3.1 Overview. 3.2 The latent class measurement model. 3.3 Homogeneity and latent class separation. 3.4 The precision with which the observed variables measure the latent variable. 3.5 Expressing the degree of uncertainty: Mean posterior probabilities and entropy. 3.6 Points to remember. 3.7 What’s next. 4. Parameter estimation and model selection. 4.1 Overview. 4.2 Maximum Likelihood estimation. 4.3 Model fit and model selection. 4.4 Finding the ML solution. 4.5 Empirical example of using many starting values. 4.6 Empirical examples of selecting the number of latent classes. 4.7 More about parameter restrictions. 4.8 Standard errors. 4.9 Suggested supplemental readings. 4.10 Points to remember. 4.11 What’s next. Part II Advanced LCA. 5. Multiple-group LCA. 5.1 Overview. 5.2 Introduction. 5.3 Multiple-group LCA: Model and notation. 5.4 Computing the number of parameters estimated. 5.5 Expressing group differences in the LCA model. 5.6 Measurement invariance. 5.7 Establishing whether the number of latent classes is identical across groups. 5.8 Establishing invariance of item-response probabilities across groups. 5.9 Interpretation when measurement invariance does not hold. 5.10 Strategies when measurement invariance does not hold. 5.11 Significant differences and important differences. 5.12 Testing equivalence of latent class prevalences across groups. 5.13 Suggested supplemental readings. 5.14 Points to remember. 5.15 What’s next. 6. LCA with Covariates. 6.1 Overview. 6.2 Empirical example: Positive health behaviors. 6.3 Preparing to conduct LCA with covariates. 6.4 LCA with covariates: Model and notation. 6.5 Hypothesis testing in LCA with covariates. 6.6 Interpretation of the intercepts and regression coefficients. 6.7 Empirical examples of LCA with a single covariate. 6.8 Empirical example of multiple covariates and interaction terms. 6.9 Multiple-group LCA with covariates: Model and notation. 6.10 Grouping variable or covariate? 6.11 Use of a Bayesian prior to stabilize estimation. 6.12 Binomial logistic regression. 6.13 Suggested supplemental readings. 6.14 Points to remember. 6.15 What’s next. Part III Latent Class Models for Longitudinal Data. 7. RMLCA and LTA. 7.1 Overview. 7.2 RMLCA. 7.3 LTA. 7.4 LTA model parameters. 7.5 LTA: Model and notation. 7.6 Degrees of freedom associated with latent transition models. 7.7 Empirical example: Adolescent depression. 7.8 Empirical example: Dating and sexual risk behavior. 7.9 Interpreting what a latent transition model reveals about change. 7.10 Parameter restrictions in LTA. 7.11 Testing the hypotheses of measurement invariance across times. 7.12 Testing the hypotheses about change between times. 7.13 Relation between RMLCA and LTA. 7.14 Invariance of the transition probability matrix. 7.15 Suggested supplemental readings. 7.16 Points to remember. 7.17 What’s next. 8. Multiple-Group LTA and LTA with Covariates. 8.1 Overview. 8.2 LTA with a grouping variable. 8.3 Multiple-group LTA: Model and notation. 8.4 Computing the number of parameters estimated in multiple-group latent transition models. 8.5 Hypothesis tests concerning group differences: General consideration. 8.6 Overall hypothesis tests about group differences in LTA. 8.7 Testing the hypothesis of equality of latent status prevalences. 8.8 Testing the hypothesis of equality of transition probabilities. 8.9 Incorporating covariates in LTA. 8.10 LTA with covariates: Model and notation. 8.11 Hypothesis testing in LTA with covariates. 8.12 Including both a grouping variable and a covariate in LTA. 8.13 Binomial logistic regression. 8.14 The relation between multiple-group LTA and LTA with a covariate. 8.15 Suggested supplemental readings. 8.16 Points to remember. Topic Index. Author Index.

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Book SynopsisPraise for the Second Edition: This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications. Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and tTable of ContentsPreface xi 1 Mathematical Models 1 1.1 Applying Mathematics 1 1.2 The Diet Problem 2 1.3 The Prisoner's Dilemma 5 1.4 The Roles of Linear Programming and Game Theory 8 2 The Linear Programming Model 9 2.1 History 9 2.2 The Blending Model 10 2.3 The Production Model 21 2.4 The Transportation Model 34 2.5 The Dynamic Planning Model 38 2.6 Summary 47 3 The Simplex Method 57 3.1 The General Problem 57 3.2 Linear Equations and Basic Feasible Solutions 63 3.3 Introduction to the Simplex Method 72 3.4 Theory of the Simplex Method 77 3.5 The Simplex Tableau and Examples 85 3.6 Artificial Variables 93 3.7 Redundant Systems 101 3.8 A Convergence Proof 106 3.9 Linear Programming and Convexity 110 3.10 Spreadsheet Solution of a Linear Programming Problem 115 4 Duality 121 4.1 Introduction to Duality 121 4.2 Definition of the Dual Problem 123 4.3 Examples and Interpretations 132 4.4 The Duality Theorem 138 4.5 The Complementary Slackness Theorem 154 5 Sensitivity Analysis 161 5.1 Examples in Sensitivity Analysis 161 5.2 Matrix Representation of the Simplex Algorithm 175 5.3 Changes in the Objective Function 183 5.4 Addition of a New Variable 189 5.5 Changes in the Constant-Term Column Vector 192 5.6 The Dual Simplex Algorithm 196 5.7 Addition of a Constraint 204 6 Integer Programming 211 6.1 Introduction to Integer Programming 211 6.2 Models with Integer Programming Formulations 214 6.3 Gomory's Cutting Plane Algorithm 228 6.4 A Branch and Bound Algorithm 237 6.5 Spreadsheet Solution of an Integer Programming Problem 244 7 The Transportation Problem 251 7.1 A Distribution Problem 251 7.2 The Transportation Problem 264 7.3 Applications 282 8 Other Topics in Linear Programming 299 8.1 An Example Involving Uncertainty 299 8.2 An Example with Multiple Goals 306 8.3 An Example Using Decomposition 314 8.4 An Example in Data Envelopment Analysis 325 9 Two-Person, Zero-Sum Games 337 9.1 Introduction to Game Theory 337 9.2 Some Principles of Decision Making in Game Theory 345 9.3 Saddle Points 350 9.4 Mixed Strategies 353 9.5 The Fundamental Theorem 360 9.6 Computational Techniques 370 9.7 Games People Play 382 10 Other Topics in Game Theory 391 10.1 Utility Theory 391 10.2 Two-Person, Non-Zero-Sum Games 393 10.3 Noncooperative Two-Person Games 397 10.4 Cooperative Two-Person Games 404 10.5 The Axioms of Nash 408 10.6 An Example 414 A Vectors and Matrices 417 B An Example of Cycling 421 C Efficiency of the Simplex Method 423 D LP Assistant 427 E Microsoft Excel and Solver 431 Bibliography 439 Solutions to Selected Problems 443 Index 457

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Book SynopsisFeatures an introduction to advanced calculus and highlights its inherent concepts from linear algebra Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers'' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis. Following an introduction dedicated to writing proofs, the book is divided into three parts: Part One explores foundational one-variable calculus topics from the viewpoint of linear spaces, norms, completeness, and linear functionals. Part Two covers Fourier series and Stieltjes integration, which are advanced one-variable topics. Part Three is dedicated to multivariable advanceTrade Review“The book is well-suited for students who have had some basic calculus and linear algebra, as an intermediate step before beginning more advanced topics as measure theory, functional analysis, and the theory of differential equations.” (Bull Belg Math Soc, 1 July 2010) "This is an excellent book, well worth considering for a textbook for an undergraduate analysis course." (MAA Reviews July, 2008)Table of ContentsPreface. Acknowledgments. Introduction. PART I. ADVANCED CALCULUS IN ONE VARIABLE. 1. Real Numbers and Limits of Sequences. 2. Continuous Functions. 3. Rieman Integral. 4. The Derivative. 5. Infinite Series. PART II. ADVANCED TOPICS IN ONE VARIABLE. 6. Fourier Series. 7. The Riemann-Stieltjes Integral. PART III. ADVANCED CALCULUS IN SEVERAL VARIABLES. 8. Euclidean Space. 9. Continuous Functions on Euclidean Space. 10. The Derivative in Euclidean Space. 11. Riemann Integration in Euclidean Space. Appendix A. Set Theory. Problem Solutions. References. Index.

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Book SynopsisProbability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probabilTable of ContentsPREFACE xxi NOTATION xxv 1 Overview and Background 1 1.1 Introduction 1 1.1.1 Signals, Signal Processing, and Communications 3 1.1.2 Probability, Random Variables, and Random Vectors 9 1.1.3 Random Sequences and Random Processes 11 1.1.4 Delta Functions 16 1.2 Deterministic Signals and Systems 19 1.2.1 Continuous Time 20 1.2.2 Discrete Time 25 1.2.3 Discrete-Time Filters 29 1.2.4 State-Space Realizations 32 1.3 Statistical Signal Processing with MATLAB® 35 1.3.1 Random Number Generation 35 1.3.2 Filtering 38 Problems 39 Further Reading 45 PART I Probability, Random Variables, and Expectation 2 Probability Theory 49 2.1 Introduction 49 2.2 Sets and Sample Spaces 50 2.3 Set Operations 54 2.4 Events and Fields 58 2.5 Summary of a Random Experiment 64 2.6 Measure Theory 64 2.7 Axioms of Probability 68 2.8 Basic Probability Results 69 2.9 Conditional Probability 71 2.10 Independence 73 2.11 Bayes’ Formula 74 2.12 Total Probability 76 2.13 Discrete Sample Spaces 79 2.14 Continuous Sample Spaces 83 2.15 Nonmeasurable Subsets of R 84 Problems 87 Further Reading 90 3 Random Variables 91 3.1 Introduction 91 3.2 Functions and Mappings 91 3.3 Distribution Function 96 3.4 Probability Mass Function 101 3.5 Probability Density Function 103 3.6 Mixed Distributions 104 3.7 Parametric Models for Random Variables 107 3.8 Continuous Random Variables 109 3.8.1 Gaussian Random Variable (Normal) 110 3.8.2 Log-Normal Random Variable 113 3.8.3 Inverse Gaussian Random Variable (Wald) 114 3.8.4 Exponential Random Variable (One-Sided) 116 3.8.5 Laplace Random Variable (Double-Sided Exponential) 119 3.8.6 Cauchy Random Variable 122 3.8.7 Continuous Uniform Random Variable 124 3.8.8 Triangular Random Variable 125 3.8.9 Rayleigh Random Variable 127 3.8.10 Rice Random Variable 129 3.8.11 Gamma Random Variable (Erlang for r ∈ N) 131 3.8.12 Beta Random Variable (Arcsine for α = β = 1/2, Power Function for β = 1) 133 3.8.13 Pareto Random Variable 136 3.8.14 Weibull Random Variable 137 3.8.15 Logistic Random Variable (Sigmoid for {μ = 0, α = 1}) 139 3.8.16 Chi Random Variable (Maxwell–Boltzmann, Half-Normal) 141 3.8.17 Chi-Square Random Variable 144 3.8.18 F-Distribution 147 3.8.19 Student’s t Distribution 149 3.8.20 Extreme Value Distribution (Type I: Gumbel) 150 3.9 Discrete Random Variables 151 3.9.1 Bernoulli Random Variable 152 3.9.2 Binomial Random Variable 154 3.9.3 Geometric Random Variable (with Support Z+ or N) 157 3.9.4 Negative Binomial Random Variable (Pascal) 160 3.9.5 Poisson Random Variable 162 3.9.6 Hypergeometric Random Variable 165 3.9.7 Discrete Uniform Random Variable 167 3.9.8 Logarithmic Random Variable (Log-Series) 168 3.9.9 Zeta Random Variable (Zipf) 170 Problems 173 Further Reading 176 4 Multiple Random Variables 177 4.1 Introduction 177 4.2 Random Variable Approximations 177 4.2.1 Binomial Approximation of Hypergeometric 177 4.2.2 Poisson Approximation of Binomial 179 4.2.3 Gaussian Approximations 181 4.2.4 Gaussian Approximation of Binomial 181 4.2.5 Gaussian Approximation of Poisson 181 4.2.6 Gaussian Approximation of Hypergeometric 183 4.3 Joint and Marginal Distributions 183 4.4 Independent Random Variables 186 4.5 Conditional Distribution 187 4.6 Random Vectors 190 4.6.1 Bivariate Uniform Distribution 193 4.6.2 Multivariate Gaussian Distribution 193 4.6.3 Multivariate Student’s t Distribution 196 4.6.4 Multinomial Distribution 197 4.6.5 Multivariate Hypergeometric Distribution 198 4.6.6 Bivariate Exponential Distributions 200 4.7 Generating Dependent Random Variables 201 4.8 Random Variable Transformations 205 4.8.1 Transformations of Discrete Random Variables 205 4.8.2 Transformations of Continuous Random Variables 207 4.9 Important Functions of Two Random Variables 218 4.9.1 Sum: Z = X + Y 218 4.9.2 Difference: Z = X − Y 220 4.9.3 Product: Z = XY 221 4.9.4 Quotient (Ratio): Z = X/Y 224 4.10 Transformations of Random Variable Families 226 4.10.1 Gaussian Transformations 226 4.10.2 Exponential Transformations 227 4.10.3 Chi-Square Transformations 228 4.11 Transformations of Random Vectors 229 4.12 Sample Mean ¯X and Sample Variance S2 232 4.13 Minimum, Maximum, and Order Statistics 234 4.14 Mixtures 238 Problems 240 Further Reading 243 5 Expectation and Moments 244 5.1 Introduction 244 5.2 Expectation and Integration 244 5.3 Indicator Random Variable 245 5.4 Simple Random Variable 246 5.5 Expectation for Discrete Sample Spaces 247 5.6 Expectation for Continuous Sample Spaces 250 5.7 Summary of Expectation 253 5.8 Functional View of the Mean 254 5.9 Properties of Expectation 255 5.10 Expectation of a Function 259 5.11 Characteristic Function 260 5.12 Conditional Expectation 265 5.13 Properties of Conditional Expectation 267 5.14 Location Parameters: Mean, Median, and Mode 276 5.15 Variance, Covariance, and Correlation 280 5.16 Functional View of the Variance 283 5.17 Expectation and the Indicator Function 284 5.18 Correlation Coefficients 285 5.19 Orthogonality 291 5.20 Correlation and Covariance Matrices 294 5.21 Higher Order Moments and Cumulants 296 5.22 Functional View of Skewness 302 5.23 Functional View of Kurtosis 303 5.24 Generating Functions 304 5.25 Fourth-Order Gaussian Moment 309 5.26 Expectations of Nonlinear Transformations 310 Problems 313 Further Reading 316 PART II Random Processes, Systems, and Parameter Estimation 6 Random Processes 319 6.1 Introduction 319 6.2 Characterizations of a Random Process 319 6.3 Consistency and Extension 324 6.4 Types of Random Processes 325 6.5 Stationarity 326 6.6 Independent and Identically Distributed 329 6.7 Independent Increments 331 6.8 Martingales 333 6.9 Markov Sequence 338 6.10 Markov Process 350 6.11 Random Sequences 352 6.11.1 Bernoulli Sequence 352 6.11.2 Bernoulli Scheme 352 6.11.3 Independent Sequences 353 6.11.4 Bernoulli Random Walk 354 6.11.5 Binomial Counting Sequence 356 6.12 Random Processes 359 6.12.1 Poisson Counting Process 359 6.12.2 Random Telegraph Signal 365 6.12.3 Wiener Process 368 6.12.4 Gaussian Process 371 6.12.5 Pulse Amplitude Modulation 372 6.12.6 Random Sine Signals 373 Problems 375 Further Reading 379 7 Stochastic Convergence, Calculus, and Decompositions 380 7.1 Introduction 380 7.2 Stochastic Convergence 380 7.3 Laws of Large Numbers 388 7.4 Central Limit Theorem 390 7.5 Stochastic Continuity 394 7.6 Derivatives and Integrals 404 7.7 Differential Equations 414 7.8 Difference Equations 422 7.9 Innovations and Mean-Square Predictability 423 7.10 Doob–Meyer Decomposition 428 7.11 Karhunen–Lo`eve Expansion 433 Problems 441 Further Reading 444 8 Systems, Noise, and Spectrum Estimation 445 8.1 Introduction 445 8.2 Correlation Revisited 445 8.3 Ergodicity 448 8.4 Eigenfunctions of RXX(τ ) 456 8.5 Power Spectral Density 457 8.6 Power Spectral Distribution 463 8.7 Cross-Power Spectral Density 465 8.8 Systems with Random Inputs 468 8.8.1 Nonlinear Systems 469 8.8.2 Linear Systems 471 8.9 Passband Signals 476 8.10 White Noise 479 8.11 Bandwidth 484 8.12 Spectrum Estimation 487 8.12.1 Periodogram 487 8.12.2 Smoothed Periodogram 493 8.12.3 Modified Periodogram 497 8.13 Parametric Models 500 8.13.1 Autoregressive Model 500 8.13.2 Moving-Average Model 505 8.13.3 Autoregressive Moving-Average Model 509 8.14 System Identification 513 Problems 515 Further Reading 518 9 Sufficient Statistics and Parameter Estimation 519 9.1 Introduction 519 9.2 Statistics 519 9.3 Sufficient Statistics 520 9.4 Minimal Sufficient Statistic 525 9.5 Exponential Families 528 9.6 Location-Scale Families 533 9.7 Complete Statistic 536 9.8 Rao–Blackwell Theorem 538 9.9 Lehmann–Scheff´e Theorem 540 9.10 Bayes Estimation 542 9.11 Mean-Square-Error Estimation 545 9.12 Mean-Absolute-Error Estimation 552 9.13 Orthogonality Condition 553 9.14 Properties of Estimators 555 9.14.1 Unbiased 555 9.14.2 Consistent 557 9.14.3 Efficient 559 9.15 Maximum A Posteriori Estimation 561 9.16 Maximum Likelihood Estimation 567 9.17 Likelihood Ratio Test 569 9.18 Expectation–Maximization Algorithm 570 9.19 Method of Moments 576 9.20 Least-Squares Estimation 577 9.21 Properties of LS Estimators 582 9.21.1 Minimum ξWLS 582 9.21.2 Uniqueness 582 9.21.3 Orthogonality 582 9.21.4 Unbiased 584 9.21.5 Covariance Matrix 584 9.21.6 Efficient: Achieves CRLB 585 9.21.7 BLU Estimator 585 9.22 Best Linear Unbiased Estimation 586 9.23 Properties of BLU Estimators 590 Problems 592 Further Reading 595 A Note on Part III of the Book 595 APPENDICES Introduction to Appendices 597 A Summaries of Univariate Parametric Distributions 599 A.1 Notation 599 A.2 Further Reading 600 A.3 Continuous Random Variables 601 A.3.1 Beta (Arcsine for α = β = 1/2, Power Function for β = 1) 601 A.3.2 Cauchy 602 A.3.3 Chi 603 A.3.4 Chi-Square 604 A.3.5 Exponential (Shifted by c) 605 A.3.6 Extreme Value (Type I: Gumbel) 606 A.3.7 F-Distribution 607 A.3.8 Gamma (Erlang for r ∈ N with (r ) = (r − 1)!) 608 A.3.9 Gaussian (Normal) 609 A.3.10 Half-Normal (Folded Normal) 610 A.3.11 Inverse Gaussian (Wald) 611 A.3.12 Laplace (Double-Sided Exponential) 612 A.3.13 Logistic (Sigmoid for {μ = 0, α = 1}) 613 A.3.14 Log-Normal 614 A.3.15 Maxwell–Boltzmann 615 A.3.16 Pareto 616 A.3.17 Rayleigh 617 A.3.18 Rice 618 A.3.19 Student’s t Distribution 619 A.3.20 Triangular 620 A.3.21 Uniform (Continuous) 621 A.3.22 Weibull 622 A.4 Discrete Random Variables 623 A.4.1 Bernoulli (with Support {0, 1}) 623 A.4.2 Bernoulli (Symmetric with Support {−1, 1}) 624 A.4.3 Binomial 625 A.4.4 Geometric (with Support Z+) 626 A.4.5 Geometric (Shifted with Support N) 627 A.4.6 Hypergeometric 628 A.4.7 Logarithmic (Log-Series) 629 A.4.8 Negative Binomial (Pascal) 630 A.4.9 Poisson 631 A.4.10 Uniform (Discrete) 632 A.4.11 Zeta (Zipf) 633 B Functions and Properties 634 B.1 Continuity and Bounded Variation 634 B.2 Supremum and Infimum 640 B.3 Order Notation 640 B.4 Floor and Ceiling Functions 641 B.5 Convex and Concave Functions 641 B.6 Even and Odd Functions 641 B.7 Signum Function 643 B.8 Dirac Delta Function 644 B.9 Kronecker Delta Function 645 B.10 Unit-Step Functions 646 B.11 Rectangle Functions 647 B.12 Triangle and Ramp Functions 647 B.13 Indicator Functions 648 B.14 Sinc Function 649 B.15 Logarithm Functions 650 B.16 Gamma Functions 651 B.17 Beta Functions 653 B.18 Bessel Functions 655 B.19 Q-Function and Error Functions 655 B.20 Marcum Q-Function 659 B.21 Zeta Function 659 B.22 Rising and Falling Factorials 660 B.23 Laguerre Polynomials 661 B.24 Hypergeometric Functions 662 B.25 Bernoulli Numbers 663 B.26 Harmonic Numbers 663 B.27 Euler–Mascheroni Constant 664 B.28 Dirichlet Function 664 Further Reading 664 C Frequency-Domain Transforms and Properties 665 C.1 Laplace Transform 665 C.2 Continuous-Time Fourier Transform 669 C.3 z-Transform 670 C.4 Discrete-Time Fourier Transform 676 Further Reading 677 D Integration and Integrals 678 D.1 Review of Riemann Integral 678 D.2 Riemann–Stieltjes Integral 681 D.3 Lebesgue Integral 684 D.4 Pdf Integrals 688 D.5 Indefinite and Definite Integrals 690 D.6 Integral Formulas 692 D.7 Double Integrals of Special Functions 692 Further Reading 696 E Identities and Infinite Series 697 E.1 Zero and Infinity 697 E.2 Minimum and Maximum 697 E.3 Trigonometric Identities 698 E.4 Stirling’s Formula 698 E.5 Taylor Series 699 E.6 Series Expansions and Closed-Form Sums 699 E.7 Vandermonde’s Identity 702 E.8 Pmf Sums and Functional Forms 703 E.9 Completing the Square 704 E.10 Summation by Parts 705 Further Reading 706 F Inequalities and Bounds for Expectations 707 F.1 Cauchy–Schwarz and H¨older Inequalities 707 F.2 Triangle and Minkowski Inequalities 708 F.3 Bienaym´e, Chebyshev, and Markov Inequalities 709 F.4 Chernoff’s Inequality 711 F.5 Jensen’s Inequality 713 F.6 Cram´er–Rao Inequality 714 Further Reading 718 G Matrix and Vector Properties 719 G.1 Basic Properties 719 G.2 Four Fundamental Subspaces 721 G.3 Eigendecomposition 722 G.4 LU, LDU, and Cholesky Decompositions 724 G.5 Jacobian Matrix and the Jacobian 726 G.6 Kronecker and Schur Products 728 G.7 Properties of Trace and Determinant 728 G.8 Matrix Inversion Lemma 729 G.9 Cauchy–Schwarz Inequality 730 G.10 Differentiation 730 G.11 Complex Differentiation 731 Further Reading 732 GLOSSARY 733 REFERENCES 743 INDEX 755 PART III Applications in Signal Processing and Communications Chapters at the Web Site www.wiley.com/go/randomprocesses 10 Communication Systems and Information Theory 771 10.1 Introduction 771 10.2 Transmitter 771 10.2.1 Sampling and Quantization 772 10.2.2 Channel Coding 777 10.2.3 Symbols and Pulse Shaping 778 10.2.4 Modulation 781 10.3 Transmission Channel 783 10.4 Receiver 786 10.4.1 Receive Filter 786 10.4.2 Demodulation 787 10.4.3 Gram–Schmidt Orthogonalization 789 10.4.4 Maximum Likelihood Detection 794 10.4.5 Matched Filter Receiver 797 10.4.6 Probability of Error 802 10.5 Information Theory 803 10.5.1 Mutual Information and Entropy 804 10.5.2 Properties of Mutual Information and Entropy 810 10.5.3 Continuous Distributions: Differential Entropy 813 10.5.4 Channel Capacity 818 10.5.5 AWGN Channel 820 Problems 821 Further Reading 824 11 Optimal Filtering www.wiley.com/go/randomprocesses 825 11.1 Introduction 825 11.2 Optimal Linear Filtering 825 11.3 Optimal Filter Applications 827 11.3.1 System Identification 827 11.3.2 Inverse Modeling 827 11.3.3 Noise Cancellation 828 11.3.4 Linear Prediction 828 11.4 Noncausal Wiener Filter 829 11.5 Causal Wiener Filter 831 11.6 Prewhitening Filter 837 11.7 FIR Wiener Filter 839 11.8 Kalman Filter 844 11.8.1 Evolution of the Mean and Covariance 846 11.8.2 State Prediction 846 11.8.3 State Filtering 848 11.9 Steady-State Kalman Filter 851 11.10 Linear Predictive Coding 857 11.11 Lattice Prediction-Error Filter 861 11.12 Levinson–Durbin Algorithm 865 11.13 Least-Squares Filtering 868 11.14 Recursive Least-Squares 872 Problems 876 Further Reading 879 12 Adaptive Filtering www.wiley.com/go/randomprocesses 880 12.1 Introduction 880 12.2 MSE Properties 880 12.3 Steepest Descent 889 12.4 Newton’s Method 894 12.5 LMS Algorithm 895 12.5.1 Convergence in the Mean 899 12.5.2 Convergence in the Mean-Square 901 12.5.3 Misadjustment 906 12.6 Modified LMS Algorithms 911 12.6.1 Sign-Error LMS Algorithm 911 12.6.2 Sign-Data LMS Algorithm 912 12.6.3 Sign-Sign LMS Algorithm 914 12.6.4 LMF Algorithm 914 12.6.5 Complex LMS Algorithm 916 12.6.6 “Leaky” LMS Algorithm 917 12.6.7 Normalized LMS Algorithm 918 12.6.8 Perceptron 920 12.6.9 Convergence of Modified LMS Algorithms 922 12.7 Adaptive IIR Filtering 923 12.7.1 Output-Error Formulation 924 12.7.2 Output-Error IIR Filter Algorithm 928 12.7.3 Equation-Error Formulation 932 12.7.4 Equation-Error Bias 933 Problems 936 Further Reading 939 13 Equalization, Beamforming, and Direction Finding www.wiley.com/go/randomprocesses 940 13.1 Introduction 940 13.2 Channel Equalization 941 13.3 Optimal Bussgang Algorithm 943 13.4 Blind Equalizer Algorithms 949 13.4.1 Sato’s Algorithm 949 13.4.2 Constant Modulus Algorithm 950 13.5 CMA Performance Surface 952 13.6 Antenna Arrays 958 13.7 Beampatterns 960 13.8 Optimal Beamforming 962 13.8.1 Known Look Direction 962 13.8.2 Multiple Constraint Beamforming 964 13.8.3 Training Signal 966 13.8.4 Maximum Likelihood 968 13.8.5 Maximum SNR and SINR 969 13.9 Adaptive Beamforming 970 13.9.1 LMS Beamforming 970 13.9.2 Constant Modulus Array 970 13.9.3 Decision-Directed Mode 973 13.9.4 Multistage CM Array 974 13.9.5 Output SINR and SNR 977 13.10 Direction Finding 981 13.10.1 Beamforming Approaches 981 13.10.2 MUSIC Algorithm 984 Problems 985 Further Reading 989

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Book SynopsisRANDOM DATA A TIMELY UPDATE OF THE CLASSIC BOOK ON THE THEORY AND APPLICATION OF RANDOM DATA ANALYSIS First published in 1971, Random Data served as an authoritative book on the analysis of experimental physical data for engineering and scientific applications. This Fourth Edition features coverage of new developments in random data management and analysis procedures that are applicable to a broad range of applied fields, from the aerospace and automotive industries to oceanographic and biomedical research. This new edition continues to maintain a balance of classic theory and novel techniques. The authors expand on the treatment of random data analysis theory, including derivations of key relationships in probability and random process theory. The book remains unique in its practical treatment of nonstationary data analysis and nonlinear system analysis, presenting the latest techniques on modern data acquisition, storage, conversion, and qualifiTable of ContentsPreface xv Preface to the Third Edition xvii Glossary of Symbols xix 1. Basic Descriptions and Properties 1 1.1. Deterministic Versus Random Data 1 1.2. Classifications of Deterministic Data 3 1.2.1. Sinusoidal Periodic Data 3 1.2.2. Complex Periodic Data 4 1.2.3. Almost-Periodic Data 6 1.2.4. Transient Nonperiodic Data 7 1.3. Classifications of Random Data 8 1.3.1. Stationary Random Data 9 1.3.2. Ergodic Random Data 11 1.3.3. Nonstationary Random Data 12 1.3.4. Stationary Sample Records 12 1.4. Analysis of Random Data 13 1.4.1. Basic Descriptive Properties 13 1.4.2. Input/Output Relations 19 1.4.3. Error Analysis Criteria 21 1.4.4. Data Analysis Procedures 23 2. Linear Physical Systems 25 2.1. Constant-Parameter Linear Systems 25 2.2. Basic Dynamic Characteristics 26 2.3. Frequency Response Functions 28 2.4. Illustrations of Frequency Response Functions 30 2.4.1. Mechanical Systems 30 2.4.2. Electrical Systems 39 2.4.3. Other Systems 41 2.5. Practical Considerations 41 3. Probability Fundamentals 45 3.1. One Random Variable 45 3.1.1. Probability Density and Distribution Functions 46 3.1.2. Expected Values 49 3.1.3. Change of Variables 50 3.1.4. Moment-Generating and Characteristic Functions 52 3.1.5. Chebyshev’s Inequality 53 3.2. Two Random Variables 54 3.2.1. Expected Values and Correlation Coefficient 55 3.2.2. Distribution for Sum of Two Random Variables 56 3.2.3. Joint Moment-Generating and Characteristic Functions 57 3.3. Gaussian (Normal) Distribution 59 3.3.1. Central Limit Theorem 60 3.3.2. Joint Gaussian (Normal) Distribution 62 3.3.3. Moment-Generating and Characteristic Functions 63 3.3.4. N-Dimensional Gaussian (Normal) Distribution 64 3.4. Rayleigh Distribution 67 3.4.1. Distribution of Envelope and Phase for Narrow Bandwidth Data 67 3.4.2. Distribution of Output Record for Narrow Bandwidth Data 71 3.5. Higher Order Changes of Variables 72 4. Statistical Principles 79 4.1. Sample Values and Parameter Estimation 79 4.2. Important Probability Distribution Functions 82 4.2.1. Gaussian (Normal) Distribution 82 4.2.2. Chi-Square Distribution 83 4.2.3. The t Distribution 84 4.2.4. The F Distribution 84 4.3. Sampling Distributions and Illustrations 85 4.3.1. Distribution of Sample Mean with Known Variance 85 4.3.2. Distribution of Sample Variance 86 4.3.3. Distribution of Sample Mean with Unknown Variance 87 4.3.4. Distribution of Ratio of Two Sample Variances 87 4.4. Confidence Intervals 88 4.5. Hypothesis Tests 91 4.5.1. Chi-Square Goodness-of-Fit Test 94 4.5.2. Nonparametric Trend Test 96 4.6. Correlation and Regression Procedures 99 4.6.1. Linear Correlation Analysis 99 4.6.2. Linear Regression Analysis 102 5. Stationary Random Processes 109 5.1. Basic Concepts 109 5.1.1. Correlation (Covariance) Functions 111 5.1.2. Examples of Autocorrelation Functions 113 5.1.3. Correlation Coefficient Functions 115 5.1.4. Cross-Correlation Function for Time Delay 116 5.2. Spectral Density Functions 118 5.2.1. Spectra via Correlation Functions 118 5.2.2. Spectra via Finite Fourier Transforms 126 5.2.3. Spectra via Filtering–Squaring–Averaging 129 5.2.4. Wavenumber Spectra 132 5.2.5. Coherence Functions 134 5.2.6. Cross-Spectrum for Time Delay 135 5.2.7. Location of Peak Value 137 5.2.8. Uncertainty Relation 138 5.2.9. Uncertainty Principle and Schwartz Inequality 140 5.3. Ergodic and Gaussian Random Processes 142 5.3.1. Ergodic Random Processes 142 5.3.2. Sufficient Condition for Ergodicity 145 5.3.3. Gaussian Random Processes 147 5.3.4. Linear Transformations of Random Processes 149 5.4. Derivative Random Processes 151 5.4.1. Correlation Functions 151 5.4.2. Spectral Density Functions 154 5.5. Level Crossings and Peak Values 155 5.5.1. Expected Number of Level Crossings per Unit Time 155 5.5.2. Peak Probability Functions for Narrow Bandwidth Data 159 5.5.3. Expected Number and Spacing of Positive Peaks 161 5.5.4. Peak Probability Functions for Wide Bandwidth Data 162 5.5.5. Derivations 164 6. Single-Input/Output Relationships 173 6.1. Single-Input/Single-Output Models 173 6.1.1. Correlation and Spectral Relations 173 6.1.2. Ordinary Coherence Functions 180 6.1.3. Models with Extraneous Noise 183 6.1.4. Optimum Frequency Response Functions 187 6.2. Single-Input/Multiple-Output Models 190 6.2.1. Single-Input/Two-Output Model 191 6.2.2. Single-Input/Multiple-Output Model 192 6.2.3. Removal of Extraneous Noise 194 7. Multiple-Input/Output Relationships 201 7.1. Multiple-Input/Single-Output Models 201 7.1.1. General Relationships 202 7.1.2. General Case of Arbitrary Inputs 205 7.1.3. Special Case of Mutually Uncorrelated Inputs 206 7.2. Two-Input/One-Output Models 207 7.2.1. Basic Relationships 207 7.2.2. Optimum Frequency Response Functions 210 7.2.3. Ordinary and Multiple Coherence Functions 212 7.2.4. Conditioned Spectral Density Functions 213 7.2.5. Partial Coherence Functions 219 7.3. General and Conditioned Multiple-Input Models 221 7.3.1. Conditioned Fourier Transforms 223 7.3.2. Conditioned Spectral Density Functions 224 7.3.3. Optimum Systems for Conditioned Inputs 225 7.3.4. Algorithm for Conditioned Spectra 226 7.3.5. Optimum Systems for Original Inputs 229 7.3.6. Partial and Multiple Coherence Functions 231 7.4. Modified Procedure to Solve Multiple-Input/Single-Output Models 232 7.4.1. Three-Input/Single-Output Models 234 7.4.2. Formulas for Three-Input/Single-Output Models 235 7.5. Matrix Formulas for Multiple-Input/Multiple-Output Models 237 7.5.1. Multiple-Input/Multiple-Output Model 238 7.5.2. Multiple-Input/Single-Output Model 241 7.5.3. Model with Output Noise 243 7.5.4. Single-Input/Single-Output Model 245 8. Statistical Errors in Basic Estimates 249 8.1. Definition of Errors 249 8.2. Mean and Mean Square Value Estimates 252 8.2.1. Mean Value Estimates 252 8.2.2. Mean Square Value Estimates 256 8.2.3. Variance Estimates 260 8.3. Probability Density Function Estimates 261 8.3.1. Bias of the Estimate 263 8.3.2. Variance of the Estimate 264 8.3.3. Normalized rms Error 265 8.3.4. Joint Probability Density Function Estimates 265 8.4. Correlation Function Estimates 266 8.4.1. Bandwidth-Limited Gaussian White Noise 269 8.4.2. Noise-to-Signal Considerations 270 8.4.3. Location Estimates of Peak Correlation Values 271 8.5. Autospectral Density Function Estimates 273 8.5.1. Bias of the Estimate 274 8.5.2. Variance of the Estimate 278 8.5.3. Normalized rms Error 278 8.5.4. Estimates from Finite Fourier Transforms 280 8.5.5. Test for Equivalence of Autospectra 282 8.6. Record Length Requirements 284 9. Statistical Errors in Advanced Estimates 289 9.1. Cross-Spectral Density Function Estimates 289 9.1.1. Variance Formulas 292 9.1.2. Covariance Formulas 293 9.1.3. Phase Angle Estimates 297 9.2. Single-Input/Output Model Estimates 298 9.2.1. Bias in Frequency Response Function Estimates 300 9.2.2. Coherent Output Spectrum Estimates 303 9.2.3. Coherence Function Estimates 305 9.2.4. Gain Factor Estimates 308 9.2.5. Phase Factor Estimates 310 9.3. Multiple-Input/Output Model Estimates 312 10. Data Acquisition and Processing 317 10.1. Data Acquisition 318 10.1.1. Transducer and Signal Conditioning 318 10.1.2. Data Transmission 321 10.1.3. Calibration 322 10.1.4. Dynamic Range 324 10.2. Data Conversion 326 10.2.1. Analog-to-Digital Converters 326 10.2.2. Sampling Theorems for Random Records 328 10.2.3. Sampling Rates and Aliasing Errors 330 10.2.4. Quantization and Other Errors 333 10.2.5. Data Storage 335 10.3. Data Qualification 335 10.3.1. Data Classification 336 10.3.2. Data Validation 340 10.3.3. Data Editing 345 10.4. Data Analysis Procedures 349 10.4.1. Procedure for Analyzing Individual Records 349 10.4.2. Procedure for Analyzing Multiple Records 351 11. Data Analysis 359 11.1. Data Preparation 359 11.1.1. Data Standardization 360 11.1.2. Trend Removal 361 11.1.3. Digital Filtering 363 11.2. Fourier Series and Fast Fourier Transforms 366 11.2.1. Standard Fourier Series Procedure 366 11.2.2. Fast Fourier Transforms 368 11.2.3. Cooley–Tukey Procedure 374 11.2.4. Procedures for Real-Valued Records 376 11.2.5. Further Related Formulas 377 11.2.6. Other Algorithms 378 11.3. Probability Density Functions 379 11.4. Autocorrelation Functions 381 11.4.1. Autocorrelation Estimates via Direct Computations 381 11.4.2. Autocorrelation Estimates via FFT Computations 381 11.5. Autospectral Density Functions 386 11.5.1. Autospectra Estimates by Ensemble Averaging 386 11.5.2. Side-Lobe Leakage Suppression Procedures 388 11.5.3. Recommended Computational Steps for Ensemble-Averaged Estimates 395 11.5.4. Zoom Transform Procedures 396 11.5.5. Autospectra Estimates by Frequency Averaging 399 11.5.6. Other Spectral Analysis Procedures 403 11.6. Joint Record Functions 404 11.6.1. Joint Probability Density Functions 404 11.6.2. Cross-Correlation Functions 405 11.6.3. Cross-Spectral Density Functions 406 11.6.4. Frequency Response Functions 407 11.6.5. Unit Impulse Response (Weighting) Functions 408 11.6.6. Ordinary Coherence Functions 408 11.7. Multiple-Input/Output Functions 408 11.7.1. Fourier Transforms and Spectral Functions 409 11.7.2. Conditioned Spectral Density Functions 409 11.7.3. Three-Input/Single-Output Models 411 11.7.4. Functions in Modified Procedure 414 12. Nonstationary Data Analysis 417 12.1. Classes of Nonstationary Data 417 12.2. Probability Structure of Nonstationary Data 419 12.2.1. Higher Order Probability Functions 420 12.2.2. Time-Averaged Probability Functions 421 12.3. Nonstationary Mean Values 422 12.3.1. Independent Samples 424 12.3.2. Correlated Samples 425 12.3.3. Analysis Procedures for Single Records 427 12.4. Nonstationary Mean Square Values 429 12.4.1. Independent Samples 429 12.4.2. Correlated Samples 431 12.4.3. Analysis Procedures for Single Records 432 12.5. Correlation Structure of Nonstationary Data 436 12.5.1. Double-Time Correlation Functions 436 12.5.2. Alternative Double-Time Correlation Functions 437 12.5.3. Analysis Procedures for Single Records 439 12.6. Spectral Structure of Nonstationary Data 442 12.6.1. Double-Frequency Spectral Functions 443 12.6.2. Alternative Double-Frequency Spectral Functions 445 12.6.3. Frequency Time Spectral Functions 449 12.6.4. Analysis Procedures for Single Records 456 12.7. Input/Output Relations for Nonstationary Data 462 12.7.1. Nonstationary Input and Time-Varying Linear System 463 12.7.2. Results for Special Cases 464 12.7.3. Frequency–Time Spectral Input/Output Relations 465 12.7.4. Energy Spectral Input/Output Relations 467 13. The Hilbert Transform 473 13.1. Hilbert Transforms for General Records 473 13.1.1. Computation of Hilbert Transforms 476 13.1.2. Examples of Hilbert Transforms 477 13.1.3. Properties of Hilbert Transforms 478 13.1.4. Relation to Physically Realizable Systems 480 13.2. Hilbert Transforms for Correlation Functions 484 13.2.1. Correlation and Envelope Definitions 484 13.2.2. Hilbert Transform Relations 486 13.2.3. Analytic Signals for Correlation Functions 486 13.2.4. Nondispersive Propagation Problems 489 13.2.5. Dispersive Propagation Problems 495 13.3. Envelope Detection Followed by Correlation 498 14. Nonlinear System Analysis 505 14.1. Zero-Memory and Finite-Memory Nonlinear Systems 505 14.2. Square-Law and Cubic Nonlinear Models 507 14.3. Volterra Nonlinear Models 509 14.4. SI/SO Models with Parallel Linear and Nonlinear Systems 510 14.5. SI/SO Models with Nonlinear Feedback 512 14.6. Recommended Nonlinear Models and Techniques 514 14.7. Duffing SDOF Nonlinear System 515 14.7.1. Analysis for SDOF Linear System 516 14.7.2. Analysis for Duffing SDOF Nonlinear System 518 14.8. Nonlinear Drift Force Model 520 14.8.1. Basic Formulas for Proposed Model 521 14.8.2. Spectral Decomposition Problem 523 14.8.3. System Identification Problem 524 Bibliography 527 Appendix A: Statistical Tables 533 Appendix B: Definitions for Random Data Analysis 545 List of Figures 557 List of Tables 565 List of Examples 567 Answers to Problems in Random Data 571 Index 599

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Book SynopsisIncorporating modern ideas, methods, and philosophies of quality management, Fundamentals of Quality Control and Improvement, Third Edition presents a quantitative approach to management-oriented techniques and enforces the integration of statistical concepts into quality assurance methods.Trade Review?Experimental design and Taguchi are will explained in the book and reliability analysis is introduced in a brief, but useful section.? (Quality World, November 2009)Table of ContentsPREFACE vii CHAPTER 1: INTRODUCTION TO QUALITY CONTROL AND THE TOTAL QUALITY SYSTEM 1 CHAPTER 2: SOME PHILOSOPHIES AND THEIR IMPACT ON QUALITY 15 CHAPTER 3: QUALITY MANAGEMENT: PRACTICES, TOOLS, AND STANDARDS 27 CHAPTER 4: FUNDAMENTALS OF STATISTICAL CONCEPTS AND TECHNIQUES IN QUALITY CONTROL AND IMPROVEMENT 45 CHAPTER 5: DATA ANALYSES AND SAMPLING 73 CHAPTER 6: STATISTICAL PROCESS CONTROL USING CONTROL CHARTS 85 CHAPTER 7: CONTROL CHARTS FOR VARIABLES 97 CHAPTER 8: CONTROL CHARTS FOR ATTRIBUTES 125 CHAPTER 9: PROCESS CAPABILITY ANALYSIS 151 CHAPTER 10: ACCEPTANCE SAMPLING PLANS FOR ATTRIBUTES AND VARIABLES 177 CHAPTER 11: RELIABILITY 197 CHAPTER 12: EXPERIMENTAL DESIGN AND THE TAGUCHI METHOD 203

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Book SynopsisExplores the major topics in Monte Carlo simulation. This title features the information that facilitates an understanding of problem solving across a wide array of subject areas, such as engineering, mathematics, and the physical and life sciences. It introduces the basic concepts of probability, Markov processes, and convex optimization.Table of ContentsPreface. Acknolwedgments. I: Problems. 1. Preliminaries. 2. Random Number, random Variable, and Stochastic Process Generation. 3. Simulatin of Discrete-Event Systems. 4. Stastical Analysis of Discrete-Event Systems. 5. Controlling the Variance. 6. Markov Chain Monte Carlo. 7. Sensitivity Analysis and Monte Carlo Optimization. 8. The Cross-Entropy Method. 9. Counting via Monte Carlo. 10. Appendix. II: Solutions. 11. Prelimiaries. 12. Random Number, Random Variable, and Stochastic Process Generation. 13. Simulatin of Discrete-Event Systems. 14. Stastical Analysis of Discrete-Event Systems. 15. Controlling the Variance. 16. Markov Chain Monte Carlo. 17. Sensitivity Analysis and Monte Carlo Optimization. 18. The Cross-Entropy Method. 19. Counting via Monte Carlo. 20. Appendix.

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Book SynopsisA uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis. The author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes: Measure spaces, outer measures, and extension theorems Lebesgue measure on the line and in Euclidean space Measurable functions, Egoroff''s theorem, and Lusin''s theorem Convergence theorems for integralsTrade Review"The book is well thought out, organized and written. It has all the results in measure theory that are necessary for both pure and applied mathematics research." (Mathematical Reviews, 2011)Table of ContentsPreface. Acknowledgments. Introduction. 1 History of the Subject. 1.1 History of the Idea. 1.2 Deficiencies of the Riemann Integral. 1.3 Motivation for the Lebesgue Integral. 2 Fields, Borel Fields and Measures. 2.1 Fields, Monotone Classes, and Borel Fields. 2.2 Additive Measures. 2.3 Carathéodory Outer Measure. 2.4 E. Hopf’s Extension Theorem. 3 Lebesgue Measure. 3.1 The Finite Interval [-N,N). 3.2 Measurable Sets, Borel Sets, and the Real Line. 3.3 Measure Spaces and Completions. 3.4 Semimetric Space of Measurable Sets. 3.5 Lebesgue Measure in Rn. 3.6 Jordan Measure in Rn. 4 Measurable Functions. 4.1 Measurable Functions. 4.2 Limits of Measurable Functions. 4.3 Simple Functions and Egoroff’s Theorem. 4.4 Lusin’s Theorem. 5 The Integral. 5.1 Special Simple Functions. 5.2 Extending the Domain of the Integral. 5.3 Lebesgue Dominated Convergence Theorem. 5.4 Monotone Convergence and Fatou’s Theorem. 5.5 Completeness of L1 and the Pointwise Convergence Lemma. 5.6 Complex Valued Functions. 6 Product Measures and Fubini’s Theorem. 6.1 Product Measures. 6.2 Fubini’s Theorem. 6.3 Comparison of Lebesgue and Riemann Integrals. 7 Functions of a Real Variable. 7.1 Functions of Bounded Variation. 7.2 A Fundamental Theorem for the Lebesgue Integral. 7.3 Lebesgue’s Theorem and Vitali’s Covering Theorem. 7.4 Absolutely Continuous and Singular Functions. 8 General Countably Additive Set Functions. 8.1 Hahn Decomposition Theorem. 8.2 Radon-Nikodym Theorem. 8.3 Lebesgue Decomposition Theorem. 9. Examples of Dual Spaces from Measure Theory. 9.1 The Banach Space Lp. 9.2 The Dual of a Banach Space. 9.3 The Dual Space of Lp. 9.4 Hilbert Space, Its Dual, and L2. 9.5 Riesz-Markov-Saks-Kakutani Theorem. 10 Translation Invariance in Real Analysis. 10.1 An Orthonormal Basis for L2(T). 10.2 Closed Invariant Subspaces of L2(T). 10.3 Schwartz Functions: Fourier Transform and Inversion. 10.4 Closed, Invariant Subspaces of L2(R). 10.5 Irreducibility of L2(R) Under Translations and Rotations. Appendix A: The Banach-Tarski Theorem. A.1 The Limits to Countable Additivity. References. Index.

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Book SynopsisWritten by two of the best-known experts in the field, Clustering is the only thoroughly comprehensive text on the subject currently available. The book looks at the full range of clustering and provides enough detail to allow users to select the method that best fits their application.Trade Review“This book provides a comprehensive and thorough presentation of this research area, describing some of the most important clustering algorithms proposed in research literature.” (Computing Reviews, June 2009) "The book covers a lot of ground in a relatively small number of pages, and should work well as a learning tool and reference." (Computing Reviews, May 28, 2009)Table of ContentsPREFACE. 1. CLUSTER ANALYSIS. 1.1. Classifi cation and Clustering. 1.2. Defi nition of Clusters. 1.3. Clustering Applications. 1.4. Literature of Clustering Algorithms. 1.5. Outline of the Book. 2. PROXIMITY MEASURES. 2.1. Introduction. 2.2. Feature Types and Measurement Levels. 2.3. Defi nition of Proximity Measures. 2.4. Proximity Measures for Continuous Variables. 2.5. Proximity Measures for Discrete Variables. 2.6. Proximity Measures for Mixed Variables. 2.7. Summary. 3. HIERARCHICAL CLUSTERING. 3.1. Introduction. 3.2. Agglomerative Hierarchical Clustering. 3.3. Divisive Hierarchical Clustering. 3.4. Recent Advances. 3.5. Applications. 3.6. Summary. 4. PARTITIONAL CLUSTERING. 4.1. Introduction. 4.2. Clustering Criteria. 4.3. K-Means Algorithm. 4.4. Mixture Density-Based Clustering. 4.5. Graph Theory-Based Clustering. 4.6. Fuzzy Clustering. 4.7. Search Techniques-Based Clustering Algorithms. 4.8. Applications. 4.9. Summary. 5. NEURAL NETWORK–BASED CLUSTERING. 5.1. Introduction. 5.2. Hard Competitive Learning Clustering. 5.3. Soft Competitive Learning Clustering. 5.4. Applications. 5.5. Summary. 6. KERNEL-BASED CLUSTERING. 6.1. Introduction. 6.2. Kernel Principal Component Analysis. 6.3. Squared-Error-Based Clustering with Kernel Functions. 6.4. Support Vector Clustering. 6.5. Applications. 6.6. Summary. 7. SEQUENTIAL DATA CLUSTERING. 7.1. Introduction. 7.2. Sequence Similarity. 7.3. Indirect Sequence Clustering. 7.4. Model-Based Sequence Clustering. 7.5. Applications—Genomic and Biological Sequence. 7.6. Summary. 8. LARGE-SCALE DATA CLUSTERING. 8.1. Introduction. 8.2. Random Sampling Methods. 8.3. Condensation-Based Methods. 8.4. Density-Based Methods. 8.5. Grid-Based Methods. 8.6. Divide and Conquer. 8.7. Incremental Clustering. 8.8. Applications. 8.9. Summary. 9. DATA VISUALIZATION AND HIGH-DIMENSIONAL DATA CLUSTERING. 9.1. Introduction. 9.2. Linear Projection Algorithms. 9.3. Nonlinear Projection Algorithms. 9.4. Projected and Subspace Clustering. 9.5. Applications. 9.6. Summary. 10. CLUSTER VALIDITY. 10.1. Introduction. 10.2. External Criteria. 10.3. Internal Criteria. 10.4. Relative Criteria. 10.5. Summary. 11. CONCLUDING REMARKS. PROBLEMS. REFERENCES. AUTHOR INDEX. SUBJECT INDEX.

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Book SynopsisA unified view of metaheuristics This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling. It presents the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. Throughout the book, the key search components of metaheuristics are considered as a toolbox for: Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems Designing efficient metaheuristics for multi-objective optimization problems Designing hybrid, Trade Review “In conclusion, I found reading Metaheuristics: From Design to Implementation to be pleasant and enjoyable. I particularly recommend it as a reference for researchers and students of computer science or operations research who want a global outlook of metaheuristics methods. It would also be extremely useful for introducing graduate and PhD students who are new to the field of heuristics and metaheuristics to the amazing world of the designing of these procedures.” (Informs, 1 July 2012) "It will be an indispensable text for advanced undergraduate and graduate students in computer science, operations research, applied mathematics, control, business and management and engineering." (Zentralblatt MATH, 2010) Table of ContentsPreface. Acknowledgments. Glossary. 1 Common Concepts for Metaheuristics. 1.1 Optimization Models. 1.2 Other Models for Optimization. 1.3 Optimization Methods. 1.4 Main Common Concepts for Metaheuristics. 1.5 Constraint Handling. 1.6 Parameter Tuning. 1.7 Performance Analysis of Metaheuristics. 1.8 Software Frameworks for Metaheuristics. 1.9 Conclusions. 1.10 Exercises. 2 Single-Solution Based Metaheuristics. 2.1 Common Concepts for Single-Solution Based Metaheuristics. 2.2 Fitness Landscape Analysis. 2.3 Local Search. 2.4 Simulated Annealing. 2.5 Tabu Search. 2.6 Iterated Local Search. 2.7 Variable Neighborhood Search. 2.8 Guided Local Search. 2.9 Other Single-Solution Based Metaheuristics. 2.10 S-Metaheuristic Implementation Under ParadisEO. 2.11 Conclusions. 2.12 Exercises. 3 Population-Based Metaheuristics. 3.1 Common Concepts for Population-Based Metaheuristics. 3.2 Evolutionary Algorithms. 3.3 Common Concepts for Evolutionary Algorithms. 3.4 Other Evolutionary Algorithms. 3.5 Scatter Search. 3.6 Swarm Intelligence. 3.7 Other Population-Based Methods. 3.8 P-metaheuristics Implementation Under ParadisEO. 3.9 Conclusions. 3.10 Exercises. 4 Metaheuristics for Multiobjective Optimization. 4.1 Multiobjective Optimization Concepts. 4.2 Multiobjective Optimization Problems. 4.3 Main Design Issues of Multiobjective Metaheuristics. 4.4 Fitness Assignment Strategies. 4.5 Diversity Preservation. 4.6 Elitism. 4.7 Performance Evaluation and Pareto Front Structure. 4.8 Multiobjective Metaheuristics Under ParadisEO. 4.9 Conclusions and Perspectives. 4.10 Exercises. 5 Hybrid Metaheuristics. 5.1 Hybrid Metaheuristics. 5.2 Combining Metaheuristics with Mathematical Programming. 5.3 Combining Metaheuristics with Constraint Programming. 5.4 Hybrid Metaheuristics with Machine Learning and Data Mining. 5.5 Hybrid Metaheuristics for Multiobjective Optimization. 5.6 Hybrid Metaheuristics Under ParadisEO. 5.7 Conclusions and Perspectives. 5.8 Exercises. 6 Parallel Metaheuristics. 6.1 Parallel Design of Metaheuristics. 6.2 Parallel Implementation of Metaheuristics. 6.3 Parallel Metaheuristics for Multiobjective Optimization. 6.4 Parallel Metaheuristics Under ParadisEO. 6.5 Conclusions and Perspectives. 6.6 Exercises. Appendix: UML and C++. A.1 A Brief Overview of UML Notations. A.2 A Brief Overview of the C++ Template Concept. References. Index.

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Book SynopsisA comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning.Trade Review“Overall, he presents the material as if he were holding a dialogue with the reader. An advanced independent reader with a very strong background in mathematics would find the book helpful in learning this area of mathematics. Summing Up: Recommended.” (Choice, April 2009) "The book would be ideas as an introduction to classical logic for students of mathematics, computer science or philosophy. Due to the author's clear and approachable style, it can be recommended to a large circle of readers interested in mathematical logic as well." (Mathematical Review, Issue 2009e) "I give this outstanding book my highest recommendation, whilst being grateful that excellence in the logic-book 'business' is the very opposite of a zero-sum game: there's plenty of room at the top." (Computing Reviews, November 5, 2008)Table of ContentsPreface. Acknowledgments. PART I: BOOLEAN LOGIC. 1. The Beginning. 1.1 Boolean Formulae. 1.2 Induction on the Complexity of WFF: Some Easy Properties of WFF. 1.3 Inductive definitions on formulae. 1.4 Proofs and Theorems. 1.5 Additional Exercises. 2. Theorems and Metatheorems. 2.1 More Hilbertstyle Proofs. 2.2 Equational-style Proofs. 2.3 Equational Proof Layout. 2.4 More Proofs: Enriching our Toolbox. 2.5 Using Special Axioms in Equational Proofs. 2.6 The Deduction Theorem. 2.7 Additional Exercises. 3. The Interplay between Syntax and Semantics. 3.1 Soundness. 3.2 Post’s Theorem. 3.3 Full Circle. 3.4 Single-Formula Leibniz. 3.5 Appendix: Resolution in Boolean Logic. 3.6 Additional Exercises. PART II: PREDICATE LOGIC. 4. Extending Boolean Logic. 4.1 The First Order Language of Predicate Logic. 4.2 Axioms and Rules of First Order Logic. 4.3 Additional Exercises. 5. Two Equivalent Logics. 6. Generalization and Additional Leibniz Rules. 6.1 Inserting and Removing "(∀x)". 6.2 Leibniz Rules that Affect Quantifier Scopes. 6.3 The Leibniz Rules "8.12". 6.4 More Useful Tools. 6.5 Inserting and Removing "(∃x)". 6.6 Additional Exercises. 7. Properties of Equality. 8. First Order Semantics -- Very Naïvely. 8.1 Interpretations. 8.2 Soundness in Predicate Logic. 8.3 Additional Exercises. Appendix A: Gödel's Theorems and Computability. A.1 Revisiting Tarski Semantics. A.2 Completeness. A.3 A Brief Theory of Computability. A.3.1 A Programming Framework for Computable Functions. A.3.2 Primitive Recursive Functions. A.3.3 URM Computations. A.3.4 Semi-Computable Relations; Unsolvability. A.4 Godel's First Incompleteness Theorem. A.4.1 Supplement: øx(x) " is first order definable in N. References. Index.

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Book SynopsisA complete guide to carrying out complex survey analysis using R As survey analysis continues to serve as a core component of sociological research, researchers are increasingly relying upon data gathered from complex surveys to carry out traditional analyses. Complex Surveys is a practical guide to the analysis of this kind of data using R, the freely available and downloadable statistical programming language. As creator of the specific survey package for R, the author provides the ultimate presentation of how to successfully use the software for analyzing data from complex surveys while also utilizing the most current data from health and social sciences studies to demonstrate the application of survey research methods in these fields. The book begins with coverage of basic tools and topics within survey analysis such as simple and stratified sampling, cluster sampling, linear regression, and categorical data regression. Subsequent chapters delve into more tTable of ContentsAcknowledgments. Preface. Acronyms. 1 Basic Tools. 1.1 Goals of Inference. 1.1.1 Population or Process? 1.1.2 Probability Samples. 1.1.3 Sampling Weights. 1.1.4 Design Effects. 1.2 An Introduction to the Data. 1.2.1 Real Surveys. 1.2.2 Populations. 1.3 Obtaining the Software. 1.3.1 Obtaining R. 1.3.2 Obtaining the Survey Package. 1.4 Using R. 1.4.1 Reading Plain Text Data. 1.4.2 Reading Data from Other Packages. 1.4.3 Simple Computation. Exercises. 2 Simple and Stratified Sampling. 2.1 Analyzing Simple Random Samples. 2.1.1 Confidence Intervals. 2.1.2 Describing the Sample to R. 2.2 Stratified Sampling. 2.3 Replicate Weights. 2.3.1 Specifying Replicate Weights to R. 2.3.2 Creating Replicate Weights in R. 2.4 Other Population Summaries. 2.4.1 Quantiles. 2.4.2 Contingency Tables. 2.5 Estimates in Subpopulations. 2.6 Design of Stratified Samples. Exercises. 3 Cluster Sampling. 3.1 Introduction. 3.1.1 Why Clusters: The NHANES II Design. 3.1.2 Single-Stage and Multistage Designs. 3.2 Describing Multistage Designs to R. 3.2.1 Strata with Only One PSU. 3.2.2 How Good is the Single-State Approximation? 3.2.3 Replicate Weights for Multistage Samples. 3.3 Sampling by Size. 3.3.1 Loss of Information from Sampling Clusters. 3.4 Repeated Measurements. Exercises. 4 Graphics. 4.1 Why is Survey Data Different? 4.2 Plotting a Table. 4.3 One Continuous Variable. 4.3.1 Graphs Based on the Distribution Function. 4.3.2 Graphs Based on the Density. 4.4 Two Continuous Variables. 4.4.1 Scatterplots. 4.4.2 Aggregation and Smoothing. 4.4.3 Scatterplot Smoothers. 4.5 Conditioning Plots. 4.6 Maps. 4.6.1 Design and Estimation Issues. 4.6.2 Drawing Maps in R. Exercises. 5 Ratios and Linear Regression. 5.1 Ratio Estimation. 5.1.1 Estimating Ratios. 5.1.2 Ratios for Subpopulation Estimates. 5.1.3 Ratio Estimators of Totals. 5.2 Linear Regression. 5.2.1 The Least-Squares Slope as an Estimated Population. 5.2.2 Regression Estimation of Population Totals. 5.2.3 Confounding and Other Criteria for Model Choice. 5.2.4 Linear Models in the Survey Package. 5.3 Is Weighting Needed in Regression Models? Exercises. 6 Categorical Data Regression. 6.1 Logistic Regression. 6.1.1 Relative Risk Regression. 6.2 Ordinal Regression. 6.2.1 Other Cumulative Link Models. 6.3 Loglinear Models. 6.3.1 Choosing Models. 6.3.2 Linear Association Models. Exercises. 7 Post-Stratification, Raking and Calibration. 7.1 Introduction. 7.2 Post-Stratification. 7.3 Raking. 7.4 Generalized Raking, GREG Estimation, and Calibration. 7.4.1 Calibration in R. 7.5 Basu’s Elephants. 7.6 Selecting Auxiliary Variables for Non-Response. 7.6.1 Direct Standardization. 7.6.2 Standard Error Estimation. Exercises. 8 Two-Phase Sampling. 8.1 Multistage and Multiphase Sampling. 8.2 Sampling for Stratification. 8.3 The Case-Control Design. 8.3.1 Simulations: Efficiency of the Design-Based Estimator. 8.3.2 Frequency Matching. 8.4 Sampling from Existing Cohorts. 8.4.1 Logistic Regression. 8.4.2 Two-Phase Case-Control Designs in R. 8.4.3 Survival Analysis. 8.4.4 Case-Cohort Designs in R. 8.5 Using Auxiliary Information from Phase One. 8.5.1 Population Calibration for Regression Models. 8.5.2 Two-Phase Designs. 8.5.3 Some History of the Two-Phase Calibration Estimator. Exercises. 9 Missing Data. 9.1 Item Non-Response. 9.2 Two-Phase Estimation for Missing Data. 9.2.1 Calibration for Item Non-Response. 9.2.2 Models for Response Probability. 9.2.3 Effect on Precision. 9.2.4 Doubly-Robust Estimators. 9.3 Imputation of Missing Data. 9.3.1 Describing Multiple Imputations to R. 9.3.2 Example: NHANES III Imputations. Exercises. 10 Causal Inference. 10.1 IPTW Estimators. 10.1.1 Randomized Trials and Calibration. 10.1.2 Estimated Weights for IPTW. 10.1.3 Double Robustness. 10.2 Marginal Structural Models. Appendix A: Analytic Details. A.1 Asymptotics. A.1.1 Embedding in an Infinite Sequence. A.1.2 Asymptotic Unbiasedness. A.1.3 Asymptotic Normality and Consistency. A.2 Variances by Linearization. A.2.1 Subpopulation Inference. A.3 Tests in Contingency Tables. A.4 Multiple Imputation. A.5 Calibration and Influence Functions. A.6 Calibration in Randomized Trials and ANCOVA. Appendix B: Basic R. B.1 Reading Data. B.1.1 Plain Text Data. B.2 Data Manipulation. B.2.1 Merging. B.2.2 Factors. B.3 Randomness. B.4 Methods and Objects. B.5 Writing Functions. B.5.1 Repetition. B.5.2 Strings. Appendix C: Computational Details. C.1 Linearization. C.1.1 Generalized Linear Models and Expected Information. C.2 Replicate Weights. C.2.1 Choice of Estimators. C.2.2 Hadamard Matrices. C.3 Scatterplot Smoothers. C.4 Quantiles. C.5 Bug Reports and Feature Requests. Appendix D: Database-Backed Design Objects. D.1 Large Data. D.2 Setting Up Database Interfaces. D.2.1 ODBC. D.2.2 DBI. Appendix E: Extending the Survey Package. E.1 A Case Study: Negative Binomial Regression. E.2 Using a Poisson Model. E.3 Replicate Weights. E.4 Linearization. References. Author Index. Topic Index.

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Book SynopsisA one-of-a-kind resource on identifying and dealing with bias in statistical research on causal effects Do cell phones cause cancer? Can a new curriculum increase student achievement? Determining what the real causes of such problems are, and how powerful their effects may be, are central issues in research across various fields of study. Some researchers are highly skeptical of drawing causal conclusions except in tightly controlled randomized experiments, while others discount the threats posed by different sources of bias, even in less rigorous observational studies. Bias and Causation presents a complete treatment of the subject, organizing and clarifying the diverse types of biases into a conceptual framework. The book treats various sources of bias in comparative studiesboth randomized and observationaland offers guidance on how they should be addressed by researchers. Utilizing a relatively simple mathematical approach, the author develops a theory of bias thatTrade Review"The book combines a useful synthesis of the literature with an original working through of issues related to bias and causal inference. Anyone with a sustained interest in this topic will find the book worth reading." (Journal of Educational and Behavioral Statistics, May 2012) "...the book provides a unified framework for understanding issues of causal inference discussed differently across disciplines...the book will also be of substantial interest to methodologically minded readers working within specific disciplines but interested in methodological literature from other disciplines." (Journal of Educational and Behavioral Statistics, May 2012) "The book covers almost all the relevant biases that can be present when designing and analyzing treatment effects in comparative studies." (Journal of Biopharmaceutical Statistics, January 2011)"A consultant who specializes in applying statistics to various business and legal issues, Weisberg explains approaches to bias and causal inference, a realm statisticians have avoided until recently because it requires intuitive skills beyond the pale of mathematics. He writes for practicing researchers and methodologists and for students with a reasonably solid grounding in basic statistics and research methods." (SciTech Book News, December 2010)Table of ContentsPreface xi 1. What Is Bias? 1 1.1 Apples and Oranges, 2 1.2 Statistics vs. Causation, 3 1.3 Bias in the Real World, 6 Guidepost 1, 23 2. Causality and Comparative Studies 24 2.1 Bias and Causation, 24 2.2 Causality and Counterfactuals, 26 2.3 Why Counterfactuals? 32 2.4 Causal Effects, 33 2.5 Empirical Effects, 38 Guidepost 2, 46 3. Estimating Causal Effects 47 3.1 External Validity, 48 3.2 Measures of Empirical Effects, 50 3.3 Difference of Means, 52 3.4 Risk Difference and Risk Ratio, 55 3.5 Potential Outcomes, 57 3.6 Time-Dependent Outcomes, 60 3.7 Intermediate Variables, 63 3.8 Measurement of Exposure, 64 3.9 Measurement of the Outcome Value, 68 3.10 Confounding Bias, 70 Guidepost 3, 71 4. Varieties of Bias 72 4.1 Research Designs and Bias, 73 4.2 Bias in Biomedical Research, 81 4.3 Bias in Social Science Research, 85 4.4 Sources of Bias: A Proposed Taxonomy, 90 Guidepost 4, 92 5. Selection Bias 93 5.1 Selection Processes and Bias, 93 5.2 Traditional Selection Model: Dichotomous Outcome, 100 5.3 Causal Selection Model: Dichotomous Outcome, 102 5.4 Randomized Experiments, 104 5.5 Observational Cohort Studies, 108 5.6 Traditional Selection Model: Numerical Outcome, 111 5.7 Causal Selection Model: Numerical Outcome, 114 Guidepost 5, 121 Appendix, 122 6. Confounding: An Enigma? 126 6.1 What is the Real Problem? 127 6.2 Confounding and Extraneous Causes, 127 6.3 Confounding and Statistical Control, 131 6.4 Confounding and Comparability, 137 6.5 Confounding and the Assignment Mechanism, 139 6.6 Confounding and Model Specifi cation, 141 Guidepost 6, 144 7. Confounding: Essence, Correction, and Detection 145 7.1 Essence: The Nature of Confounding, 146 7.2 Correction: Statistical Control for Confounding, 172 7.3 Detection: Adequacy of Statistical Adjustment, 180 Guidepost 7, 191 Appendix, 192 8. Intermediate Causal Factors 195 8.1 Direct and Indirect Effects, 195 8.2 Principal Stratifi cation, 200 8.3 Noncompliance, 209 8.4 Attrition, 214 Guidepost 8, 215 9. Information Bias 217 9.1 Basic Concepts, 218 9.2 Classical Measurement Model: Dichotomous Outcome, 223 9.3 Causal Measurement Model: Dichotomous Outcome, 230 9.4 Classical Measurement Model: Numerical Outcome, 239 9.5 Causal Measurement Model: Numerical Outcome, 242 9.6 Covariates Measured with Error, 246 Guidepost 9, 250 10. Sources of Bias 252 10.1 Sampling, 254 10.2 Assignment, 260 10.3 Adherence, 266 10.4 Exposure Ascertainment, 269 10.5 Outcome Measurement, 273 Guidepost 10, 277 11. Contending with Bias 279 11.1 Conventional Solutions, 280 11.2 Standard Statistical Paradigm, 286 11.3 Toward a Broader Perspective, 288 11.4 Real-World Bias Revisited, 293 11.5 Statistics and Causation, 303 Glossary 309 Bibliography 321 Index 340

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Book SynopsisExplores wide-ranging applications of modeling and simulation techniques that allow readers to conduct research and ask "What if??" Principles of Modeling and Simulation: A Multidisciplinary Approach is the first book to provide an introduction to modeling and simulation techniques across diverse areas of study.Trade Review"This work could supplement a graduate course on modeling and simulation (selected chapters could supplement an undergraduate course) and would be of interest to graduate students and professionals wishing to learn some of the basics of modeling and simulation." (CHOICE, December 2009) Table of ContentsPreface. Contributors. PART ONE: PRINCIPLES OF MODELING AND SIMULATION: A MULTIDISCIPLINARY APPROACH. Chapter 1: What is Modeling and Simulation? Introduction. Models: Approximations of Real World Events. A Brief History of Modeling and Simulation. Application Areas. Using Modeling and Simulation: Advantages and Disadvantages. Conclusion. Key Terms. Further Reading. References. Chapter 2: The Role of Modeling and Simulation. Introduction. Using Simulations to Solve Problems. Uncertainty and Its Effects. Gaining Insight. A Simulation’s Lifetime. Conclusion. Key Terms. Further Reading. PART TWO: THEORETICAL UNDERPINNINGS. Chapter 3: Simulation: Models That Vary Over Time. Introduction. Discrete Event Simulation. Continuous Simulation. Conclusion. Key Terms. References. Chapter 4: Queue Modeling and Simulation. Introduction. Analytical Solution. Queuing Models. Sequential Simulation. SimPack Queuing Implementation. Parallel Simulation. Conclusion. Key Terms. Further Reading. References. Chapter 5: Human Interaction with Simulations. Introduction. Simulation and Data Dependency. Visual Representation. Conclusion. Key Terms. References. Chapter 6: Verification and Validation. Introduction. Performing Verification and Validation. Verification and Validation Examples. Conclusion. Key Terms. References. PART THREE: PRACTICAL DOMAINS. Chapter 7: Uses of Simulation. Introduction. The Many Facets of Simulation. Experimentation Aspect of Simulation. Experience Aspect of Simulation. Examples of Uses of Simulation. Ethics in the Use of Simulation. Some Excuses to Avoid Simulation. Conclusion. Key Terms. Further Exploration. References. Appendix A-Simulation Associations/Groups/Research Centers. CHAPTER 8: MODELING AND SIMULATION: REAL-WORLD EXAMPLES. Introduction. Transportation. Business M&S. Medical M&S. Social Science M&S. Conclusion. Key Terms. Further Reading. References. Chapter 9: The Future of Simulation. Introduction. A Brief . . . and Selective . . . History of Simulation. Convergent Simulations. Serious Games. Human-Simulator Interfaces. Computing Technology. The Role of Education in Simulation. The Future of Simulation. Index.

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Book SynopsisAn introductory guide to smoothing techniques, semiparametric estimators, and their related methods, this book describes the methodology via a selection of carefully explained examples and data sets. It also demonstrates the potential of these techniques using detailed empirical examples drawn from the social and political sciences.Trade Review"The strength of Keele's book is that it offers clear, straightforward explanations of the models, illustrated with social science (primarily political science) applications. Applied social science researchers should be able to incorporate these methods in their own research relatively easily after reading this book." (The Political Methodologist, 2009)Table of ContentsList of Tables. List of Figures. Preface. 1 Introduction: Global versus Local Statistics. 1.1 The Consequences of Ignoring Nonlinearity. 1.2 Power Transformations. 1.3 Nonparametric and Semiparametric Techniques. 1.4 Outline of the Text. 2 Smoothing and Local Regression. 2.1 Simple Smoothing. 2.1.1 Local Averaging. 2.1.2 Kernel Smoothing. 2.2 Local Polynomial Regression. 2.3 Nonparametric Modeling Choices. 2.3.1 The Span. 2.3.2 Polynomial Degree and Weight Function. 2.3.3 A Note on Interpretation. 2.4 Statistical Inference for Local Polynomial Regression. 2.5 Multiple Nonparametric Regression. 2.6 Conclusion. 2.7 Exercises. 3 Splines. 3.1 Simple Regression Splines. 3.1.1 Basis Functions. 3.2 Other Spline Models and Bases. 3.2.1 Quadratic and Cubic Spline Bases. 3.2.2 Natural Splines. 3.2.3 B-splines. 3.2.4 Knot Placement and Numbers. 3.2.5 Comparing Spline Models. 3.3 Splines and Overfitting. 3.3.1 Smoothing Splines. 3.3.2 Splines as Mixed Models. 3.3.3 Final Notes on Smoothing Splines. 3.3.4 Thin Plate Splines. 3.4 Inference for Splines. 3.5 Comparisons and Conclusions. 3.6 Exercises. 4 Automated Smoothing Techniques. 4.1 Span by Cross-Validation. 4.2 Splines and Automated Smoothing. 4.2.1 Estimating Smoothing Through the Likelihood. 4.2.2 Smoothing Splines and Cross-Validation. 4.3 Automated Smoothing in Practice. 4.4 Automated Smoothing Caveats. 4.5 Exercises. 5 Additive and Semiparametric Regression Models. 5.1 Additive Models. 5.2 Semiparametric Regression Models. 5.3 Estimation. 5.3.1 Backfitting. 5.4 Inference. 5.5 Examples. 5.5.1 Congressional Elections. 5.5.2 Feminist Attitudes. 5.6 Discussion. 5.7 Exercises. 6 Generalized Additive Models. 6.1 Generalized Linear Models. 6.2 Estimation of GAMS. 6.3 Statistical Inference. 6.4 Examples. 6.4.1 Logistic Regression: The Liberal Peace. 6.4.2 Ordered Logit: Domestic Violence. 6.4.3 Count Models: Supreme Court Overrides. 6.4.4 Survival Models: Race Riots. 6.5 Discussion. 6.6 Exercises. 7 Extensions of the Semiparametric Regression Model. 7.1 Mixed Models. 7.2 Bayesian Smoothing. 7.3 Propensity Score Matching. 7.4 Conclusion. 8 Bootstrapping. 8.1 Classical Inference. 8.2 Bootstrapping – An Overview. 8.2.1 Bootstrapping. 8.2.2 An Example: Bootstrapping the Mean. 8.2.3 Bootstrapping Regression Models. 8.2.4 An Example: Presidential Elections. 8.3 Bootstrapping Nonparametric and Semiparametric Regression Models. 8.3.1 Bootstrapping Nonparametric Fits. 8.3.2 Bootstrapping Nonlinearity Tests. 8.4 Conclusion. 8.5 Exercises. 9 Epilogue. Appendix: Software. Bibliography. Author Index. Subject Index.

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Book SynopsisModeling Random Processes for Engineers and Managers provides students with a gentle introduction to stochastic processes, emphasizing full explanations and many examples rather than formal mathematical theorems and proofs. The text offers an accessible entry into a very useful and versatile set of tools for dealing with uncertainty and variation. Many practical examples of models, as well as complete explanations of the thought process required to create them, motivate the presentation of the computational methods. In addition, the text contains a previously unpublished computational approach to solving many of the equations that occur in Markov processes. Modeling Random Processes is intended to serve as an introduction, but more advanced students can use the case studies and problems to expand their understanding of practical uses of the theory.Table of ContentsPreface ix 1 Probability Review 1 1.1 Interpreting and Using Probabilities 2 1.2 Sample Spaces and Events 3 1.3 Probability 4 1.4 Random Variables 6 1.5 Probability Distributions 6 1.6 Joint, Marginal, and Conditional Distributions 11 1.7 Expectation 14 1.8 Variance and Other Moments 16 1.9 The Law of Total Probability 18 1.10 Discrete Probability Distributions 20 1.11 Continuous Probability Distributions 23 1.12 Where Do Distributions Come From? 26 1.13 The Binomial Process 28 1.14 Recommended Reading 29 2 Formulating Markov Chain Models 32 2.1 An Example 33 2.2 Modeling the Progress of Time 34 2.3 Modeling Possibilities as States 36 2.4 Simplifying Assumptions 38 2.5 Modeling Changes of State as Transitions 40 2.6 Obtaining the Data 45 2.7 Another Example 46 2.8 A Case Study 47 2.9 Higher Order Markov Chains 50 2.10 Reducing the Number of States 52 2.11 Nonstationary Markov Chains 53 2.12 Other Example 54 2.13 Summary 67 2.14 Recommended Reading 67 3 Markov Chain Calculations 72 3.1 Walk Probabilities 73 3.2 Transition Probabilities 74 3.3 State Probabilities 78 3.4 A Numerical Example 79 3.5 Expected Number of Visits 80 3.6 Sojourn Times 82 3.7 First Passage and Return Probabilities 83 3.8 Computational Formulas for All Markov Chains 86 3.9 Special Classes of Markov Chains 86 3.10 Steady-State Probabilities 87 3.11 The Uses of Steady-State Results 92 3.12 Mean First Passage Times 93 3.13 Computational Formulas for Ergodic Markov Chains 96 3.14 Terminating Markov Chains 96 3.15 Expected Number of Visits 98 3.16 Expected Duration of a Terminating Process 99 3.17 Absorption Probabilities 100 3.18 Hit Probabilities 102 3.19 Conditional Mean First Passage Times to Absorbing States 103 3.20 Computational Formulas for Terminating Processes 105 3.21 Call Center Calculations 105 3.22 Classification Terminology 106 3.23 Additional Complications in Infinite Chains 111 3.24 Dealing with a Reducible Process 112 3.25 Periodic Chains 113 3.26 Ergodic Chains 114 3.27 Recommended Reading 115 4 Rewards on Markov Chains 119 4.1 Formulation 120 4.2 A Numerical Example 120 4.3 Expected Total Reward 121 4.4 Random Variable Rewards 124 4.5 Semi-Markov Processes 126 4.6 Limiting Results for Ergodic Processes 126 4.7 Total Reward for Terminating Processes 130 4.8 Case Study 132 4.9 Discounting 133 4.10 Case Study 135 4.11 Recommended Reading 137 5 Continuous Time Markov Processes 140 5.1 An Example 141 5.2 Interpreting Transition Rates 146 5.3 The Assumptions Reconsidered 149 5.4 Aging Does Not Affect the Transition Time 150 5.5 Competing Transitions 152 5.6 Sojourn Times 153 5.7 Embedded Markov Chains 154 5.8 Deriving the Differential Equations 155 5.9 Solving the Differential Equations 157 5.10 State Probabilities 159 5.11 First Passage Probability Functions 159 5.12 State Classification 160 5.13 Steady-State Probabilities 161 5.14 Other Computable Quantities 163 5.15 Case Study 165 5.16 Birth-Death Processes 167 5.17 The Poisson Process 169 5.18 Properties of Poisson Processes 171 5.19 Khintchine’s Theorem 172 5.20 Phase-Type Distributions 173 5.21 Conclusions 175 5.22 Recommended Reading 175 6 Queueing Models 179 6.1 An Example 180 6.2 General Characteristics 182 6.3 Performance Measures 186 6.4 Relations Among Performance Measures 188 6.5 Little’s Formula 190 6.6 Markovian Queueing Models 191 6.7 The M/M/1 Model 193 6.8 The Significance of Traffic Intensity 198 6.9 Unnormalized Solutions 200 6.10 Limited Queue Capacity 202 6.11 Multiple Servers 204 6.12 Is It Better to Merge or Separate Servers? 207 6.13 Which is Better: More Servers or Faster Servers 208 6.14 Case Study: A Grain Elevator 209 6.15 The M/M/c/c and M/M/1 Models 210 6.16 Finite Sources 212 6.17 The Machine Repairmen Model 214 6.18 Numerical Calculations Using a Spreadsheet 214 6.19 Queue Discipline Variations 217 6.20 Non-Markovian Queues 218 6.21 The M/G/1 Model 219 6.22 Approximate Solutions for Other Models 220 6.23 Conclusion 221 6.24 Recommended Reading 221 7 Networks of Queues 225 7.1 Open Networks of Markovian Queues 226 7.2 An Example Open Network 227 7.3 Extensions 228 7.4 Closed Networks 229 7.5 A Preliminary Example 229 7.6 Relative Arrival Rates 230 7.7 Unnormalized Solutions for Individual Stations 232 7.8 Assembling the Pieces of the Solution 234 7.9 Calculating the Normalization Constant 235 7.10 Performance Measures for Closed Networks 237 7.11 Creating a Closed Model 239 7.12 Case Study 242 7.13 Extensions 247 7.14 Approximate Methods 247 7.15 Recommended Reading 248 8 Using the Transition Diagram to Compute 251 8.1 An Example 252 8.2 Definitions 254 8.3 Steady-State Probabilities 258 8.4 How to Generate All In-trees 259 8.5 Check Your Understanding 262 8.6 Generalization to Other Quantities 263 8.7 Mean First Passage Times 264 8.8 Results for Terminating Processes 265 8.9 How to Simplify the Arithmetic 266 8.10 How to Systematically Generate r-Forests 267 8.11 Summary of Results 267 8.12 How to Remember the Formulas 268 8.13 Advanced Topics 268 8.14 Recommended Reading 269 Appendix 1 271 Appendix 2 278 Index 300

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Book SynopsisThis book offers an innovative introduction to social research. The book explores all stages of the research process and it features both quantitative and qualitative methods. Research design topics include sampling techniques, choosing a research design, and determining research question that inform public opinion and direct future studies. Throughout the book, the authors provide vivid and engaging examples that reinforce the reading and understanding of social science research. Your Turn boxes contain activities that allow students to practice research skills, such as sampling, naturalistic observation, survey collection, coding, analysis, and report writing.Table of ContentsAbout the Authors. Preface. Introduction. CHAPTER 1: UNDERSTANDING RESEARCH. The Research Process. Types of Research. Research Proposals. Research Ethics. Getting Acquainted with SPSS. Summary. Key Terms. CHAPTER 2: THE WHO, HOW, AND WHY OF RESEARCH. Who: Selecting a Sample. How: Selecting a Research Strategy. Why: Doing Research That Makes a Difference. Summary. Key Terms. CHAPTER 3: QUANTITATIVE RESEARCH: MEASUREMENT AND DATA COLLECTION. Measurement: Turning Abstractions into Variables. Characteristics of Good Measures. Collecting Data. Summary. Key Terms. CHAPTER 4: QUANTITATIVE RESEARCH: DESCRIPTIVE AND CORRELATIONAL DESIGNS. Basic Concepts. Causation and Prediction. Data Gathering. Data Analysis. Summary. Key Terms. CHAPTER 5: QUANTITATIVE RESEARCH: BASIC EXPERIMENTAL DESIGNS. Experimental Validity. Types of Variables. Characteristics of Experiments. Types of Experimental Designs. Data Analysis. Summary. Key Terms. CHAPTER 6: QUANTITATIVE RESEARCH: ADVANCED EXPERIMENTAL DESIGNS. Basic Concepts. Repeated-Measures Designs. Complex Designs. Quasi-Experimental Designs. Data Analysis. Summary. Key Terms. CHAPTER 7: WHAT IS QUALITATIVE RESEARCH? Telling a Story . . . Qualitatively. Two Worldviews on Research: Reality and Knowledge. Comparison of Quantitative and Qualitative Research. Critique of Quantitative Research. Crisis of Representation. Summary. Key Terms. CHAPTER 8: PLANNING YOUR QUALITATIVE STUDY: DESIGN, SAMPLING, AND DATA ANALYSIS. Designing Qualitative Research. Summary. Key Terms. CHAPTER 9: QUALITATIVE RESEARCH METHODS: ETHNOGRAPHY, PHENOMENOLOGY, CASE STUDY, TEXTUAL ANALYSIS, AND APPLIED RESEARCH. Ethnography. Phenomenology. Case Study. Textual Analysis. Applied Research Methods: Action and Evaluation Research. Summary. Key Terms. CHAPTER 10: QUALITATIVE RESEARCH TOOLS: INTERVIEWING, FOCUS GROUPS, AND OBSERVATION. The First Tool: Defi ning the Context. Qualitative Research Tools: How to Collect Data. Summary. Key Terms. CHAPTER 11: PRESENTING YOUR RESEARCH FINDINGS. Presenting Your Research with a Poster. Presenting Your Research in an Oral Presentation. Presenting Your Research in a Paper. Reducing Bias in Research Reporting. Summary. Key Terms. References. Appendix A: A Sample Manuscript from a Quantitative Study. Appendix B: A Sample Manuscript from a Qualitative Study. Glossary. Index.

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Book SynopsisThis new edition continues to provide basic, comprehensive coverage of key methods in categorical data analysis with multiple variables. Maintaining the same nontechnical, user-friendly approach, coverage has been added to the Second Edition to take the topic of categorical data analysis into a more applied direction.Trade Review"The book works out, in painstaking detail, many analytical and numerical examples." (Journal of Biopharmaceutical Statistics, 2010)Table of ContentsPreface. Preface to the First Edition. 1 Introduction. 1.1 A Prototype Example. 1.2 A Review of Likelihood-Based Methods. 1.3 Interval Estimation for a Proportion. 1.4 About This Book. 2 Contingency Tables. 2.1 Some Sampling Models for Categorical Data. 2.1.1 The Binomial and Multinomial Distributions. 2.1.2 The Hypergeometric Distributions. 2.2 Inferences for 2-by-2 Contingency Tables. 2.2.1 Comparison of Two Proportions. 2.2.2 Tests for Independence. 2.2.3 Fisher’s Exact Test. 2.2.4 Relative Risk and Odds Ratio. 2.2.5 Etiologic Fraction. 2.2.6 Crossover Designs. 2.3 The Mantel–Haenszel Method. 2.4 Inferences for General Two-Way Tables. 2.4.1 Comparison of Several Proportions. 2.4.2 Testing for Independence in Two-Way Tables. 2.4.3 Ordered 2-by-k Contingency Tables. 2.5 Sample Size Determination. Exercises. 3 Loglinear Models. 3.1 Loglinear Models for Two-Way Tables. 3.2 Loglinear Models for Three-Way Tables. 3.2.1 The Models of Independence. 3.2.2 Relationships Between Terms and Hierarchy of Models. 3.2.3 Testing a Specific Model. 3.2.4 Searching for the Best Model. 3.2.5 Collapsing Tables. 3.3 Loglinear Models for Higher-Dimensional Tables. 3.3.1 Testing a Specific Model. 3.3.2 Searching for the Best Model. 3.3.3 Measures of Association with an Effect Modification. 3.3.4 Searching for a Model with a Dependent Variable. Exercises. 4 Logistic Regression Models. 4.1 Modeling a Probability. 4.1.1 The Logarithmic Transformation. 4.1.2 The Probit Transformation. 4.1.3 The Logistic Transformation. 4.2 Simple Regression Analysis. 4.2.1 The Logistic Regression Model. 4.2.2 Measure of Association. 4.2.3 Tests of Association. 4.2.4 Use of the Logistic Model for Different Designs. 4.2.5 Overdispersion. 4.3 Multiple Regression Analysis. 4.3.1 Logistic Regression Model with Several Covariates. 4.3.2 Effect Modifications. 4.3.3 Polynomial Regression. 4.3.4 Testing Hypotheses in Multiple Logistic Regression. 4.3.5 Measures of Goodness-of-Fit. 4.4 Ordinal Logistic Model. 4.5 Quantal Bioassays. 4.5.1 Types of Bioassays. 4.5.2 Quantal Response Bioassays. Exercises. 5 Methods for Matched Data. 5.1 Measuring Agreement. 5.2 Pair-Matched Case-Control Studies. 5.2.1 The Model. 5.2.2 The Analysis. 5.2.3 The Case of Small Samples. 5.2.4 Risk Factors with Multiple Categories and Ordinal Risks. 5.3 Multiple Matching. 5.3.1 The Conditional Approach. 5.3.2 Estimation of the Odds Ratio. 5.3.3 Testing for Exposure Effect. 5.3.4 Testing for Homogeneity. 5.4 Conditional Logistic Regression. 5.4.1 Simple Regression Analysis. 5.4.2 Multiple Regression Analysis. Exercises. 6 Methods for Count Data. 6.1 The Poisson Distribution. 6.2 Testing Goodness-of-Fit. 6.3 The Poisson Regression Model. 6.3.1 Simple Regression Analysis. 6.3.2 Multiple Regression Analysis. 6.3.3 Overdispersion. 6.3.4 Stepwise Regression. Exercise. 7 Categorical Data and Translational Research. 7.1 Types of Clinical Studies. 7.2 From Bioassays to Translational Research. 7.2.1 Analysis of In Vitro Experiments. 7.2.2 Design and Analysis of Experiments for Combination Therapy. 7.3 Phase I Clinical Trials. 7.3.1 Standard Design. 7.3.2 Fast Track Design. 7.3.3 Continual Reassessment Method. 7.4 Phase II Clinical Trials. 7.4.1 Sample Size Determination for Phase II Clinical Trials. 7.4.2 Phase II Clinical Trial Designs for Selection. 7.4.3 Two-Stage Phase II Design. 7.4.4 Toxicity Monitoring in Phase II Trials. 7.4.5 Multiple Decisions. Exercises. 8 Categorical Data and Diagnostic Medicine. 8.1 Some Examples. 8.2 The Diagnosis Process. 8.2.1 The Developmental Stage. 8.2.2 The Applicational Stage. 8.3 Some Statistical Issues. 8.3.1 The Response Rate. 8.3.2 The Issue of Population Random Testing. 8.3.3 Screenable Disease Prevalence. 8.3.4 An Index for Diagnostic Competence. 8.4 Prevalence Surveys. 8.4.1 Known Sensitivity and Specificity. 8.4.2 Unknown Sensitivity and Specificity. 8.4.3 Prevalence Survey with a New Test. 8.5 The Receiver Operating Characteristic Curve. 8.5.1 The ROC Function and ROC Curve. 8.5.2 Some Parametric ROC Models. 8.5.3 Estimation of the ROC Curve. 8.5.4 Index for Diagnostic Accuracy. 8.5.5 Estimation of Area Under ROC Curve. 8.6 The Optimization Problem. 8.6.1 Basic Criterion: Youden’s Index. 8.6.2 Possible Solutions. 8.7 Statistical Considerations. 8.7.1 Evaluation of Screening Tests. 8.7.2 Comparison of Screening Tests. 8.7.3 Consideration of Subjects’ Characteristics. Exercises. 9 Transition from Categorical to Survival Data. 9.1 Survival Data. 9.2 Introductory Survival Analysis. 9.2.1 Kaplan–Meier Curve. 9.2.2 Comparison of Survival Distributions. 9.3 Simple Regression and Correlation. 9.3.1 Model and Approach. 9.3.2 Measures of Association. 9.3.3 Tests of Association. 9.4 Multiple Regression and Correlation. 9.4.1 Proportional Hazards Models with Several Covariates. 9.4.2 Testing Hypotheses in Multiple Regression. 9.4.3 Time-Dependent Covariates and Applications. 9.5 Competing Risks. 9.5.1 Redistribution to the Right Method. 9.5.2 Estimation of the Cumulative Incidence. 9.5.3 Brief Discussion of Proportional Hazards Regression. Exercise. Bibliography. Index.

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Book SynopsisAn accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis. The book begins with an outline of basic calculus, including a close examination of problems illustrating links and potential difficulties. Next, a fluid introduction to real analysis is presented, guiding readers through the basic topology of real numbers, limits, integration, and a series of functions in natural progression. The book moves on to analysis with more rigorous investigations, and the topology of the line is presented along with a discussion of limits and Table of ContentsPreface. Acknowledgments. 1 Elementary Calculus. 1.1 Preliminary Concepts. 1.2 Limits and Continuity. 1.3 Differentiation. 1.4 Integration. 1.5 Sequences and Series of Constants. 1.6 Power Series and Taylor Series. Summary. Exercises. Interlude: Fermat, Descartes, and theTangent Problem. 2 Introduction to Real Analysis. 2.1 Basic Topology of the Real Numbers. 2.2 Limits and Continuity. 2.3 Differentiation. 2.4 Riemann and Riemann-Stieltjes Integration. 2.5 Sequences, Series, and Convergence Tests. 2.6 Pointwise and Uniform Convergence. Summary. Exercises. Interlude: Euler and the "Basel Problem". 3 A Brief Introduction to Lebesgue Theory. 3.1 Lebesgue Measure and Measurable Sets. 3.2 The Lebesgue Integral. 3.3 Measure, Integral, and Convergence. 3.4 Littlewood’s Three Principles. Summary. Exercises. Interlude: The Set of Rational Numbers isVery Large andVery Small. 4 Special Topics. 4.1 Modeling with Logistic Functions—Numerical Derivatives. 4.2 Numerical Quadrature. 4.3 Fourier Series. 4.4 Special Functions—The Gamma Function. 4.5 Calculus Without Limits: Differential Algebra. Summary. Exercises. Appendix A: Definitions and Theorems of Elementary Real Analysis. A.1 Limits. A.2 Continuity. A.3 The Derivative. A.4 Riemann Integration. A.5 Riemann-Stieltjes Integration. A.6 Sequences and Series of Constants. A.7 Sequences and Series of Functions. Appendix B: A Very Brief Calculus Chronology. Appendix C: Projects in Real Analysis. C.1 Historical Writing Projects. C.2 Induction Proofs: Summations, Inequalities, and Divisibility. C.3 Series Rearrangements. C.4 Newton and the Binomial Theorem. C.5 Symmetric Sums of Logarithms. C.6 Logical Equivalence: Completeness of the Real Numbers. C.7 Vitali’s Nonmeasurable Set. C.8 Sources for Real Analysis Projects. C.9 Sources for Projects for Calculus Students. Bibliography. Index.

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Book SynopsisOverall, this is an appealing work for students and professionals, and is certain to remain as one of the key works in natural resource analysis. Mathematical Reviews Biological renewable resources, essential to the survival of mankind, are increasingly overexploited by individuals and corporations that often sacrifice long-term economic health and sustainability for short-term gains. Mathematical Bioeconomics: The Mathematics of Conservation, Third Edition analyzes the economic forces underlying these misuses of renewable resources and discusses more effective methods of resource management. Promoting a complete understanding of general principles, the book allows readers to discover how rigorous mathematical models that incorporate both economic and biological factors should replace intuitive arguments for conservation and sustainability. This Third Edition continues to combine methodologies from the fields of economics, biology, and matheTable of ContentsPreface. Acknowledgments. 1 A Generic Bioeconomic Model. 1.1 What is Conservation? 1.2 What is a Model? 1.3 A Dynamic Resource-Harvesting Model. 1.4 A Bioeconomic Model. 1.5 A Dynamic Optimization Model. 1.6 A Model of Individual Behavior. 1.7 Individual Vessel Quotas. 1.8 The Veil of Uncertainty. 1.9 Other Resources. 2 Dynamic Optimization. 2.1 Constrained Optimization. 2.2 Optimal Control Theory in One Dimension. 2.3 Nonlinear Control Problems. 2.4 Discrete-time Optimal Control. 2.5 Appendix. 3 Basic Economic Concepts. 3.1 Interest and Discounting. 3.2 Supply and Demand. 3.3 Demand-limited Bionomic Equilibrium. 3.4 Optimal Harvesting Strategies. 3.5 External Costs. 3.6 Competition, Cooperation, and the Theory of Games. 3.7 The Economics of Uncertainty. 4 Investing in Harvesting Capacity. 4.1 Optimal Harvesting Capacity. 4.2 Investment Decisions under Competition. 4.3 Eliminating Excess Capacity. 4.4 Appendix: Optimal Investment. 5 Regulation of Renewable Resource Harvesting. 5.1 The Consequences of Unregulated Resource Harvesting. 5.2 Methods of Regulating Resource Harvesting. 5.3 Shadow Prices, Taxes and Tradeable Quotas. 5.4 Regulation without Taxes or Tradeable Quotas. 6 Growth and Aging. 6.1 Forestry Models. 6.2 Fisheries: The Cohort Model. 6.3 Multicohort Fisheries. 7 Resource Management under Uncertainty. 7.1 Process and Observational Uncertainty. 7.2 Understanding Uncertainty. 7.3 Process Uncertainty. 7.4 An Introduction to Decision Analysis. 7.5 Economic Uncertainties. 7.6 Appendix. 8 Disaggregated Resource Models. 8.1 Source-sink Models. 8.2 Predator-prey Models. 8.3 Mixed-species Harvesting. 9 Synopsis. Problem Solutions. References. Index.

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Book SynopsisAn accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. SubsequTrade Review"Thoroughly classroom-tested, Applied integer programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels." (Mathematical Reviews, 2011) "The book is intended as a textbook for an application oriented course for senior undergraduate or postgraduate students, mainly with an engineering, business school, or applied mathematics background. Each chapter comes with several exercises, solutions of which are provided in an appendix. Many figures illustrate the flow of algorithms and other concepts." (Zentralblatt MATH, 2010)Table of ContentsPREFACE. PART I MODELING. 1 Introduction. 1.1 Integer Programming. 1.2 Standard Versus Nonstandard Forms. 1.3 Combinatorial Optimization Problems. 1.4 Successful Integer Programming Applications. 1.5 Text Organization and Chapter Preview. 1.6 Notes. 1.7 Exercises. 2 Modeling and Models. 2.1 Assumptions on Mixed Integer Programs. 2.2 Modeling Process. 2.3 Project Selection Problems. 2.4 Production Planning Problems. 2.5 Workforce/Staff Scheduling Problems. 2.6 Fixed-Charge Transportation and Distribution Problems. 2.7 Multicommodity Network Flow Problem. 2.8 Network Optimization Problems with Side Constraints. 2.9 Supply Chain Planning Problems. 2.10 Notes. 2.11 Exercises. 3 Transformation Using 0–1 Variables. 3.1 Transform Logical (Boolean) Expressions. 3.2 Transform Nonbinary to 0–1 Variable. 3.3 Transform Piecewise Linear Functions. 3.4 Transform 0–1 Polynomial Functions. 3.5 Transform Functions with Products of Binary and Continuous Variables: Bundle Pricing Problem. 3.6 Transform Nonsimultaneous Constraints. 3.7 Notes. 3.8 Exercises. 4 Better Formulation by Preprocessing. 4.1 Better Formulation. 4.2 Automatic Problem Preprocessing. 4.3 Tightening Bounds on Variables. 4.4 Preprocessing Pure 0–1 Integer Programs. 4.5 Decomposing a Problem into Independent Subproblems. 4.6 Scaling the Coefficient Matrix. 4.7 Notes. 4.8 Exercises. 5 Modeling Combinatorial Optimization Problems I. 5.1 Introduction. 5.2 Set Covering and Set Partitioning. 5.3 Matching Problem. 5.4 Cutting Stock Problem. 5.5 Comparisons for Above Problems. 5.6 Computational Complexity of COP. 5.7 Notes. 5.8 Exercises. 6 Modeling Combinatorial Optimization Problems II. 6.1 Importance of Traveling Salesman Problem. 6.2 Transformations to Traveling Salesman Problem. 6.3 Applications of TSP. 6.4 Formulating Asymmetric TSP. 6.5 Formulating Symmetric TSP. 6.6 Notes. 6.7 Exercises. PART II REVIEW OF LINEAR PROGRAMMING AND NETWORK FLOWS. 7 Linear Programming—Fundamentals. 7.1 Review of Basic Linear Algebra. 7.2 Uses of Elementary Row Operations. 7.3 The Dual Linear Program. 7.4 Relationships Between Primal and Dual Solutions. 7.5 Notes. 7.6 Exercises. 8 Linear Programming: Geometric Concepts. 8.1 Geometric Solution. 8.2 Convex Sets. 8.3 Describing a Bounded Polyhedron. 8.4 Describing Unbounded Polyhedron. 8.5 Faces, Facets, and Dimension of a Polyhedron. 8.6 Describing a Polyhedron by Facets. 8.7 Correspondence Between Algebraic and Geometric Terms. 8.8 Notes. 8.9 Exercises. 9 Linear Programming: Solution Methods. 9.1 Linear Programs in Canonical Form. 9.2 Basic Feasible Solutions and Reduced Costs. 9.3 The Simplex Method. 9.4 Interpreting the Simplex Tableau. 9.5 Geometric Interpretation of the Simplex Method. 9.6 The Simplex Method for Upper Bounded Variables. 9.7 The Dual Simplex Method. 9.8 The Revised Simplex Method. 9.9 Notes. 9.10 Exercises. 10 Network Optimization Problems and Solutions. 10.1 Network Fundamentals. 10.2 A Class of Easy Network Problems. 10.3 Totally Unimodular Matrices. 10.4 The Network Simplex Method. 10.5 Solution via LINGO. 10.6 Notes. 10.7 Exercises. PART III SOLUTIONS. 11 Classical Solution Approaches. 11.1 Branch-and-Bound Approach. 11.2 Cutting Plane Approach. 11.3 Group Theoretic Approach. 11.4 Geometric Concepts. 11.5 Notes. 11.6 Exercises. 12 Branch-and-Cut Approach. 12.1 Introduction. 12.2 Valid Inequalities. 12.3 Cut Generating Techniques. 12.4 Cuts Generated from Sets Involving Pure Integer Variables. 12.5 Cuts Generated from Sets Involving Mixed Integer Variables. 12.6 Cuts Generated from 0–1 Knapsack Sets. 12.7 Cuts Generated from Sets Containing 0–1 Coefficients and 0–1 Variables. 12.8 Cuts Generated from Sets with Special Structures. 12.9 Notes. 12.10 Exercises. 13 Branch-and-Price Approach. 13.1 Concepts of Branch-and-Price. 13.2 Dantzig–Wolfe Decomposition. 13.3 Generalized Assignment Problem. 13.4 GAP Example. 13.5 Other Application Areas. 13.6 Notes. 13.7 Exercises. 14 Solution via Heuristics, Relaxations, and Partitioning. 14.1 Introduction. 14.2 Overall Solution Strategy. 14.3 Primal Solution via Heuristics. 14.4 Dual Solution via Relaxation. 14.5 Lagrangian Dual. 14.6 Primal–Dual Solution via Benders’ Partitioning. 14.7 Notes. 14.8 Exercises. 15 Solutions with Commercial Software. 15.1 Introduction. 15.2 Typical IP Software Components. 15.3 The AMPL Modeling Language. 15.4 LINGO Modeling Language. 15.5 MPL Modeling Language. REFERENCES. APPENDIX: ANSWERS TO SELECTED EXERCISES. INDEX.

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Book SynopsisEmphasizing the statistical aspects of survey methods, Applied Survey Methods describes the complete survey process, from design to publication. This valuable book provides an overview of the theory as well as the practical applications of survey research methods, such as item and unit non-response and the associated treatment.Table of ContentsPreface. 1. The Survey Process. 1.1. About Surveys. 1.2. A Survey, Step-by-Step. 1.3. Some History of Survey Research. 1.4. This Book. 1.5. Samplonia. Exercises. 2. Basic Concepts. 2.1. The Survey Objectives. 2.2. The Target Population. 2.3. The Sampling Frame. 2.4. Sampling. 2.5. Estimation. Exercises. 3. Questionnaire Design. 3.1. The Questionnaire. 3.2. Factual and Nonfactual Questions. 3.3. The Question Text. 3.4. Answer Types. 3.5. Question Order. 3.6. Questionnaire Testing. Exercises. 4. Single Sampling Designs. 4.1. Simple Random Sampling. 4.2. Systematic Sampling. 4.3. Unequal Probability Sampling. 4.4. Systematic Sampling with Unequal Probabilities. Exercises. 5. Composite Sampling Designs. 5.1. Stratified Sampling. 5.2. Cluster Sampling. 5.3. Two-Stage Sampling. 5.4. Two-Dimensional Sampling. Exercises. 6. Estimators. 6.1. Use of Auxiliary Information. 6.2. A Descriptive Model. 6.3. The Direct Estimator. 6.4. The Ratio Estimator. 6.5. The Regression Estimator. 6.6. The Poststratification Estimator. Exercises. 7. Data Collection. 7.1. Traditional Data Collection. 7.2. Computer-Assisted Interviewing. 7.3. Mixed-Mode Data Collection. 7.4. Electronic Questionnaires. 7.5. Data Collection with Blaise. Exercises. 8. The Quality of the Results. 8.1. Errors in Surveys. 8.2. Detection and Correction of Errors. 8.3. Imputation Techniques. 8.4. Data Editing Strategies. Exercises. 9. The Nonresponse Problem. 9.1. Nonresponse. 9.2. Response Rates. 9.3. Models for Nonresponse. 9.4. Analysis of Nonresponse. 9.5. Nonresponse Correction Techniques. Exercises. 10. Weighting Adjustment. 10.1. Introduction. 10.2. Poststratification. 10.3. Linear Weighting. 10.4. Multiplicative Weighting. 10.5. Calibration Estimation. 10.6. Other Weighting Issues. 10.7. Use of Propensity Scores. 10.8. A Practical Example. Exercises. 11. Online Surveys. 11.1. The Popularity of Online Research. 11.2. Errors in Online Surveys. 11.3. The Theoretical Framework. 11.4. Correction by Adjustment Weighting. 11.5. Correction Using a Reference Survey. 11.6. Sampling the Non-Internet Population. 11.7. Propensity Weighting. 11.8. Simulating the Effects of Undercoverage. 11.9. Simulating the Effects of Self-Selection. 11.10. About the Use of Online Surveys. Exercises. 12. Analysis and Publication. 12.1. About Data Analysis. 12.2. The Analysis of Dirty Data. 12.3. Preparing a Survey Report. 12.4. Use of Graphs. Exercises. 13. Statistical Disclosure Control. 13.1. Introduction. 13.2. The Basic Disclosure Problem. 13.3. The Concept of Uniqueness. 13.4. Disclosure Scenarios. 13.5. Models for the Disclosure Risk. 13.6. Practical Disclosure Protection. Exercises. References. Index.

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Book SynopsisThis book is an accessible introduction to quantitative data analysis, concentrating on the key issues facing those new to research, such as how to decide which statistical procedure is suitable, and how to interpret the subsequent results.Table of ContentsTables, Figures, Exhibits, and Boxes xi Preface xxiii The Author xxvii Introduction xxix 1 CROSS-TABULATIONS 1 What This Chapter Is About 1 Introduction to the Book via a Concrete Example 2 Cross-Tabulations 8 What This Chapter Has Shown 19 2 MORE ON TABLES 21 What This Chapter Is About 21 The Logic of Elaboration 22 Suppressor Variables 25 Additive and Interaction Effects 26 Direct Standardization 28 A Final Note on Statistical Controls Versus Experiments 43 What This Chapter Has Shown 45 3 STILL MORE ON TABLES 47 What This Chapter Is About 47 Reorganizing Tables to Extract New Information 48 When to Percentage a Table "Backwards" 50 Cross-Tabulations in Which the Dependent Variable Is Represented by a Mean 52 Index of Dissimilarity 58 Writing About Cross-Tabulations 61 What This Chapter Has Shown 63 4 ON THE MANIPULATION OF DATA BY COMPUTER 65 What This Chapter Is About 65 Introduction 66 How Data Files Are Organized 67 Transforming Data 72 What This Chapter Has Shown 80 Appendix 4.A Doing Analysis Using Stata 80 Tips on Doing Analysis Using Stata 80 Some Particularly Useful Stata 10.0 Commands 84 5 INTRODUCTION TO CORRELATION AND REGRESSION (ORDINARY LEAST SQUARES) 87 What This Chapter Is About 87 Introduction 88 Quantifying the Size of a Relationship: Regression Analysis 89 Assessing the Strength of a Relationship: Correlation Analysis 91 The Relationship Between Correlation and Regression Coeffi cients 94 Factors Affecting the Size of Correlation (and Regression) Coeffi cients 94 Correlation Ratios 99 What This Chapter Has Shown 102 6 INTRODUCTION TO MULTIPLE CORRELATION AND REGRESSION (ORDINARY LEAST SQUARES) 103 What This Chapter Is About 103 Introduction 104 A Worked Example: The Determinants of Literacy in China 113 Dummy Variables 120 A Strategy for Comparisons Across Groups 124 A Bayesian Alternative for Comparing Models 133 Independent Validation 135 What This Chapter Has Shown 136 7 MULTIPLE REGRESSION TRICKS: TECHNIQUES FOR HANDLING SPECIAL ANALYTIC PROBLEMS 139 What This Chapter Is About 139 Nonlinear Transformations 140 Testing the Equality of Coeffi cients 147 Trend Analysis: Testing the Assumption of Linearity 149 Linear Splines 152 Expressing Coeffi cients as Deviations from the Grand Mean (Multiple Classifi cation Analysis) 164 Other Ways of Representing Dummy Variables 166 Decomposing the Difference Between Two Means 172 What This Chapter Has Shown 179 8 MULTIPLE IMPUTATION OF MISSING DATA 181 What This Chapter Is About 181 Introduction 182 A Worked Example: The Effect of Cultural Capital on Educational Attainment in Russia 187 What This Chapter Has Shown 194 9 SAMPLE DESIGN AND SURVEY ESTIMATION 195 What This Chapter Is About 195 Survey Samples 196 Conclusion 223 What This Chapter Has Shown 224 10 REGRESSION DIAGNOSTICS 225 What This Chapter Is About 225 Introduction 226 A Worked Example: Societal Differences in Status Attainment 229 Robust Regression 237 Bootstrapping and Standard Errors 238 What This Chapter Has Shown 240 11 SCALE CONSTRUCTION 241 What This Chapter Is About 241 Introduction 242 Validity 242 Reliability 243 Scale Construction 246 Errors-in-Variables Regression 258 What This Chapter Has Shown 261 12 LOG-LINEAR ANALYSIS 263 What This Chapter Is About 263 Introduction 264 Choosing a Preferred Model 265 Parsimonious Models 277 A Bibliographic Note 294 What This Chapter Has Shown 295 Appendix 12.A Derivation of the Effect Parameters 295 Appendix 12.B Introduction to Maximum Likelihood Estimation 297 Mean of a Normal Distribution 298 Log-Linear Parameters 299 13 BINOMIAL LOGISTIC REGRESSION 301 What This Chapter Is About 301 Introduction 302 Relation to Log-Linear Analysis 303 A Worked Logistic Regression Example: Predicting Prevalence of Armed Threats 304 A Second Worked Example: Schooling Progression Ratios in Japan 314 A Third Worked Example (Discrete-Time Hazard-Rate Models): Age at First Marriage 318 A Fourth Worked Example (Case-Control Models): Who Was Appointed to a Nomenklatura Position in Russia? 327 What This Chapter Has Shown 329 Appendix 13.A Some Algebra for Logs and Exponents 330 Appendix 13.B Introduction to Probit Analysis 330 14 MULTINOMIAL AND ORDINAL LOGISTIC REGRESSION AND TOBIT REGRESSION 335 What This Chapter Is About 335 Multinomial Logit Analysis 336 Ordinal Logistic Regression 342 Tobit Regression (and Allied Procedures) for Censored Dependent Variables 353 Other Models for the Analysis of Limited Dependent Variables 360 What This Chapter Has Shown 361 15 IMPROVING CAUSAL INFERENCE: FIXED EFFECTS AND RANDOM EFFECTS MODELING 363 What This Chapter Is About 363 Introduction 364 Fixed Effects Models for Continuous Variables 365 Random Effects Models for Continuous Variables 371 A Worked Example: The Determinants of Income in China 372 Fixed Effects Models for Binary Outcomes 375 A Bibliographic Note 380 What This Chapter Has Shown 380 16 FINAL THOUGHTS AND FUTURE DIRECTIONS: RESEARCH DESIGN AND INTERPRETATION ISSUES 381 What this Chapter is About 381 Research Design Issues 382 The Importance of Probability Sampling 397 A Final Note: Good Professional Practice 400 What This Chapter Has Shown 405 Appendix A: Data Descriptions and Download Locations for the Data Used in This Book 407 Appendix B: Survey Estimation with the General Social Survey 411 References 417 Index 431

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Book SynopsisA modern and comprehensive treatment of tolerance intervals and regions The topic of tolerance intervals and tolerance regions has undergone significant growth during recent years, with applications arising in various areas such as quality control, industry, and environmental monitoring. Statistical Tolerance Regions presents the theoretical development of tolerance intervals and tolerance regions through computational algorithms and the illustration of numerous practical uses and examples. This is the first book of its kind to successfully balance theory and practice, providing a state-of-the-art treatment on tolerance intervals and tolerance regions. The book begins with the key definitions, concepts, and technical results that are essential for deriving tolerance intervals and tolerance regions. Subsequent chapters provide in-depth coverage of key topics including: Univariate normal distribution Non-normal distributions UnivariTable of ContentsList of Tables. Preface. 1 Preliminaries. 1.1 Introduction. 1.2 Some Technical Results. 1.3 The Modified Large Sample (MLS) Procedure. 1.4 The Generalized P-value and Generalized Confidence Interval. 1.5 Exercises. 2 Univariate Normal Distribution. 2.1 Introduction. 2.2 One-Sided Tolerance Limits for a Normal Population. 2.3 Two-Sided Tolerance Intervals. 2.4 Tolerance Limits for X1 - X2. 2.5 Simultaneous Tolerance Limits for Normal Populations. 2.6 Exercises. 3 Univariate Linear Regression Model. 3.1 Notations and Preliminaries. 3.2 One-Sided Tolerance Intervals and Simultaneous Tolerance Intervals. 3.3 Two-sided Tolerance Intervals and Simultaneous Tolerance Intervals. 3.4 The Calibration Problem. 3.5 Exercises. 4 The One-Way Random Model with Balanced Data. 4.1 Notations and Preliminaries. 4.2 Two Examples. 4.3 One-Sided Tolerance Limits for N(µ, σ²τ + σ²τe). 4.4 One-Sided Tolerance Limits for N(µ, σ²τ¨). 4.5 Two-Sided Tolerance Intervals for N(µ, σ²τ + σ²τe). 4.6 Two-Sided Tolerance Intervals for N(µ, σ²τ¨). 4.7 Exercises. 5 The One-Way Random Model with Unbalanced Data. 5.1 Notations and Preliminaries. 5.2 Two Examples. 5.3 One-Sided Tolerance Limits for N(µ, σ²τ + σ²e). 5.4 One-Sided Tolerance Limits for N(µ, σ²τ). 5.5 Two-Sided Tolerance Intervals. 5.6 Exercises. 6 Some General Mixed Models. 6.1 Notations and Preliminaries. 6.2 Some Examples. 6.3 Tolerance Intervals in a General Setting. 6.4 A General Model with Two Variance Components. 6.5 A One-Way Random Model with Covariates and Unequal Variances. 6.5 Testing Individual Bioequivalence. 6.6 Exercises. 7 Some Non-Normal Distributions. 7.1 Introduction. 7.2 Lognormal Distribution. 7.3 Gamma Distribution. 7.4 Two-Parameter Exponential Distribution. 7.5 Weibull Distribution. 7.6 Exercises. 8 Nonparametric Tolerance Intervals. 8.1 Notations and Preliminaries. 8.2 Order Statistics and Their Distributions. 8.3 One-Sided Tolerance Limits and Exceedance Probabilities. 8.4 Tolerance Intervals. 8.5 Confidence Intervals for Population Quantiles. 8.6 Sample Size Calculation. 8.7 Nonparametric Multivariate Tolerance Regions. 8.8 Exercises. 9 The Multivariate Normal Distribution. 9.1 Introduction. 9.2 Notations and Preliminaries. 9.3 Some Approximate Tolerance Factors. 9.4 Methods Based on Monte Carlo Simulation. 9.5 Simultaneous Tolerance Intervals. 9.6 Tolerance Regions for Some Special Cases. 9.7 Exercises. 10 The Multivariate Linear Regression Model. 10.1 Preliminaries. 10.2 Approximations for the Tolerance Factor. 10.3 Accuracy of the Approximate Tolerance Factors. 10.4 Methods Based on Monte Carlo Simulation. 10.5 Application to the Example. 10.6 Multivariate Calibration. 10.7 Exercises. 11 Bayesian Tolerance Intervals. 11.1 Notations and Preliminaries. 11.2 The Univariate Normal Distribution. 11.3 The One-Way Random Model With Balanced Data. 11.4 Two Examples. 11.5 Exercises. 12 Miscellaneous Topics. 12.1 Introduction. 12.2 β-Expectation Tolerance Regions. 12.3 Tolerance Limits for a Ratio of Normal Random Variables. 12.4 Sample Size Determination. 12.5 Reference Limits and Coverage Intervals. 12.6 Tolerance Intervals for Binomial and Poisson Distributions. 12.7 Tolerance Intervals Based on Censored Samples. 12.8 Exercises. Appendix A: Data Sets. Appendix B: Tables. References. Index.

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Book SynopsisPraise for the First Edition . . . [this book] should be on the shelf of everyone interested in . . . longitudinal data analysis. Journal of the American Statistical Association Features newly developed topics and applications of the analysis of longitudinal data Applied Longitudinal Analysis, Second Edition presents modern methods for analyzing data from longitudinal studies and now features the latest state-of-the-art techniques. The book emphasizes practical, rather than theoretical, aspects of methods for the analysis of diverse types of longitudinal data that can be applied across various fields of study, from the health and medical sciences to the social and behavioral sciences. The authors incorporate their extensive academic and research experience along with various updates that have been made in response to reader feedback. The Second Edition features six newly added chapters that explore topics currently evolving in Trade Review“The text is well-organized and clearly written. It is accessible to researchers with varying levels of statistical expertise, with plenty of data examples that make reading and learning enjoyable. I recommend it to biostatisticians as well as to clinicians and other health researchers who may not have much statistical training . . . Applied Longitudinal Analysisis generally my first recommendation when asked for a valuable resource in the field due to the breadth of topics covered and its practical utility.” (Journal of Biopharmaceutical Statistics, 1 January 2013) “The book also serves as a valuable reference for researchers and professionals in the medical, public health, and pharmaceutical fields, as well as those in social and behavioral sciences who would like to learn more about analysing longitudinal data.” (Zentralblatt MATH, 2012) "This book provides very broad coverage of modern methods for longitudinal data analysis from an applied perspective ... I highly recommend this book to statisticians and quantitative researchers who encounter longitudinal and/or clustered data. In addition, I think the book would be an excellent choice as the primary textbook in an applied longitudinal data course." (Journal of Biopharmaceutical Statistics, 2013) Table of ContentsPreface xvii Preface to First Edition xxi Acknowledgments xxv Part I. Introduction to Longitudinal and Clustered Data 1. Longitudinal and Clustered Data 1 2. Longitudinal Data. Basic Concepts 19 Part II. Linear Models for Longitudinal Continuous Data 3. Overview of Linear Models for Longitudinal Data 49 4. Estimation and Statistical Inference 89 5. Modelling the Mean: Analyzing Response Profiles 105 6. Modelling the Mean: Parametric Curves 143 7. Modelling the Covariance 165 8. Linear Mixed Effect Models 189 9. Fixed Effects versus Random Effects Models 241 10. Residual Analyses and Diagnostics 265 Part III. Generalized Linear Models for Longitudinal Data 11. Review of Generalized Linear Models 291 12. Marginal Models: Introduction and Overview 341 13. Marginal Models: Generalized Estimating Equations (GEE) 353 14. Generalized Linear Mixed Effects Models 395 15. Generalized Linear Mixed Effects Models: Approximate Methods of Estimation 441 16. Contrasting Marginal and Mixed Effects Models 473 Part IV. Missing Data and Dropout 17. Missing Data and Dropout: Overview of Concepts and Methods 489 18. Missing Data and Dropout: Multiple Imputation and Weighting Methods 515 Part V. Advanced Topics for Longitudinal and Clustered Data 19. Smoothing Longitudinal Data: Semiparametric Regression Models 553 20. Sample Size and Power 581 21. Repeated Measures and Related Designs 611 22. Multilevel Models 627 Appendix A. Gentle Introduction to Vectors and Matrices 655 Appendix B. Properties of Expectations and Variance 665 Appendix C. Critical Points for a 50:50 Mixture of Chi-Squared Distributions 669 References 671 Index 695

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Book SynopsisThis title develops introductory topics in probability and statistics with particular emphasis on concepts that arise in computer science. It starts with the basic definitions of probability distributions and random variables and elaborates their properties and applications.Trade Review"Undoubtedly, this is an excellent and well-organized book." (Computing Reviews, August 27, 2008)Table of ContentsPreface. 1. Combinatorics and Probability. 1.1 Combinatorics. 1.2 Summations. 1.3 Probability spaces and random variables. 1.4 Conditional probability. 1.5 Joint distributions. 1.6 Summary. 2. Discrete Distributions. 2.1 The Bernoulli and binomial distributions. 2.2 Power series. 2.3 Geometric and negative binomial forms. 2.4 The Poisson distribution. 2.5 The hypergeometric distribution. 2.6 Summary. 3. Simulation. 3.1 Random number generation. 3.2 Inverse transforms and rejection filters. 3.3 Client-server systems. 3.4 Markov chains. 3.5 Summary. 4. Discrete Decision Theory. 4.1 Decision methods without samples. 4.2 Statistics and their properties. 4.3 Sufficient statistics. 4.4 Hypothesis testing. 4.5 Summary. 5. Real Line-Probability. 5.1 One-dimensional real distributions. 5.2 Joint random variables. 5.3 Differentiable distributions. 5.4 Summary. 6. Continuous Distributions. 6.1 The normal distributions. 6.2 Limit theorems. 6.3 Gamma and beta distributions. 6.4 The X2 and related distributions. 6.5 Computer simulations. 6.6 Summary. 7. Parameter Estimation. 7.1 Bias, consistency, and efficiency. 7.2 Normal inference. 7.3 Sums of squares. 7.4 Analysis of variance. 7.5 Linear regression. 7.6 Summary. A. Analytical Tools. B. Statistical Tables. Bibliography. Index.

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Book SynopsisCovering classification and regression, Statistical Learning is the first of its kind to use visualization techniques to identify, test, and analyze classifiers for their most accurate exploration of data.Trade Review“Altogether, the book provides a very nice overview of nonparametric and semiparametric regression methods with interesting applications to problems in quantitative finance.” (Mathematical Reviews, 1 October 2015) Table of ContentsPreface xvii Introduction xix I.1 Estimation of Functionals of Conditional Distributions xx I.2 Quantitative Finance xxi I.3 Visualization xxi I.4 Literature xxiii PART I METHODS OF REGRESSION AND CLASSIFICATION 1 Overview of Regression and Classification 3 1.1 Regression 3 1.2 Discrete Response Variable 29 1.3 Parametric Family Regression 33 1.4 Classification 37 1.5 Applications in Quantitative Finance 42 1.6 Data Examples 52 1.7 Data Transformations 53 1.8 Central Limit Theorems 58 1.9 Measuring the Performance of Estimators 61 1.10 Confidence Sets 73 1.11 Testing 75 2 Linear Methods and Extensions 77 2.1 Linear Regression 78 2.2 Varying Coefficient Linear Regression 97 2.3 Generalized Linear and Related Models 102 2.4 Series Estimators 107 2.5 Conditional Variance and ARCH models 111 2.6 Applications in Volatility and Quantile Estimation 115 2.7 Linear Classifiers 124 3 Kernel Methods and Extensions 127 3.1 Regressogram 129 3.2 Kernel Estimator 130 3.3 Nearest Neighborhood Estimator 147 3.4 Classification with Local Averaging 148 3.5 Median Smoothing 151 3.6 Conditional Density Estimators 152 3.7 Conditional Distribution Function Estimation 158 3.8 Conditional Quantile Estimation 160 3.9 Conditional Variance Estimation 162 3.10 Conditional Covariance Estimation 176 3.11 Applications in Risk Management 181 3.12 Applications in Portfolio Selection 205 4 Semiparametric and Structural Models 229 4.1 Single Index Model 230 4.2 Additive Model 234 4.3 Other Semiparametric Models 237 5 Empirical Risk Minimization 241 5.1 Empirical Risk 243 5.2 Local Empirical Risk 247 5.3 Support Vector Machines 257 5.4 Stagewise Methods 259 5.5 Adaptive Regressograms 264 PART II VISUALIZATION 6 Visualization of Data 277 6.1 Scatter Plots 278 6.2 Histogram and Kernel Density Estimator 282 6.3 Dimension Reduction 284 6.4 Observations as Objects 288 7 Visualization of Functions 295 7.1 Slices 296 7.2 Partial Dependence Functions 296 7.3 Reconstruction of Sets 299 7.4 Level Set Trees 303 7.5 Unimodal Densities 326 7.5.1 Probability Content of Level Sets 327 7.5.2 Set Visualization 328 Appendix A: R Tutorial 329 A.1 Data Visualization 329 A.2 Linear Regression 331 A.3 Kernel Regression 332 A.4 Local Linear Regression 341 A.5 Additive Models: Backfitting 344 A.6 Single Index Regression 345 A.7 Forward Stagewise Modeling 347 A.8 Quantile Regression 349 References 351 Author Index 361 Topic Index 365

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Book SynopsisProvides an in-depth treatment of ANOVA and ANCOVA techniques from a linear model perspective ANOVA and ANCOVA: A GLM Approach provides a contemporary look at the general linear model (GLM) approach to the analysis of variance (ANOVA) of one- and two-factor psychological experiments. With its organized and comprehensive presentation, the book successfully guides readers through conventional statistical concepts and how to interpret them in GLM terms, treating the main single- and multi-factor designs as they relate to ANOVA and ANCOVA. The book begins with a brief history of the separate development of ANOVA and regression analyses, and then goes on to demonstrate how both analyses are incorporated into the understanding of GLMs. This new edition now explains specific and multiple comparisons of experimental conditions before and after the Omnibus ANOVA, and describes the estimation of effect sizes and power analyses leading to the determination of approTable of ContentsAcknowledgments. CHAPTER 1 AN INTRODUCTION TO GENERAL LINEAR MODELS: REGRESSION, ANALYSIS OF VARIANCE AND ANALYSIS OF COVARIANCE. 1.1 Regression, analysis of variance and analysis of covariance. 1.2 A pocket history of regression, ANOVA and ANCOVA. 1.3 An outline of general linear models (GLMs). 1.4 The "general" in GLM. 1.5 The "linear" in GLM. 1.6 Least squares estimates. 1.7 Fixed, random and mixed effects analyses. 1.8 The benefits of a GLM approach to ANOVA and ANCOVA. 1.9 The GLM presentation. 1.10 Statistical packages for computers. CHAPTER 2 TRADITIONAL AND GLM APPROACHES TO INDEPENDENT MEASURES SINGLE FACTOR DESIGNS. 2.1 Independent measures designs. 2.2 Balanced data designs. 2.3 Factors and independent variables. 2.4 An outline of traditional ANOVA for single factor designs. 2.5 Variance. 2.6 Traditional ANOVA calculations for single factor designs. 2.7 GLM approaches to single factor ANOVA. CHAPTER 3 COMPARING EXPERIMENTAL CONDITION MEANS, MULTIPLE HYPOTHESIS TESTING, TYPE 1 ERROR AND A BASIC DATA ANALYSIS STRATEGY. 3.1 Introduction. 3.2 Comparisons between experimental condition means. 3.3 Linear contrasts. 3.4 Comparison sum of squares. 3.5 Orthogonal contrasts. 3.6 Testing multiple hypotheses. 3.7 Planned and unplanned comparisons. 3.8 A basic data analysis strategy. 3.9 The Role of the Omnibus F-Test. CHAPTER 4 SIGNIFICANCE TESTING, CONFIDENCE INTERVALS, EFFECT SIZE AND POWER. 4.1 Introduction. 4.2 Effect size as a standardized mean difference. 4.3 Effect size as strength of association (SOA). 4.4 Small, medium and large effect sizes. 4.5 Effect size in related measures designs. 4.6 Overview of standardized mean difference and SOA measures of effect size. 4.7 Power. CHAPTER 5 GLM APPROACHES TO INDEPENDENT MEASURES FACTORIAL DESIGNS. 5.1 Factorial designs. 5.2 Factor main effects and factor interactions. 5.3 Regression GLMs for factorial ANOVA. 5.4 Estimating effects with incremental analysis. 5.5 Effect size estimation. 5.6 Further analyses. 5.7 Power. CHAPTER 6 GLM APPROACHES TO RELATED MEASURES DESIGNS. 6.1 Introduction. 6.2 Order effect controls. 6.3 The GLM approach to single factor repeated measures designs. 6.4 Estimating effects by comparing Full and Reduced repeated measures design GLMs. 6.5 Regression GLMs for single factor repeated measures designs. 6.6 Effect size estimation. 6.7 Further analyses. 6.8 Power. CHAPTER 7 GLM APPROACHES TO FACTORIAL RELATED MEASURES DESIGNS. 7.1 Factorial related measures designs. 7.2 Fully related factorial design. 7.3 Estimating effects by comparing Full and Reduced experimental design GLMs. 7.4 Regression GLMs for the fully related factorial ANOVA. 7.5 Effect size estimation. 7.6 Further analyses. 7.7 Power. CHAPTER 8 GLM APPROACHES TO FACTORIAL MIXED MEASURES DESIGNS. 8.1 Factorial mixed measures designs. 8.2 Estimating effects by comparing Full and Reduced experimental design GLMs. 8.3 Regression GLM for the two factor mixed measures ANOVA. 8.4 Effect size estimation. 8.5 Further analyses. 8.6 Power. CHAPTER 9 THE GLM APPROACH TO ANCOVA. 9.1 The nature of ANCOVA. 9.2 Single factor independent measures ANCOVA designs. 9.3 Estimating effects by comparing Full and Reduced ANCOVA GLMs. 9.4 Regression GLMs for the single factor single covariate ANCOVA. 9.5 Further analyses. 9.6 Effect size estimation. 9.7 Power. 9.8 Other ANCOVA designs. CHAPTER 10 ASSUMPTIONS UNDERLYING ANOVA, TRADITIONAL ANCOVA AND GLMs. 10.1 Introduction. 10.2 ANOVA and GLM assumptions. 10.3 A strategy for checking ANOVA and traditional ANCOVA assumptions. 10.4 Assumption checks and some assumption violation consequences. 10.5 Should the assumptions underlying the main statistical analysis be checked?. CHAPTER 11 SOME ALTERNATIVES TO TRADITIONAL ANCOVA. 11.1 Alternatives to traditional ANCOVA. 11.2 The heterogeneous regression problem. 11.3 The heterogeneous regression ANCOVA GLM. 11.4 Single factor independent measures heterogeneous regression ANCOVA. 11.5 Estimating heterogeneous regression ANCOVA effects. 11.6 Regression GLMs for heterogeneous ANCOVA. 11.7 Covariate - experimental condition relations. 11.8 Other alternatives. 11.9 The role of ANCOVA. CHAPTER 12 MULTILEVEL ANALYSIS FOR THE SINGLE FACTOR REPEATED MEASURES DESIGN. 12.1 Introduction to multilevel analysis. 12.2 Review of the single factor repeated measures experimental design GLM and ANOVA. 12.3 The multilevel approach to the single factor repeated measures experimental design. 12.4 Parameter estimation in multilevel analysis. 12.5 Applying multilevel models with different error variance-covariance structures. 12.6 Empirically Assessing different multilevel models. Appendix A. Appendix B. Appendix C. References. Index.

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Book SynopsisPraise for the Second Edition This book should be an essential part of the personal library of every practicing statistician.Technometrics Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation. Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or Table of ContentsPreface xiii 1. Introduction 1 1.1. Advantages of Nonparametric Methods 1 1.2. The Distribution-Free Property 2 1.3. Some Real-World Applications 3 1.4. Format and Organization 6 1.5. Computing with R 8 1.6. Historical Background 9 2. The Dichotomous Data Problem 11 Introduction 11 2.1. A Binomial Test 11 2.2. An Estimator for the Probability of Success 22 2.3. A Confidence Interval for the Probability of Success (Wilson) 24 2.4. Bayes Estimators for the Probability of Success 33 3. The One-Sample Location Problem 39 Introduction 39 Paired Replicates Analyses by Way of Signed Ranks 39 3.1. A Distribution-Free Signed Rank Test (Wilcoxon) 40 3.2. An Estimator Associated with Wilcoxon’s Signed Rank Statistic (Hodges–Lehmann) 56 3.3. A Distribution-Free Confidence Interval Based on Wilcoxon’s Signed Rank Test (Tukey) 59 Paired Replicates Analyses by Way of Signs 63 3.4. A Distribution-Free Sign Test (Fisher) 63 3.5. An Estimator Associated with the Sign Statistic (Hodges–Lehmann) 76 3.6. A Distribution-Free Confidence Interval Based on the Sign Test (Thompson, Savur) 80 One-Sample Data 84 3.7. Procedures Based on the Signed Rank Statistic 84 3.8. Procedures Based on the Sign Statistic 90 3.9. An Asymptotically Distribution-Free Test of Symmetry (Randles–Fligner–Policello–Wolfe, Davis–Quade) 94 Bivariate Data 102 3.10. A Distribution-Free Test for Bivariate Symmetry (Hollander) 102 3.11. Efficiencies of Paired Replicates and One-Sample Location Procedures 112 4. The Two-Sample Location Problem 115 Introduction 115 4.1. A Distribution-Free Rank Sum Test (Wilcoxon, Mann and Whitney) 115 4.2. An Estimator Associated with Wilcoxon’s Rank Sum Statistic (Hodges–Lehmann) 136 4.3. A Distribution-Free Confidence Interval Based on Wilcoxon’s Rank Sum Test (Moses) 142 4.4. A Robust Rank Test for the Behrens–Fisher Problem (Fligner–Policello) 145 4.5. Efficiencies of Two-Sample Location Procedures 149 5. The Two-Sample Dispersion Problem and Other Two-Sample Problems 151 Introduction 151 5.1. A Distribution-Free Rank Test for Dispersion–Medians Equal (Ansari–Bradley) 152 5.2. An Asymptotically Distribution-Free Test for Dispersion Based on the Jackknife–Medians Not Necessarily Equal (Miller) 169 5.3. A Distribution-Free Rank Test for Either Location or Dispersion (Lepage) 181 5.4. A Distribution-Free Test for General Differences in Two Populations (Kolmogorov–Smirnov) 190 5.5. Efficiencies of Two-Sample Dispersion and Broad Alternatives Procedures 200 6. The One-Way Layout 202 Introduction 202 6.1. A Distribution-Free Test for General Alternatives (Kruskal–Wallis) 204 6.2. A Distribution-Free Test for Ordered Alternatives (Jonckheere–Terpstra) 215 6.3. Distribution-Free Tests for Umbrella Alternatives (Mack–Wolfe) 225 6.3A. A Distribution-Free Test for Umbrella Alternatives, Peak Known (Mack–Wolfe) 226 6.3B. A Distribution-Free Test for Umbrella Alternatives, Peak Unknown (Mack–Wolfe) 241 6.4. A Distribution-Free Test for Treatments Versus a Control (Fligner–Wolfe) 249 Rationale For Multiple Comparison Procedures 255 6.5. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings–General Configuration (Dwass, Steel, and Critchlow–Fligner) 256 6.6. Distribution-Free One-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings-Ordered Treatment Effects (Hayter–Stone) 265 6.7. Distribution-Free One-Sided Treatments-Versus-Control Multiple Comparisons Based on Joint Rankings (Nemenyi, Damico–Wolfe) 271 6.8. Contrast Estimation Based on Hodges–Lehmann Two-Sample Estimators (Spjøtvoll) 278 6.9. Simultaneous Confidence Intervals for All Simple Contrasts (Critchlow–Fligner) 282 6.10. Efficiencies of One-Way Layout Procedures 287 7. The Two-Way Layout 289 Introduction 289 7.1. A Distribution-Free Test for General Alternatives in a Randomized Complete Block Design (Friedman, Kendall-Babington Smith) 292 7.2. A Distribution-Free Test for Ordered Alternatives in a Randomized Complete Block Design (Page) 304 Rationale for Multiple Comparison Procedures 315 7.3. Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Friedman Rank Sums–General Configuration (Wilcoxon, Nemenyi, McDonald-Thompson) 316 7.4. Distribution-Free One-Sided Treatments Versus Control Multiple Comparisons Based on Friedman Rank Sums (Nemenyi, Wilcoxon-Wilcox, Miller) 322 7.5. Contrast Estimation Based on One-Sample Median Estimators (Doksum) 328 Incomplete Block Data–Two-Way Layout with Zero or One Observation Per Treatment–Block Combination 331 7.6. A Distribution-Free Test for General Alternatives in a Randomized Balanced Incomplete Block Design (BIBD) (Durbin–Skillings–Mack) 332 7.7. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for Balanced Incomplete Block Designs (Skillings–Mack) 341 7.8. A Distribution-Free Test for General Alternatives for Data From an Arbitrary Incomplete Block Design (Skillings–Mack) 343 Replications–Two-Way Layout with at Least One Observation for Every Treatment–Block Combination 354 7.9. A Distribution-Free Test for General Alternatives in a Randomized Block Design with an Equal Number c(>1) of Replications Per Treatment–Block Combination (Mack–Skillings) 354 7.10. Asymptotically Distribution-Free Two-Sided All-Treatments Multiple Comparisons for a Two-Way Layout with an Equal Number of Replications in Each Treatment–Block Combination (Mack–Skillings) 367 Analyses Associated with Signed Ranks 370 7.11. A Test Based on Wilcoxon Signed Ranks for General Alternatives in a Randomized Complete Block Design (Doksum) 370 7.12. A Test Based on Wilcoxon Signed Ranks for Ordered Alternatives in a Randomized Complete Block Design (Hollander) 376 7.13. Approximate Two-Sided All-Treatments Multiple Comparisons Based on Signed Ranks (Nemenyi) 379 7.14. Approximate One-Sided Treatments-Versus-Control Multiple Comparisons Based on Signed Ranks (Hollander) 382 7.15. Contrast Estimation Based on the One-Sample Hodges–Lehmann Estimators (Lehmann) 386 7.16. Efficiencies of Two-Way Layout Procedures 390 8. The Independence Problem 393 Introduction 393 8.1. A Distribution-Free Test for Independence Based on Signs (Kendall) 393 8.2. An Estimator Associated with the Kendall Statistic (Kendall) 413 8.3. An Asymptotically Distribution-Free Confidence Interval Based on the Kendall Statistic (Samara-Randles, Fligner–Rust, Noether) 415 8.4. An Asymptotically Distribution-Free Confidence Interval Based on Efron’s Bootstrap 420 8.5. A Distribution-Free Test for Independence Based on Ranks (Spearman) 427 8.6. A Distribution-Free Test for Independence Against Broad Alternatives (Hoeffding) 442 8.7. Efficiencies of Independence Procedures 450 9. Regression Problems 451 Introduction 451 One Regression Line 452 9.1. A Distribution-Free Test for the Slope of the Regression Line (Theil) 452 9.2. A Slope Estimator Associated with the Theil Statistic (Theil) 458 9.3. A Distribution-Free Confidence Interval Associated with the Theil Test (Theil) 460 9.4. An Intercept Estimator Associated with the Theil Statistic and Use of the Estimated Linear Relationship for Prediction (Hettmansperger–McKean–Sheather) 463 k(≥2) Regression Lines 466 9.5. An Asymptotically Distribution-Free Test for the Parallelism of Several Regression Lines (Sen, Adichie) 466 General Multiple Linear Regression 475 9.6. Asymptotically Distribution-Free Rank-Based Tests for General Multiple Linear Regression (Jaeckel, Hettmansperger–McKean) 475 Nonparametric Regression Analysis 490 9.7. An Introduction to Non-Rank-Based Approaches to Nonparametric Regression Analysis 490 9.8. Efficiencies of Regression Procedures 494 10. Comparing Two Success Probabilities 495 Introduction 495 10.1. Approximate Tests and Confidence Intervals for the Difference between Two Success Probabilities (Pearson) 496 10.2. An Exact Test for the Difference between Two Success Probabilities (Fisher) 511 10.3. Inference for the Odds Ratio (Fisher, Cornfield) 515 10.4. Inference for k Strata of 2 × 2 Tables (Mantel and Haenszel) 522 10.5. Efficiencies 534 11. Life Distributions and Survival Analysis 535 Introduction 535 11.1. A Test of Exponentiality Versus IFR Alternatives (Epstein) 536 11.2. A Test of Exponentiality Versus NBU Alternatives (Hollander–Proschan) 545 11.3. A Test of Exponentiality Versus DMRL Alternatives (Hollander–Proschan) 555 11.4. A Test of Exponentiality Versus a Trend Change in Mean Residual Life (Guess–Hollander–Proschan) 563 11.5. A Confidence Band for the Distribution Function (Kolmogorov) 568 11.6. An Estimator of the Distribution Function When the Data are Censored (Kaplan–Meier) 578 11.7. A Two-Sample Test for Censored Data (Mantel) 594 11.8. Efficiencies 605 12. Density Estimation 609 Introduction 609 12.1. Density Functions and Histograms 609 12.2. Kernel Density Estimation 617 12.3. Bandwidth Selection 624 12.4. Other Methods 628 13. Wavelets 629 Introduction 629 13.1. Wavelet Representation of a Function 630 13.2. Wavelet Thresholding 644 13.3. Other Uses of Wavelets in Statistics 655 14. Smoothing 656 Introduction 656 14.1. Local Averaging (Friedman) 657 14.2. Local Regression (Cleveland) 662 14.3. Kernel Smoothing 667 14.4. Other Methods of Smoothing 675 15. Ranked Set Sampling 676 Introduction 676 15.1. Rationale and Historical Development 676 15.2. Collecting a Ranked Set Sample 677 15.3. Ranked Set Sampling Estimation of a Population Mean 685 15.4. Ranked Set Sample Analogs of the Mann–Whitney–Wilcoxon Two-Sample Procedures (Bohn–Wolfe) 717 15.5. Other Important Issues for Ranked Set Sampling 737 15.6. Extensions and Related Approaches 742 16. An Introduction to Bayesian Nonparametric Statistics via the Dirichlet Process 744 Introduction 744 16.1. Ferguson’s Dirichlet Process 745 16.2. A Bayes Estimator of the Distribution Function (Ferguson) 749 16.3. Rank Order Estimation (Campbell and Hollander) 752 16.4. A Bayes Estimator of the Distribution When the Data are Right-Censored (Susarla and Van Ryzin) 755 16.5. Other Bayesian Approaches 759 Bibliography 763 R Program Index 791 Author Index 799 Subject Index 809

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Book SynopsisA self-contained, elementary introduction to wavelet theory and applications Exploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications. The book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets,Trade Review"The book, putting emphasize on an analytic facet of wavelets, can be seen as complementary to the previous Patrick J. Van Fleet's book, DiscreteWavelet Transformations: An Elementary Approach with Applications, focused on their algebraic properties." (Zentralblatt MATH, 2011) "Requiring only a prerequisite knowledge of calculus and linear algebra, Wavelet theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level." (Mathematical Reviews, 2011) Table of Contents²Preface xi Acknowledgments xix 1 The Complex Plane and the Space L²(R) 1 1.1 Complex Numbers and Basic Operations 1 Problems 5 1.2 The Space L²(R) 7 Problems 16 1.3 Inner Products 18 Problems 25 1.4 Bases and Projections 26 Problems 28 2 Fourier Series and Fourier Transformations 31 2.1 Euler's Formula and the Complex Exponential Function 32 Problems 36 2.2 Fourier Series 37 Problems 49 2.3 The Fourier Transform 53 Problems 66 2.4 Convolution and 5-Splines 72 Problems 82 3 Haar Spaces 85 3.1 The Haar Space Vo 86 Problems 93 3.2 The General Haar Space Vj 93 Problems 107 3.3 The Haar Wavelet Space W0 108 Problems 119 3.4 The General Haar Wavelet Space Wj 120 Problems 133 3.5 Decomposition and Reconstruction 134 Problems 140 3.6 Summary 141 4 The Discrete Haar Wavelet Transform and Applications 145 4.1 The One-Dimensional Transform 146 Problems 159 4.2 The Two-Dimensional Transform 163 Problems 171 4.3 Edge Detection and Naive Image Compression 172 5 Multiresolution Analysis 179 5.1 Multiresolution Analysis 180 Problems 196 5.2 The View from the Transform Domain 200 Problems 212 5.3 Examples of Multiresolution Analyses 216 Problems 224 5.4 Summary 225 6 Daubechies Scaling Functions and Wavelets 233 6.1 Constructing the Daubechies Scaling Functions 234 Problems 246 6.2 The Cascade Algorithm 251 Problems 265 6.3 Orthogonal Translates, Coding, and Projections 268 Problems 276 7 The Discrete Daubechies Transformation and Applications 277 7.1 The Discrete Daubechies Wavelet Transform 278 Problems 290 7.2 Projections and Signal and Image Compression 293 Problems 310 7.3 Naive Image Segmentation 314 Problems 322 8 Biorthogonal Scaling Functions and Wavelets 325 8.1 A Biorthogonal Example and Duality 326 Problems 333 8.2 Biorthogonality Conditions for Symbols and Wavelet Spaces 334 Problems 350 8.3 Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair 353 Problems 368 8.4 Decomposition and Reconstruction 370 Problems 375 8.5 The Discrete Biorthogonal Wavelet Transform 375 Problems 388 8.6 Riesz Basis Theory 390 Problems 397 9 Wavelet Packets 399 9.1 Constructing Wavelet Packet Functions 400 Problems 413 9.2 Wavelet Packet Spaces 414 Problems 424 9.3 The Discrete Packet Transform and Best Basis Algorithm 424 Problems 439 9.4 The FBI Fingerprint Compression Standard 440 Appendix A: Huffman Coding 455 Problems 462 References 465 Topic Index 469 Author Index 479

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Book SynopsisA new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis. Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features: A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems Methods for extending independent modeling schemes to the dependent case, covering techniques for geneTrade Review"Overall, an excellent book for readers interested in qualitative data analysis. Highly recommended. Upper-division undergraduates through professionals." (Choice, 1 October 2011) "This new edition continues to illustrate the application of statistical methods to research across various disciplines, including medicine, engineering, business/finance, and the social sciences. Thoroughly revised and updated, the authors have refreshed this book to reflect the changes and current trends in statistical distribution theory that have occured since the publication of the previous edition eight years ago . . . key facts and formulas for forty major probability distributions are presented, making the book an ideal introduction to the general theory of statistical distributions as well as a quick reference on its basic principles". (MyCFO, 22 December 2010) "This new edition continues to illustrate the application of statistical methods to research across various disciplines, including medicine, engineering, business/finance, and the social sciences. Thoroughly revised and updated, the authors have refreshed this book to reflect the changes and current trends in statistical distribution theory that have occured since the publication of the previous edition eight years ago. The introductory chapters introduce the fundamental concepts of the distributions and the relationships between variables. For each distribution that follows, the key formulae, tables and diagrams are presented in a concise, user-friendly format. Key facts and formulas for forty major probability distributions are presented, making the book an ideal introduction to the general theory of statistical distributions as well as a quick reference on its basic principles". (MyCFO, 22 December 2010) Table of Contents1 Introduction. 2 Terms and Symbols. 2.1 Probability, Random Variable, Variate and Number. 2.2 Range, Quantile, Probability and Domain. 2.3 Distribution Function and Survival Function. 2.4 Inverse Distribution and Inverse Survival Function. 2.5 Probability Density Function and Probability Function. 2.6 Other Associated Functions and Quantities. 3 General Variate Relationships. 3.1 Introduction. 3.2 Function of a Variate. 3.3 One-to-One Transformations and Inverses. 3.4 Variate Relationships Under One-to-One Transformation. 3.5 Parameters, Variate, and Function Notation. 3.6 Transformation of Location and Scale. 3.7 Transformation from the Rectangular Variate. 3.8 Many-to-One Transformations. 4 Multivariate Distributions. 4.1 Joint Distributions. 4.2 Marginal Distributions. 4.3 Independence. 4.4 Conditional Distributions. 4.5 Bayes' Theorem. 4.6 Functions of a Multivariate. 5 Stochastic Modeling. 5.1 Introduction. 5.2 Independent Variates. 5.3 Mixture Distributions. 5.4 Skew-Symmetric Distributions. 5.5 Conditional Skewness. 5.6 Dependent Variates. 6 Parameter Inference. 6.1 Introduction. 6.2 Method of Percentiles Estimation. 6.3 Method of Moments Estimation. 6.4 Maximum Likelihood Inference. 6.5 Bayesian Inference. 7 Bernoulli Distribution. 7.1 Random Number Generation. 7.2 Curtailed Bernoulli Trial Sequences. 7.3 Urn Sampling Scheme. 7.4 Note. 8 Beta Distribution. 8.1 Notes on Beta and Gamma Functions. 8.2 Variate Relationships. 8.3 Parameter Estimation. 8.4 Random Number Generation. 8.5 Inverted Beta Distribution. 8.6 Noncentral Beta Distribution. 8.7 Beta Binomial Distribution. 9 Binomial Distribution. 9.1 Variate Relationships. 9.2 Parameter Estimation. 9.3 Random Number Generation. 10 Cauchy Distribution. 10.1 Note. 10.2 Variate Relationships. 10.3 Random Number Generation. 10.4 Generalized Form. 11 Chi-Squared Distribution. 11.1 Variate Relationships. 11.2 Random Number Generation. 11.3 Chi Distribution. 12 Chi-Squared (Noncentral) Distribution. 12.1 Variate Relationships. 13 Dirichlet Distribution. 13.1 Variate Relationships. 13.2 Dirichlet Multinomial Distribution. 14 Empirical Distribution Function. 14.1 Estimation from Uncensored Data. 14.2 Estimation from Censored Data. 14.3 Parameter Estimation. 14.4 Example. 14.5 Graphical Method for the Modified Order-Numbers. 14.6 Model Accuracy. 15 Erlang Distribution. 15.1 Variate Relationships. 15.2 Parameter Estimation. 15.3 Random Number Generation. 16 Error Distribution. 16.1 Note. 16.2 Variate Relationships. 17 Exponential Distribution. 17.1 Note. 17.2 Variate Relationships. 17.3 Parameter Estimation. 17.4 Random Number Generation. 18 Exponential Family. 18.1 Members of the Exponential Family. 18.2 Univariate One-Parameter Exponential Family. 18.3 Estimation. 18.4 Generalized Exponential Distributions. 19 Extreme Value (Gumbel) Distribution. 19.1 Note. 19.2 Variate Relationships. 19.3 Parameter Estimation. 19.4 Random Number Generation. 20 F (Variance Ratio) or Fisher{ Snedecor Distribution. 20.1 Variate Relationships. 21 F (Noncentral) Distribution. 21.1 Variate Relationships. 22 Gamma Distribution. 22.1 Variate Relationships. 22.2 Parameter Estimation. 22.3 Random Number Generation. 22.4 Inverted Gamma Distribution. 22.5 Normal Gamma Distribution. 22.6 Generalized Gamma Distribution. 22.6.1 Variate Relationships. 23 Geometric Distribution. 23.1 Notes. 23.2 Variate Relationships. 23.3 Random Number Generation. 24 Hypergeometric Distribution. 24.1 Note. 24.2 Variate Relationships. 24.3 Parameter Estimation. 24.4 Random Number Generation. 24.5 Negative Hypergeometric Distribution. 24.6 Generalized Hypergeometric (Series) Distribution. 25 Inverse Gaussian (Wald) Distribution. 25.1 Variate Relationships. 25.2 Parameter Estimation. 26 Laplace Distribution. 26.1 Variate Relationships. 26.2 Parameter Estimation. 26.3 Random Number Generation. 27 Logarithmic Series Distribution. 27.1 Variate Relationships. 27.2 Parameter Estimation. 28 Logistic Distribution. 28.1 Notes. 28.2 Variate Relationships. 28.3 Parameter Estimation. 28.4 Random Number Generation. 29 Lognormal Distribution. 29.1 Variate Relationships. 29.2 Parameter Estimation. 29.3 Random Number Generation. 30 Multinomial Distribution. 30.1 Variate Relationships. 30.2 Parameter Estimation. 31 Multivariate Normal (Multinormal) Distribution. 31.1 Variate Relationships. 31.2 Parameter Estimation. 32 Negative Binomial Distribution. 32.1 Note. 32.2 Variate Relationships. 32.3 Parameter Estimation. 32.4 Random Number Generation. 33 Normal (Gaussian) Distribution. 33.1 Variate Relationships. 33.2 Parameter Estimation. 33.3 Random Number Generation. 33.4 Truncated Normal Distribution. 33.5 Variate Relationships. 34 Pareto Distribution. 34.1 Note. 34.2 Variate Relationships. 34.3 Parameter Estimation. 34.4 Random Number Generation. 35 Poisson Distribution. 35.1 Note. 35.2 Variate Relationships. 35.3 Parameter Estimation. 35.4 Random Number Generation. 36 Power Function Distribution. 36.1 Variate Relationships. 36.2 Parameter Estimation. 36.3 Random Number Generation. 37 Power Series (Discrete) Distribution. 37.1 Note. 37.2 Variate Relationships. 37.3 Parameter Estimation. 38 Queuing Formulas. 38.1 Characteristics of Queuing Systems. 38.2 Definitions, Notation and Terminology. 38.3 General Formulas. 38.4 Some Standard Queuing Systems. 39 Rayleigh Distribution. 39.1 Variate Relationships. 39.2 Parameter Estimation. 40 Rectangular (Uniform) Continuous Distribution. 40.1Variate Relationships. 40.2 Parameter Estimation. 40.3 Random Number Generation. 41 Rectangular (Uniform) Discrete Distribution. 41.1 General Form. 41.2 Parameter Estimation. 42 Student's t Distribution. 42.1 Variate Relationships. 42.2 Random Number Generation. 43 Student's t (Noncentral) Distribution. 43.1 Variate Relationships. 44 Triangular Distribution. 44.1 Variate Relationships. 44.2 Random Number Generation. 45 von Mises Distribution. 45.1 Note. 45.2 Variate Relationships. 45.3 Parameter Estimation. 46 Weibull Distribution. 46.1 Note. 46.2 Variate Relationships. 46.3 Parameter Estimation. 46.4 Random Number Generation. 46.5 Three-Parameter Weibull Distribution. 46.6Three-Parameter Weibull Random Number Generation. 46.7 Bi-Weibull Distribution. 46.8 Five-Parameter Bi-Weibull Distribution. Bi-Weibull Random Number Generation. Bi-Weibull Graphs. 46.9 Weibull Family. 47 Wishart (Central) Distribution. 47.1 Note. 47.2 Variate Relationships. 48 Statistical Tables. Bibliography.

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Book SynopsisEmerging Infectious Diseases Emerging Infectious Diseases offers an introduction to emerging and reemerging infectious disease, focusing on significant illnesses found in various regions of the world. Many of these diseases strike tropical regions or developing countries with particular virulence, others are found in temperate or developed areas, and still other microbes and infections are more indiscriminate. This volume includes information on the underlying mechanisms of microbial emergence, the technology used to detect them, and the strategies available to contain them. The author describes the diseases and their causative agents that are major factors in the health of populations the world over. The book contains up-to-date selections from infectious disease journals as well as information from the Centers for Disease Control and Prevention, the World Health Organization, MedLine Plus, and the American Society for Microbiology. Perfect for studenTable of ContentsTables and Figures vii Preface xv The Author xvii Acknowledgments xviii Part 1: Introduction to Emerging Infectious Diseases Chapter 1: Infectious Diseases Past and Present 3 Major Concepts 4 • History of Infectious Diseases 5 • The Role of Infectious Diseases in the World Today 8 • The Links Between Infectious Diseases, Poverty, and Civil Unrest 10 • Emerging and Reemerging Infectious Diseases 12 • Factors Contributing to the Emergence of New Infectious Diseases and the Spread and Evolution of Older Diseases 15 • Timeline 18 Chapter 2: Of Microbes and Men 27 Major Concepts 28 • Introduction 30 • Infectious Agents: The Enemy Combatants 30 • Genetic Information and the Making of Proteins: Preparing the Armament 36 • The Immune Response: Humans Fight Back, Part One 40 • Antimicrobial Agents: Humans Fight Back, Part Two 46 Part 2: Bacterial Infections Chapter 3: Lyme Disease 55 Major Concepts 56 • Introduction 58 • History 60 • The Disease 61 • The Causative Agent 63 • The Immune Response 66 • Diagnosis 67 • Treatment 68 • Prevention 69 • Surveillance 71 Chapter 4: Human Ehrlichiosis 75 Major Concepts 76 • Introduction 77 • History 78 • The Diseases 79 • The Causative Agents 88 • The Immune Response 89 • Diagnosis 90 • Treatment 91 • Prevention 92 • Surveillance 92 Chapter 5: Bartonella Infections 97 Major Concepts 98 • Introduction 99 • History 99 • The Diseases 101 • The Causative Agents 106 • The Immune Response 109 • Diagnosis 110 • Treatment 111 • Prevention 111 • Surveillance 112 Chapter 6: Group A Streptococci 117 Major Concepts 118 • Introduction 119 • History 120 • The Diseases 121 • The Causative Agents 127 • The Immune Response 131 • Diagnosis 132 • Treatment 133 • Prevention 134 • Surveillance 135 Chapter 7: Escherichia coli O157:H7 139 Major Concepts 140 • Introduction 141 • History 142 • The Diseases 143 • The Causative Agents 145 • The Immune Response 151 • Diagnosis 152 • Treatment 153 • Prevention 153 • Surveillance 155 Chapter 8: Helicobacter pylori, Ulcers, and Cancer 161 Major Concepts 162 • Introduction 163 • History 164 • The Diseases 165 • The Causative Agent 168 • The Immune Response 171 • Diagnosis 172 • Treatment 173 • Prevention 174 • Surveillance 175 Chapter 9: Legionnaires’ Disease and Pontiac Fever 181 Major Concepts 182 • Introduction 183 • History 184 • The Diseases 185 • The Causative Agent 186 • The Immune Response 191 • Diagnosis 194 • Treatment 197 • Prevention 197 • Surveillance 199 Chapter 10: Pulmonary Tuberculosis and Multidrug Resistance 205 Major Concepts 206 • Introduction 207 • History 208 • The Disease 209 • The Causative Agents 212 • The Immune Response 213 • Detection and Diagnosis 214 • Treatment and Drug Resistance 216 • Prevention 219 • Surveillance 220 Chapter 11: Emerging Bacterial Drug Resistance 225 Major Concepts 226 • Introduction 227 • History 228 • The Diseases, Causative Agents, and Treatment Options 229 • Mechanisms of Resistance 235 • Diagnosis 239 • Prevention 240 • Surveillance 240 Part 3: Viral Infections Chapter 12: Marburg and Ebola Hemorrhagic Fevers 247 Major Concepts 248 • Introduction 249 • History 250 • The Diseases 254 • The Causative Agents 257 • The Immune Response 262 • Diagnosis 263 • Treatment 264 • Prevention 264 • Surveillance 267 Chapter 13: American Hemorrhagic Fevers 273 Major Concepts 274 • Introduction 275 • History 277 • The Diseases 278 • The Causative Agents 282 • The Immune Response 285 • Diagnosis 286 • Treatment 287 • Prevention 287 • Surveillance 288 Chapter 14: Lassa Hemorrhagic Fever 293 Major Concepts 294 • Introduction 295 • History 296 • The Disease 298 • The Causative Agent 300 • The Immune Response 303 • Diagnosis 304 • Treatment 304 • Prevention 306 • Surveillance 308 Chapter 15: Dengue Fever and Dengue Hemorrhagic Fever 313 Major Concepts 314 • Introduction 315 • History 316 • The Diseases 318 • The Causative Agent 321 • The Immune Response 324 • Diagnosis 327 • Treatment 327 • Prevention 328 • Surveillance 329 Chapter 16: The Human Immunodeficiency Virus and Acquired Immune Deficiency Syndrome 335 Major Concepts 336 • Introduction 338 • History 339 • The Diseases 341 • The Causative Agent 344 • The Immune Response 350 • Diagnosis and Detection 355 • Treatment 355 • Prevention 357 • Surveillance 358 Chapter 17: Human Herpesvirus 8 and Kaposi’s Sarcoma 365 Major Concepts 366 • Introduction 367 • History 368 • The Diseases 368 • The Causative Agent 373 • The Immune Response 378 • Diagnosis 379 • Treatment 380 • Prevention 383 • Surveillance 383 Chapter 18: Hepatitis C 389 Major Concepts 390 • Introduction 391 • History 392 • The Diseases 392 • The Causative Agent 397 • The Immune Response 399 • Diagnosis 401 • Treatment 402 • Prevention 403 • Surveillance 404 Chapter 19: Epidemic and Pandemic Influenza 409 Major Concepts 410 • Introduction 411 • History 412 • The Disease 414 • The Causative Agent 415 • The Immune Response 421 • Diagnosis 421 • Treatment 422 • Prevention 422 • Surveillance 425 Chapter 20: Hantavirus Pulmonary Syndrome 431 Major Concepts 432 • Introduction 433 • History 435 • The Diseases 435 • The Causative Agents 439 • The Immune Response 444 • Diagnosis 445 • Treatment 446 • Prevention 447 • Surveillance 450 Chapter 21: Severe Acute Respiratory Syndrome 455 Major Concepts 456 • Introduction 457 • History 457 • The Disease 460 • The Causative Agent 461 • The Immune Response 464 • Diagnosis 465 • Treatment 466 • Prevention 467 • Surveillance 469 Chapter 22: West Nile Disease in the United States 475 Major Concepts 476 • Introduction 477 • History 477 • The Diseases 481 • The Causative Agent 484 • The Immune Response 487 • Diagnosis 488 • Treatment 489 • Prevention 490 • Surveillance 493 Chapter 23: Monkeypox 499 Major Concepts 500 • Introduction 501 • History 502 • The Disease 505 • The Causative Agent 508 • The Immune Response 511 • Diagnosis 513 • Treatment 514 • Prevention 514 • Surveillance 516 Part 4: Parasitic Infections Chapter 24: Malaria: Reemergence and Recent Successes 523 Major Concepts 524 • Introduction 526 • History 526 • The Disease 528 • The Causative Agents 529 • The Immune Response 533 • Diagnosis 535 • Treatment and Drug Resistance 535 • Prevention: Failures and Successes 537 • Surveillance 541 Chapter 25: Babesiosis 547 Major Concepts 548 • Introduction 549 • History 549 • The Disease 550• The Causative Agent 553 • The Immune Response 557 • Diagnosis 558 • Treatment 558 • Prevention 560 • Surveillance 560 Chapter 26: Cryptosporidiosis 565 Major Concepts 566 • Introduction 567 • History 568 • The Disease 569 • The Causative Agents 570 • The Immune Response 576 • Diagnosis 577 • Treatment 578 • Prevention 580 • Surveillance 581 Chapter 27: Chagas’ Disease and Its Emergence in the United States 585 Major Concepts 586 • Introduction 587 • History 587 • The Disease 588 • The Causative Agent 591 • The Immune Response 595 • Diagnosis 598 • Treatment 599 • Prevention 600 • Surveillance 601 Part 5: Infectious Proteins Chapter 28: Creutzfeldt-Jakob Disease and Other Transmissible Spongiform Encephalopathies 609 Major Concepts 610 • Introduction 611 • History 612 • The Diseases 613 • The Causative Agents 621 • The Immune Response 625 • Diagnosis 626 • Treatment 627 • Prevention 628 • Surveillance 628 Part 6: Special Issues in Infectious Diseases Chapter 29: The Emerging Importance of Infectious Diseases in the Immunosuppressed 635 Major Concepts 636 • Introduction 637 • Immunosuppressed Populations 637 • Selected Causes of Immunosuppression 638 • Infectious Diseases of the Immunosuppressed 642 Chapter 30: The Emerging Threat of Bioweapons 667 Major Concepts 668 • Introduction 669 • History 670 • Bioterrorism Agents and Diseases 671 • The Threat of Agroterrorism 692 • Preparation for Biological Attacks 693 • Protective Vaccines 694 Glossary 701 Index 723

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Book SynopsisA comprehensive look at how probability and statistics is applied to the investment process Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before.Table of ContentsPreface xv About the Authors xvii Chapter 1 Introduction 1 Probability vs. Statistics 4 Overview of the Book 5 Part One Descriptive Statistics 15 Chapter 2 Basic Data Analysis 17 Data Types 17 Frequency Distributions 22 Empirical Cumulative Frequency Distribution 27 Data Classes 32 Cumulative Frequency Distributions 41 Concepts Explained in this Chapter 43 Chapter 3 Measures of Location and Spread 45 Parameters vs. Statistics 45 Center and Location 46 Variation 59 Measures of the Linear Transformation 69 Summary of Measures 71 Concepts Explained in this Chapter 73 Chapter 4 Graphical Representation of Data 75 Pie Charts 75 Bar Chart 78 Stem and Leaf Diagram 81 Frequency Histogram 82 Ogive Diagrams 89 Box Plot 91 QQ Plot 96 Concepts Explained in this Chapter 99 Chapter 5 Multivariate Variables and Distributions 101 Data Tables and Frequencies 101 Class Data and Histograms 106 Marginal Distributions 107 Graphical Representation 110 Conditional Distribution 113 Conditional Parameters and Statistics 114 Independence 117 Covariance 120 Correlation 123 Contingency Coefficient 124 Concepts Explained in this Chapter 126 Chapter 6 Introduction to Regression Analysis 129 The Role of Correlation 129 Regression Model: Linear Functional Relationship Between Two Variables 131 Distributional Assumptions of the Regression Model 133 Estimating the Regression Model 134 Goodness of Fit of the Model 138 Linear Regression of Some Nonlinear Relationship 140 Two Applications in Finance 142 Concepts Explained in this Chapter 149 Chapter 7 Introduction to Time Series Analysis 153 What Is Time Series? 153 Decomposition of Time Series 154 Representation of Time Series with Difference Equations 159 Application: The Price Process 159 Concepts Explained in this Chapter 163 Part Two Basic Probability Theory 165 Chapter 8 Concepts of Probability Theory 167 Historical Development of Alternative Approaches to Probability 167 Set Operations and Preliminaries 170 Probability Measure 177 Random Variable 179 Concepts Explained in this Chapter 185 Chapter 9 Discrete Probability Distributions 187 Discrete Law 187 Bernoulli Distribution 192 Binomial Distribution 195 Hypergeometric Distribution 204 Multinomial Distribution 211 Poisson Distribution 216 Discrete Uniform Distribution 219 Concepts Explained in this Chapter 221 Chapter 10 Continuous Probability Distributions 229 Continuous Probability Distribution Described 229 Distribution Function 230 Density Function 232 Continuous Random Variable 237 Computing Probabilities from the Density Function 238 Location Parameters 239 Dispersion Parameters 239 Concepts Explained in this Chapter 245 Chapter 11 Continuous Probability Distributions with Appealing Statistical Properties 247 Normal Distribution 247 Chi-Square Distribution 254 Student’s t-Distribution 256 F-Distribution 260 Exponential Distribution 262 Rectangular Distribution 266 Gamma Distribution 268 Beta Distribution 269 Log-Normal Distribution 271 Concepts Explained in this Chapter 275 Chapter 12 Continuous Probability Distributions Dealing with Extreme Events 277 Generalized Extreme Value Distribution 277 Generalized Pareto Distribution 281 Normal Inverse Gaussian Distribution 283 α-Stable Distribution 285 Concepts Explained in this Chapter 292 Chapter 13 Parameters of Location and Scale of Random Variables 295 Parameters of Location 296 Parameters of Scale 306 Concepts Explained in this Chapter 321 Appendix: Parameters for Various Distribution Functions 322 Chapter 14 Joint Probability Distributions 325 Higher Dimensional Random Variables 326 Joint Probability Distribution 328 Marginal Distributions 333 Dependence 338 Covariance and Correlation 341 Selection of Multivariate Distributions 347 Concepts Explained in this Chapter 358 Chapter 15 Conditional Probability and Bayes’ Rule 361 Conditional Probability 362 Independent Events 365 Multiplicative Rule of Probability 367 Bayes’ Rule 372 Conditional Parameters 374 Concepts Explained in this Chapter 377 Chapter 16 Copula and Dependence Measures 379 Copula 380 Alternative Dependence Measures 406 Concepts Explained in this Chapter 412 Part Three Inductive Statistics 413 Chapter 17 Point Estimators 415 Sample, Statistic, and Estimator 415 Quality Criteria of Estimators 428 Large Sample Criteria 435 Maximum Likehood Estimator 446 Exponential Family and Sufficiency 457 Concepts Explained in this Chapter 461 Chapter 18 Confidence Intervals 463 Confidence Level and Confidence Interval 463 Confidence Interval for the Mean of a Normal Random Variable 466 Confidence Interval for the Mean of a Normal Random Variable with Unknown Variance 469 Confidence Interval for the Variance of a Normal Random Variable 471 Confidence Interval for the Variance of a Normal Random Variable with Unknown Mean 474 Confidence Interval for the Parameter p of a Binomial Distribution 475 Confidence Interval for the Parameter λ of an Exponential Distribution 477 Concepts Explained in this Chapter 479 Chapter 19 Hypothesis Testing 481 Hypotheses 482 Error Types 485 Quality Criteria of a Test 490 Examples 496 Concepts Explained in this Chapter 518 Part Four Multivariate Linear Regression Analysis 519 Chapter 20 Estimates and Diagnostics for Multivariate Linear Regression Analysis 521 The Multivariate Linear Regression Model 522 Assumptions of the Multivariate Linear Regression Model 523 Estimation of the Model Parameters 523 Designing the Model 526 Diagnostic Check and Model Significance 526 Applications to Finance 531 Concepts Explained in this Chapter 543 Chapter 21 Designing and Building a Multivariate Linear Regression Model 545 The Problem of Multicollinearity 545 Incorporating Dummy Variables as Independent Variables 548 Model Building Techniques 561 Concepts Explained in this Chapter 565 Chapter 22 Testing the Assumptions of the Multivariate Linear Regression Model 567 Tests for Linearity 568 Assumed Statistical Properties about the Error Term 570 Tests for the Residuals Being Normally Distributed 570 Tests for Constant Variance of the Error Term (Homoskedasticity) 573 Absence of Autocorrelation of the Residuals 576 Concepts Explained in this Chapter 581 Appendix A Important Functions and Their Features 583 Continuous Function 583 Indicator Function 586 Derivatives 587 Monotonic Function 591 Integral 592 Some Functions 596 Appendix B Fundamentals of Matrix Operations and Concepts 601 The Notion of Vector and Matrix 601 Matrix Multiplication 602 Particular Matrices 603 Positive Semidefinite Matrices 614 Appendix C Binomial and Multinomial Coefficients 615 Binomial Coefficient 615 Multinomial Coefficient 622 Appendix D Application of the Log-Normal Distribution to the Pricing of Call Options 625 Call Options 625 Deriving the Price of a European Call Option 626 Illustration 631 References 633 Index 635

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Book SynopsisJust the math skills you need to excel in the study or practice of engineering Good math skills are indispensable for all engineers regardless of their specialty, yet only a relatively small portion of the math that engineering students study in college mathematics courses is used on a frequent basis in the study or practice of engineering.Trade Review"Summarizing, this is a very nice textbook, covering many interesting topics and written in a very digestible manner, which can be warmly recommended to students in natural sciences, computer science, and all branches of engineering." (Zentralblatt MATH, 2011)Table of ContentsPreface. 1 What Do Engineers Do? 2 Miscellaneous Math Skills. 2.1 Equations of Lines, Planes, and Circles. 2.2 Areas and Volumes of Common Shapes. 2.3 Roots of a Quadratic Equation. 2.4 Logarithms. 2.5 Reduction of Fractions and Lowest Common Denominators. 2.6 Long Division. 2.7 Trigonometry. 2.7.1 The Common Trigonometric Functions: Sine, Cosine, and Tangent. 2.7.2 Areas of Triangles. 2.7.3 The Hyperbolic Trigonometric Functions: Sinh, Cosh, and Tanh. 2.8 Complex Numbers and Algebra, and Euler’s Identity. 2.8.1 Solution of Differential Equations Having Sinusoidal Forcing Functions. 2.9 Common Derivatives and Their Interpretation. 2.10 Common Integrals and Their Interpretation. 2.11 Numerical Integration. 3 Solution of Simultaneous, Linear, Algebraic Equations. 3.1 How to Identify Simultaneous, Linear, Algebraic Equations. 3.2 The Meaning of a Solution. 3.3 Cramer’s Rule and Symbolic Equations. 3.4 Gauss Elimination. 3.5 Matrix Algebra. 4 Solution of Linear, Constant-Coeffi cient, Ordinary Differential Equations. 4.1 How to Identify Linear, Constant-Coeffi cient, Ordinary Differential Equations. 4.2 Where They Arise: The Meaning of a Solution. 4.3 Solution of First-Order Equations. 4.3.1 The Homogeneous Solution. 4.3.2 The Forced Solution for “Nice” f(t). 4.3.3 The Total Solution. 4.3.4 A Special Case. 4.4 Solution of Second-Order Equations. 4.4.1 The Homogeneous Solution. 4.4.2 The Forced Solution for “Nice” f(t). 4.4.3 The Total Solution. 4.4.4 A Special Case. 4.5 Stability of the Solution. 4.6 Solution of Simultaneous Sets of Ordinary Differential Equations with the Differential Operator. 4.6.1 Using the Differential Operator to Verify Solutions. 4.7 Numerical (Computer) Solutions. 5 Solution of Linear, Constant-Coeffi cient, Difference Equations. 5.1 Where Difference Equations Arise. 5.2 How to Identify Linear, Constant-Coeffi cient Difference Equations. 5.3 Solution of First-Order Equations. 5.3.1 The Homogeneous Solution. 5.3.2 The Forced Solution for “Nice” f(n). 5.3.3 The Total Solution. 5.3.4 A Special Case. 5.4 Solution of Second-Order Equations. 5.4.1 The Homogeneous Solution. 5.4.2 The Forced Solution for “Nice” f(n). 5.4.3 The Total Solution. 5.4.4 A Special Case. 5.5 Stability of the Solution. 5.6 Solution of Simultaneous Sets of Difference Equations with the Difference Operator. 5.6.1 Using the Difference Operator to Verify Solutions. 6 Solution of Linear, Constant-Coeffi cient, Partial Differential Equations. 6.1 Common Engineering Partial Differential Equations. 6.2 The Linear, Constant-Coeffi cient, Partial Differential Equation. 6.3 The Method of Separation of Variables. 6.4 Boundary Conditions and Initial Conditions. 6.5 Numerical (Computer) Solutions via Finite Differences: Conversion to Difference Equations. 7 The Fourier Series and Fourier Transform. 7.1 Periodic Functions. 7.2 The Fourier Series. 7.3 The Fourier Transform. 8 The Laplace Transform. 8.1 Transforms of Important Functions. 8.2 Useful Transform Properties. 8.3 Transforming Differential Equations. 8.4 Obtaining the Inverse Transform Using Partial Fraction Expansions. 9 Mathematics of Vectors. 9.1 Vectors and Coordinate Systems. 9.2 The Line Integral. 9.3 The Surface Integral. 9.4 Divergence. 9.4.1 The Divergence Theorem. 9.5 Curl. 9.5.1 Stokes’ Theorem. 9.6 The Gradient of a Scalar Field. Index.

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Book SynopsisInspired by the Encyclopedia of Statistical Sciences, Second Edition, this volume outlines the statistical tools for successfully working with modern life and health sciences research Data collection holds an essential part in dictating the future of health sciences and public health, as the compilation of statistics allows researchers and medical practitioners to monitor trends in health status, identify health problems, and evaluate the impact of health policies and programs. Methods and Applications of Statistics in the Life and Health Sciences serves as a single, one-of-a-kind resource on the wide range of statistical methods, techniques, and applications that are applied in modern life and health sciences in research. Specially designed to present encyclopedic content in an accessible and self-contained format, this book outlines thorough coverage of the underlying theory and standard applications to research in related disciplines such as bioTrade Review"The well-written and authoritative articles come from an impressive list of experts in their fields." (CHOICE, 2010) Table of ContentsPreface v Contributors vii 1 Aalen’s Additive Risk Model 1 2 Aggregation 9 3 AIDS Stochastic Models 15 4 All-or-None Compliance 37 5 Ascertainment Sampling 43 6 Assessment Bias 47 7 Bioavailability and Bioequivalence 53 8 Cancer Stochastic Models 61 9 Centralized Genomic Control: A Simple Approach Correcting for Population Structures in Case-Control Association Studies 81 10 Change Point Methods in Genetics 95 11 Classical Biostatistics 117 12 Clinical Trials-II 131 13 Cluster Randomization 143 14 Cohort Analysis 157 15 Comparisons with a Control 167 16 Competing Risks 179 17 Countermatched Sampling 189 18 Counting Processes 193 19 Cox’s Proportional Hazards Model 203 20 Crossover Trials 215 21 Design and Analysis for Repeated Measurements 225 22 DNA Fingerprinting 259 23 Epidemics 269 24 Epidemiological Statistics I 279 25 Epidemiological Statistics II 299 26 Event History Analysis 319 27 FDA Statistical Programs: An Overview 329 28 FDA Statistical Programs: Human Drugs 335 29 Follow-Up 343 30 Frailty Models 349 31 Framingham: An Evolving Longitudinal Study 353 32 Genetic Linkage 359 33 Group-Sequential Methods in Biomedical Research 365 34 Group-Sequential Tests 377 35 Grouped Data in Survival Analysis 391 36 Image Processing 397 37 Image Restoration and Reconstruction 415 38 Imputation and Multiple Imputation 425 39 Incomplete Data 441 40 Interval Censoring 451 41 Interrater Agreement 461 42 Kaplan-Meier Estimator I 481 43 Kaplan-Meier Estimator II 489 44 Landmark Data 501 45 Longitudinal Data Analysis 515 46 Meta-Analysis 531 47 Missing Data: Sensitivity Analysis 535 48 Multiple Testing in Clinical Trials 547 49 Mutation Processes 555 50 Nested Case-Control Sampling 559 51 Observational Studies 567 52 One- and Two-Armed Bandit Problems 573 53 Opthalmology 579 54 Panel Count Data 585 55 Planning and Analysis of Group-Randomized Trials 605 56 Predicting Preclinical Disease Using the Mixed-Effects Regression Model 613 57 Predicting Random Effects in Group-Randomized Trials 635 58 Probabilistic and Statistical Models for Conception 647 59 Probit Analysis 669 60 Prospective Studies 677 61 Quality Assessment for Clinical Trials 683 62 Repeated Measurements 695 63 Reproduction Rates 709 64 Retrospective Studies 713 65 Sample Size Determination for Clinical Trials 719 66 Scan Statistics 733 67 Semiparametric Analysis of Competing-Risk Data 749 68 Size and Shape Analysis 769 69 Stability Study Designs 781 70 Statistical Analysis of DNA Microarray Data 795 71 Statistical Genetics 801 72 Statistical Methods in Bioassay 807 73 Statistical Modeling of Human Fecundity 815 74 Statistical Quality of Life 839 75 Statistics at CDC 865 76 Statistics in Dentistry 871 77 Statistics in Evolutionary Genetics 873 78 Statistics in Forensic Science 879 79 Statistics in Human Genetics I 887 80 Statistics in Human Genetics II 893 81 Statistics in Medical Diagnosis 909 82 Statistics in Medicine 915 83 Statistics in the Pharmaceutical Industry 927 84 Statistics in Spatial Epidemiology 933 85 Stochastic Compartment Models 939 86 Surrogate Markers 945 87 Survival Analysis 953 Index 967

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Book SynopsisA comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic tools and exact distributional results of multivariate statistics, and, in addition, the derivations of most distributional results are provided. Statistical methods for high-dimensional data, such as curve data, spectra, images, and DNA microarrays, are discussed. Bootstrap approximations from a methodological point of view, theoretical accuracies in MANOVA tests, and modTrade Review"The book is designed for readers interested in multivariate analysis with a good background in matrix algebra, mathematical statistical inference and probability theory. Its contents are, in general, well organised and the intuitive ideas behind the different multivariate methods, the asymptotic expansion techniques and the calculation of error bounds using scale mixtures, are well expressed . The mathematical proofs are well presented and selected and I have found the mathematical appendices to be very useful as guides to following the proofs." (Mathematical Reviews, 2011) Table of ContentsPreface. Glossary of Notation and Abbreviations. 1 Multivariate Normal and Related Distributions. 1.1 Random Vectors. 1.1.1 Mean Vector and Covariance Matrix. 1.1.2 Characteristic Function and Distribution. 1.2 Multivariate Normal Distribution. 1.2.1 Bivariate Normal Distribution. 1.2.2 Definition. 1.2.3 Some Properties. 1.3 Spherical and Elliptical Distributions. 1.4 Multivariate Cumulants. Problems. 2 Wishart Distribution. 2.1 Definition. 2.2 Some Basic Properties. 2.3 Functions of Wishart Matrices. 2.4 Cochran's Theorem. 2.5 Asymptotic Distributions. Problems. 3 Hotelling's T2 and Lambda Statistics. 3.1 Hotelling's T2 and Lambda Statistics. 3.1.1 Distribution of the T2 Statistic. 3.1.2 Decomposition of T2 and D2. 3.2 Lambda-Statistic. 3.2.1 Motivation of Lambda Statistic. 3.2.2 Distribution of Lambda Statistic. 3.3 Test for Additional Information. 3.3.1 Decomposition of Lambda Statistic. Problems. 4 Correlation Coefficients. 4.1 Ordinary Correlation Coefficients. 4.1.1 Population Correlation. 4.1.2 Sample Correlation. 4.2 Multiple Correlation Coefficient. 4.2.1 Population Multiple Correlation. 4.2.2 Sample Multiple Correlation. 4.3 Partial Correlation. 4.3.1 Population Partial Correlation. 4.3.2 Sample Partial Correlation. 4.3.3 Covariance Selection Model. Problems. 5 Asymptotic Expansions for Multivariate Basic Statistics. 5.1 Edgeworth Expansion and its Validity. 5.2 The Sample Mean Vector and Covariance Matrix. 5.3 T2Statistic. 5.3.1 Outlines of Two Methods. 5.3.2 Multivariate t-Statistic. 5.3.3 Asymptotic Expansions. 5.4 Statistics with a Class of Moments. 5.4.1 Large-Sample Expansions. 5.4.2 High-Dimensional Expansions. 5.5 Perturbation Method. 5.6 Cornish-Fisher Expansions. 5.6.1 Expansion Formulas. 5.6.2 Validity of Cornish-Fisher Expansions. 5.7 Transformations for Improved Approximations. 5.8 Bootstrap Approximations. 5.9 High-Dimensional Approximations. 5.9.1 Limiting Spectral Distribution. 5.9.2 Central Limit Theorem. 5.9.3 Martingale Limit Theorem. 5.9.4 Geometric Representation. Problems. 6 MANOVA Models. 6.1 Multivariate One-Way Analysis of Variance. 6.2 Multivariate Two-Way Analysis of Variance. 6.3 MANOVA Tests. 6.3.1 Test Criteria. 6.3.2 Large-Sample Approximations. 6.3.3 Comparison of Powers. 6.3.4 High-Dimensional Approximations. 6.4 Approximations Under Nonnormality. 6.4.1 Asymptotic Expansions. 6.4.2 Bootstrap Tests. 6.5 Distributions of Characteristic Roots. 6.5.1 Exact Distributions. 6.5.2 Large-Sample Case. 6.5.3 High-Dimensional Case. 6.6 Tests for Dimensionality. 6.6.1 Three Test Criteria. 6.6.2 Large-Sample and High-Dimensional Asymptotics. 6.7 High-Dimensional Tests. Problems. 7 Multivariate Regression. 7.1 Multivariate Linear Regression Model. 7.2 Statistical Inference. 7.3 Selection of Variables. 7.3.1 Stepwise Procedure. 7.3.2 Cp Criterion. 7.3.3 AIC Criterion. 7.3.4 Numerical Example. 7.4 Principal Component Regression. 7.5 Selection of Response Variables. 7.6 General Linear Hypotheses and Confidence Intervals. 7.7 Penalized Regression Models. Problems. 8 Classical and High-Dimensional Tests for Covariance Matrices. 8.1 Specified Covariance Matrix. 8.1.1 Likelihood Ratio Test and Moments. 8.1.2 Asymptotic Expansions. 8.1.3 High-Dimensional Tests. 8.2 Sphericity. 8.2.1 Likelihood Ratio Tests and Moments. 8.2.2 Asymptotic Expansions. 8.2.3 High-Dimensional Tests. 8.3 Intraclass Covariance Structure. 8.3.1 Likelihood Ratio Tests and Moments. 8.3.2 Asymptotic Expansions. 8.3.3 Numerical Accuracy. 8.4 Test for Independence. 8.4.1 Likelihood Ratio Tests and Moments. 8.4.2 Asymptotic Expansions. 8.4.3 High-Dimensional Tests. 8.5 Tests for Equality of Covariance Matrices. 8.5.1 Likelihood Ratio Test and Moments. 8.5.2 Asymptotic Expansions. 8.5.3 High-Dimensional Tests. Problems. 9 Discriminant Analysis. 9.1 Classification Rules for Known Distributions. 9.2 Sample Classification Rules for Normal Populations. 9.2.1 Two Normal Populations with S1 = S2. 9.2.2 Case of Several Normal Populations. 9.3 Probability of Misclassifications. 9.3.1 W-Rule. 9.3.2 Z-Rule. 9.3.3 High-Dimensional Asymptotic Results. 9.4 Canonical Discriminant Analysis. 9.4.1 Canonical Discriminant Method. 9.4.2 Test for Additional Information. 9.4.3 Selection of Variables. 9.4.4 Estimation of Dimensionality. 9.5 Regression Approach. 9.6 High-Dimensional Approach. 9.6.1 Penalized Discriminant Analysis. 9.6.2 Other Approaches. Problems. 10 Principal Component Analysis. 10.1 Definition of Principal Components. 10.2 Optimality of Principal Components. 10.3 Sample Principal Components. 10.4 MLEs of the Characteristic Roots and Vectors. 10.5 Distributions of the Characteristic Roots. 10.5.1 Exact Distribution. 10.5.2 Large-Sample Case. 10.5.3 High-Dimensional Case. 10.6 Model Selection Approach for Covariance Structures. 10.6.1 General Approach. 10.6.2 Models for Equality of the Smaller Roots. 10.6.3 Selecting a Subset of Original Variables. 10.7 Methods Related to Principal Components. 10.7.1 Fixed-Effect Principal Component Model. 10.7.2 Random-Effect Principal Components Model. Problems. 11 Canonical Correlation Analysis. 11.1 Definition of Population Canonical Correlations and Variables. 11.2 Sample Canonical Correlations. 11.3 Distributions of Canonical Correlations. 11.3.1 Distributional Reduction. 11.3.2 Large-Sample Asymptotic Distributions. 11.3.3 High-Dimensional Asymptotic Distributions. 11.3.4 Fisher's z-Transformation. 11.4 Inference for Dimensionality. 11.4.1 Test of Dimensionality. 11.4.2 Estimation of Dimensionality. 11.5 Selection of Variables. 11.5.1 Test for Redundancy. 11.5.2 Selection of Variables. Problems. 12 Growth Curve Analysis. 12.1 Growth Curve Model. 12.2 Statistical Inference: One Group. 12.2.1 Test for Adequacy. 12.2.2 Estimation and Test. 12.2.3 Confidence Intervals. 12.3 Statistical Methods: Several Groups. 12.4 Derivation of Statistical Inference. 12.4.1 A General Multivariate Linear Model. 12.4.2 Estimation. 12.4.3 LR Tests for General Linear Hypotheses. 12.4.4 Confidence Intervals. 12.5 Model Selection. 12.5.1 AIC and CAIC. 12.5.2 Derivation of CAIC. 12.5.3 Extended Growth Curve Model. Problems. 13 Approximation to the Scale-Mixted Distributions. 13.1 Introduction. 13.1.1 Simple Example: Student's t-Distribution. 13.1.2 Improving the Approximation. 13.2 Error Bounds Evaluated in Sup-Norm. 13.2.1 General Theory. 13.2.2 Scale-Mixed Normal. 13.2.3 Scale-Mixed Gamma. 13.3 Error Bounds Evaluated in L1-Norm. 13.3.1 Some Basic Results. 13.3.2 Scale-Mixed Normal Density. 13.3.3 Scale-Mixed Gamma Density. 13.3.4 Scale-Mixed Chi-square Density. 13.4 Multivariate Scale Mixtures. 13.4.1 General Theory. 13.4.2 Normal Case. 13.4.3 Gamma Case. Problems. 14 Approximation to Some Related Distributions. 14.1 Location and Scale Mixtures. 14.2 Maximum of Multivariate Variables. 14.2.1 Distribution of the Maximum Component of a Multivariate Variable. 14.2.2 Multivariate t-Distribution. 14.2.3 Multivariate F-Distribution. 14.3 Scale Mixtures of the F-Distribution. 14.4 Non-Uniform Error Bounds. 14.5 Method of Characteristic Functions. Problems. 15 Error Bounds for Approximations of Multivariate Tests. 15.1 Multivariate Scale Mixture and MANOVA Tests. 15.2 A Function of Multivariate Scale Mixture. 15.3 Hotelling's T²0 Statistic. 15.4 Wilk's Lambda Distribution. 15.4.1 Univariate Case. 15.4.2 Multivariate Case. Problems. 16 Error Bounds for Approximations to Some Other Statistics. 16.1 Linear Discriminant Function. 16.1.1 Representation as Location and Scale Mixture. 16.1.2 Large-Sample Approximations. 16.1.3 High-Dimensional Approximations. 16.1.4 Some Related Topics. 16.2 Profile Analysis. 16.2.1 Parallelism Model and MLE. 16.2.2 Distributions of γ. 16.2.3 Confidence Interval for γ. 16.3 Estimators in the Growth Curve Model. 16.3.1 Error Bounds. 16.3.2 Distribution of the Bilinear Form. 16.4 Generalized Least Squares Estimators. Problems. Appendix. A.1 Some Results on Matrices. A.1.1 Determinants and Inverse Matrices. A.1.2 Characteristic Roots and Vectors. A.1.3 Matrix Factorizations. A.1.4 Idempotent Matrices. A.2 Inequalities and Max-Min Problems. A.3 Jacobians of Transformations. Bibliography. Index.

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Book SynopsisActivity-Based Statistics helps build real statistical understandingthrough a set of innovative hands-on activities that can be used each day in conjunction with other texts.The second edition continues to emphasize discovery by motivating students toapply the skills they have learned to discover the everyday relevance of statistics. There are over 45 activities and five long-term projects that have been updated and extended to encourage students to experience statistics in context. While the second edition includes updated technology extensions for Fathom, technology is used throughout the book to extend activities and is not required to complete them.Table of ContentsPreface. To the Student. Acknowledgments. I. EXPLORING DATA. A Living Histogram. How to build a histogram out of people. Getting to Know the Class. Surveying the class. Exploratory data analysis. Displaying categorical and quantitative data. A Living Box Plot. How to construct a box-and-whisker plot with people. Shape, center, and spread. V Is for Variation: How Far Are You from the Mean? Measuring variability in data. Matching Plots to Variables. Connecting our knowledge of real-life distributions to their graphs. Matching Statistics to Plots. Matching summary statistics to graphs of distributions. How the mean can differ from the median. Variation in Measurement. Collecting measurement data and looking at its distribution. Measurement Bias. Experiencing measurement bias. Let Us Count. Variation due to the process of measurement. Matching Descriptions to Scatter Plots. Making the correspondence between scatter plots and statistics (regression line and r). The Regression Effect. Find out about the regression effect. Leonardo's Model Bodies. Looking at correlation between the sizes of different body parts. Relating to Correlation. How the correlation coefficient from a sample varies about the true population coefficient. Models, Models, Models . . . . Modeling time series data with lines. Breaking the time series into two pieces. Predictable Pairs. Relationships between categorical variables. Association in two-way tables. Ratings and Ranks. The relationship between ratings and ranks. II. PLANNING A STUDY. Random Rectangles. Sampling bias. The importance of random sampling. The Rating Game. Analyzing ratings that are results from a questionnaire you design. Stringing Students Along. Learning about selection bias. Gummy Bears in Space. Factorial designs and interaction. Controlling variables. Funnel Swirling. Experimental design, particularly factorial design.Variability in an experiment. Jumping Frogs. Experiments in a factorial situation. Estimating the effects of each factor and of the interaction. How to Ask Questions: Designing a Survey How the way a question is worded can affect the outcome of a survey. III. ANTICIPATING PATTERNS. What Is Random Behavior? Gambler's fallacy. It’s hard to predict short-term random behavior. The Law of Averages. What is the law of averages? How probability helps us predict in the long term. Streaky Behavior. Runs in Bernoulli trials. Randomness is streakier than we think. Counting Successes. How to create simulations to study problems about the number of successes in repetitions of an event with a known probability. Waiting for Sammy Sosa. The geometric, or waiting-time, distribution. The Lazy Student. What happens to the spread when you add random variables. What's the Chance? Dependent and independent trials. Spinning Pennies. Sampling distributions. Distribution of sample proportions where p 0.5. Cents and the Central Limit Theorem. How the sampling distribution of the mean of a nonnormal distribution looks normal. Sampling Error and Estimation. How an estimate (for example, of a mean) based on a sample differs from the population value. How Accurate Are the Polls? How an estimate of a proportion differs from the population value. How the spread of sampling distributions defines a margin of sampling error. IV. STATISTICAL INFERENCE. How Many Tanks? Estimating a population from serial numbers. Unbiased estimators. Estimating the Total of a Restaurant Bill. Sources of bias in estimation. Compensating for bias. What Is a Confidence Interval Anyway? Explaining the confidence interval as the range of plausible population values. Confidence Intervals for the Proportion of Even Digits. The meaning of the confidence level.What affects whether 95% of the confidence intervals contain the true value. Capture/Recapture. Estimating population size using a capture/recapture technique. How to Ask Sensitive Questions. Randomized response sampling. Using probability techniques to disguise survey answers and preserve confidentiality. Estimating a Total. It is not always clear how to sample to get the best estimate. The Bootstrap. Creating an interval estimate for statistics when the traditional confidence interval may be inappropriate. Statistical Evidence of Discrimination. Using the randomization test to show that variables are associated. How Typical Are Our Households’ Ages? The Chi-Square Test Using chi-square to show that (binned) age distributions are different. Coins on Edge. The power of a hypothesis test increases as the sample size increases. V. PROJECTS. Theme: Exploration of Data and Improvement in Quality. Application: Improved Payment Processing in a Utilities Firm. Theme: Sample Survey. Application 1: A Typical Election Poll. Application 2: The Nielsens. Theme: Experiment. Application: Does Aspirin Help Prevent Heart Attacks? The Physicians' Health Study. Theme: Modeling. Application: Body Composition. References. Index.

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Book SynopsisA Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell's equation, and the Gaussian primes.Table of ContentsPreface. Notation. Chapter 1 Fundamentals. 1.0 Introduction. 1.1 A Famous Sequence of Numbers. 1.2 The Euclidean ALgorithm. The Oldest Algorithm. Reversing the Euclidean Algorithm. The Extended GCD Algorithm. The Fundamental Theorem of Arithmetic. Two Applications. 1.3 Modular Arithmetic. 1.4 Fast Powers. A Fast Alforithm for ExponentiationPowers of Matrices, Big-O Notation. Chapter 2 Congruences, Equations, and Powers. 2.0 Introduction. 2.1 Solving Linear Congruences. Linear Diophantine Equations in Two Variables. The Conductor. An Importatnt Quadratic Congruence. 2.2 The Chinese Remainder Theorem. 2.3 PowerMod Patterns. Fermat's Little Theorem. More Patterns in Powers. 2.4 Pseudoprimes. Using the Pseudoprime Test. Chapter 3 Euler's Function. 3.0 Introduction. 3.1 Euler's Function. 3.2 Perfect Numbers and Their Relatives. The Sum of Divisors Function. Perfect Numbers. Amicalbe, Abundant, and Deficient Numbers. 3.3 Euler's Theorem. 3.4 Primitive Roots for Primes. The order of an Integer. Primes Have PRimitive roots. Repeating Decimals. 3.5 Primitive Roots for COmposites. 3.6 The Universal Exponent. Universal Exponents. Power Towers. The Form of Carmichael Numbers. Chapter 4 Prime Numbers. 4.0 Introduction. 4.1 The Number of Primes. We'll Never Run Out of Primes. The Sieve of Eratosthenes. Chebyshev's Theorem and Bertrand's Postulate. 4.2 Prime Testing and Certification. Strong Pseudoprimes. Industrial-Grade Primes. Prime Certification Via Primitive Roots. An Improvement. Pratt Certificates. 4.3 Refinements and Other Directions. Other PRimality Tests. Strong Liars are Scarce. Finding the nth Prime. 4.4 A Doszen Prime Mysteries. Chapter 5 Some Applications. 5.0 Introduction. 5.1 Coding Secrets. Tossing a Coin into a Well. The RSA Cryptosystem. Digital Signatures. 5.2 The Yao Millionaire Problem. 5.3 Check Digits. Basic Check Digit Schemes. A Perfect Check Digit Method. Beyond Perfection: Correcting Errors. 5.4 Factoring Algorithms. Trial Division. Fermat's Algorithm. Pollard Rho. Pollard p-1. The Current Scene. Chapter 6 Quadratic Residues. 6.0 Introduction. 6.1 Pepin's Test. Quadratic Residues. Pepin's Test. Primes Congruent to 1 (Mod. 6.2 Proof of Quadratic Reciprocity. Gauss's Lemma. Proof of Quadratic Recipocity. Jacobi's Extension. An Application to Factoring. 6.3 Quadratic Equations. Chapter 7 Continuec Faction. 7.0 Introduction. 7.1 FInite COntinued Fractions. 7.2 Infinite Continued Fractions. 7.3 Periodic Continued Fractions. 7.4 Pell's Equation. 7.5 Archimedes and the Sun God's Cattle. Wurm's Version: Using Rectangular Bulls. The Real Cattle Problem. 7.6 Factoring via Continued Fractions. Chapter 8 Prime Testing with Lucas Sequences. 8.0 Introduction. 8.1 Divisibility Properties of Lucas Sequencese. 8.2 Prime Tests Using Lucas Sequencesse. Lucas Certification. The Lucas-Lehmer Algorithm Explained. Luca Pseudoprimes. Strong Quadratic Pseudoprimes. Primality Testing's Holy Grail. Chapter 9 Prime Imaginaries and Imaginary Primes. 9.0 Introduction. 9.1 Sums of Two Squares. 9.2 The Gaussian Intergers. Complex Number Theory. Gaussian Primes. The Moat Problem. The Gaussian Zoo. 9.3 Higher Reciprocity 325. Appendix A. Maathematica Basics. 1.0 Introduction. A.1 Plotting. A.2 Typesetting. Sending Files By E-Mail. A.3 Types of Functions. A.4 Lists. A.5 Programs. A.6 Solving Equations. A.7 Symbolic Algebra. Appendix B Lucas Certificates Exist. References. Index of Mathematica Objects. Subject Index.

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