Mathematics Books

Book SynopsisStatistics have helped shape every area of science. Without the means to analyze critical data, none of the great disoveries of the past would be possible. This paperback reprint of a Wiley bestseller shows the development of these data analysis tools and the manner in which they aided technological development prior to 1750.Trade Review"...the account goes into great detail...very accessible...useful for teachers..." (Short Book Reviews, Vol 24(1), 2004)Table of Contents1. The Book and Its Relation to Other Works. 2. A Sketch of the Background in Mathematics and Natural Philosophy. 3. Early Concepts of Probability and Chance. 4. Cardano and Liber de Ludo Aleae, c. 1565. 5. The Foundation of Probability Theory by Pascal and Fermat in 1654. 6. Huygens and De Ratiociniis in Ludo Aleae, 1657. 7. John Graunt and the Observations Made upon the Bills of Mortality, 1662. 8. The Probabilistic Interpretation of Graunt's Life Table. 9. The Early History of Life Insurance Mathematics. 10. Mathematical Models and Statistical Methods in Astronomy from Hipparchus to Kepler and Galileo. 11. The Newtonian Revolution in Mathematics and Science. 12. Miscellaneous Contributions Between 1657 and 1708. 13. The Great Leap Forward, 1708 - 1718: A Survey. 14. New Solutions to Old Problems, 1708 - 1718. 15. James Bernoulli and Ars Conjectandi, 1713. 16. Bernoulli's Theorem. 17. Tests of Significance Based on the Sex Ratio at Birth and the Binomial Distribution, 1712 - 1713. 18. Montmort and the Essay d'Analyse sur les Jeux de Hazard, 1708 and 1713. 19. The Problem of Coincidences and the Compound Probability Theorem. 20. The Problems of the Duration of Play, 1708–1718. 21. Nicholas Bernoulli. 22. De Moivre and the Doctrine of Chances, 1718, 1738, and 1756. 23. The Problem of the Duration of Play and the Method of Difference Equations. 24. De Moivre's Normal Approximation to the Binomial Distribution, 1733. 25. The Insurance Mathematics of de Moivre and Simpson, 1725-1756. References. Index.

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Book SynopsisWILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of A User's Guide to Principal Components The book is aptly and correctly namedA User's Guide. It is the kind of book that a user at any level, novice or skilled practitioner, would want to have at hand for autotutorial, for refresher, or as a general-purpose guide through the maze of modern PCA. Technometrics I recommend A User's Guide to Principal Components to anyone who is running multivariate analyses, or who contemplates performing such analyses. Those who write their own software will find the book helpful in designing better programsTable of ContentsPreface. Introduction. 1. Getting Started. 2. PCA with More Than Two Variables. 3. Scaling of Data. 4. Inferential Procedures. 5. Putting It All Together—Hearing Loss I. 6. Operations with Group Data. 7. Vector Interpretation I : Simplifications and Inferential Techniques. 8. Vector Interpretation II: Rotation. 9. A Case History—Hearing Loss II. 10. Singular Value Decomposition: Multidimensional Scaling I. 11. Distance Models: Multidimensional Scaling II. 12. Linear Models I : Regression; PCA of Predictor Variables. 13. Linear Models II: Analysis of Variance; PCA of Response Variables. 14. Other Applications of PCA. 15. Flatland: Special Procedures for Two Dimensions. 16. Odds and Ends. 17. What is Factor Analysis Anyhow? 18. Other Competitors. Conclusion. Appendix A. Matrix Properties. Appendix B. Matrix Algebra Associated with Principal Component Analysis. Appendix C. Computational Methods. Appendix D. A Directory of Symbols and Definitions for PCA. Appendix E. Some Classic Examples. Appendix F. Data Sets Used in This Book. Appendix G. Tables. Bibliography. Author Index. Subject Index.

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Book SynopsisProvides a survey of aspects of model building and statistical inference. This book presents a synthesis of theoretical literature, requiring only familiarity with linear regression methods. It contains three chapters on central computational questions that comprise a self contained introduction to unconstrained optimization.Trade Review"…a classic well written book that attempts to understand statistical ideas and computing tools in building nonlinear regression." (Journal of Statistical Computation and Simulation, July 2005) "I hope that Wiley's release of this book will rekindle some interest in this important and inappropriately overlooked subject." (International Society of Clinical Biostatistics, December 2005) "...should be present in any statistical library." (Biometrical Journal, 2006) Table of Contents1. Model Building. 2. Estimation Methods. 3. Commonly Encountered Problems. 4. Measures of Curvature and Nonlinearity. 5. Statistical Inference. 6. Autocorrelated Errors. 7. Growth Models. 8. Compartmental Models. 9. Multiphase and Spline Regressions. 10. Errors-In-Variables Models. 11. Multiresponse Nonlinear Models. 12. Asymptotic Theory. 13. Unconstrained Optimization. 14. Computational Methods for Nonlinear Least Squares. 15. Software Considerations. Appendix A. Vectors and Matrices Appendix B. Differential Geometry. Appendix C. Stochastic Differential Equations. Appendix D. Multiple Linear Regression. Appendix E. Minimization Subject to Linear Constraints. References. Author Index. Subject Index.

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Book SynopsisIncorporates mixed-effects modeling techniques for more powerful and efficient methods This book presents current and effective nonparametric regression techniques for longitudinal data analysis and systematically investigates the incorporation of mixed-effects modeling techniques into various nonparametric regression models. The authors emphasize modeling ideas and inference methodologies, although some theoretical results for the justification of the proposed methods are presented. With its logical structure and organization, beginning with basic principles, the text develops the foundation needed to master advanced principles and applications. Following a brief overview, data examples from biomedical research studies are presented and point to the need for nonparametric regression analysis approaches. Next, the authors review mixed-effects models and nonparametric regression models, which are the two key building blocks of the proposed modeling techniques.<Trade Review"The authors should be congratulated for their contribution…a nice addition to the personal collection of any statistician." (Journal of the American Statistical Association, June 2007) "...can serve as a textbook for both undergraduate and graduate students. Also it will help researchers in this area…[because of its] comprehensive coverage of the materials." (Mathematical Reviews, 2007b) "…an excellent survey of many of the nonparametric regression techniques used in longitudinal studies…highly recommended." (CHOICE, October 2006)Table of ContentsPreface. Acronyms. 1. Introduction. 2. Parametric Mixed-Effects Models. 3. Nonparametric Regression Smoothers. 4. Local Polynomial Methods. 5. Regression Spline Methods. 6. Smoothing Splines Methods. 7. Penalized Spline Methods. 8. Semiparametric Models. 9. Time-Varying Coefficient Models. 10. Discrete Longitudinal Data. References. Index.

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Book SynopsisThis effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout.Table of ContentsIntroduction to the Tutorials. Graphs of Functions. 1. Plotting a Function. 2. Plotting Several Curves. 3. Piecewise-Defined Functions. 4. Engineering Functions. First-Order ODEs. 5. Numerical Solutions of ODEs. 6. Slope Fields. 7. Integral Curves. 8. Solution Formulas. 9. Euler's Method, Heun's Method, 4th-Order Runge-Kutta. 10. Laplace Transforms: Discontinuous Driving Terms. Second-Order ODEs. 11. Orbits, Solution Curves, Component Curves. 12. Time-State Curves. 13. Discontinuous Driving Terms. 14. Solution Formulas. 15. Laplace Transforms: Dirac-Delta Driving Terms. Systems of First-Order ODEs. 16. Orbits and Component Graphs. 17. Time-State Curves. 18. Direction Fields. 19. System of Three or More ODEs. 20. Solution Formulas. 21. Fourth-Order Runge-Kutta. 22. System of ODEs in Polar Form. Additional Topics. 23. Plotting Partial Sums: Fourier Series. 24. Fourier Coefficients. 25. Recursion Relations: Series Solutions. Glossary. Common Functions and Constants in Mathematica. Index of Mathematica Commands.

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Book SynopsisFast technological advances have allowed investors and traders to make increasingly sophisticated analysis of market momentum. The current trend in the financial world continues towards momentum analysis. This book looks at both the theory and the application.Table of ContentsTHEORY. Introduction. Momentum Preliminaries. Indicator Creation. Indicator Selection. Indicator Combination. System Maintenance. Risk Management. Summary. APPLICATION. Spreadsheet Preliminaries. How to Apply Indicator Creation. How to Apply Indicator Selection. How to Apply Indicator Combination. Performance and Maintenance. Appendix 1: Excel Functions. Appendix 2: Indicator Variations. Glossary. Index.

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Book SynopsisThis comprehensive book provides readers with an applications--oriented introduction to robust regression and outlier detection - emphasising A"high--breakdownA" methods which can cope with a sizeable fraction of contamination. Its self--contained treatment allows readers to skip the mathematical material, which is concentrated in a few sections.Trade Review"…a wonderful book about methods of identifying outliers and then developing robust regression." (Journal of Statistical Computation and Simulation, July 2005)Table of Contents1. Introduction. 2. Simple Regression. 3. Multiple Regression. 4. The Special Case of One-Dimensional Location. 5. Algorithms. 6. Outlier Diagnostics. 7. Related Statistical Techniques. References. Table of Data Sets. Index.

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Book SynopsisTaking a fresh approach to graph theory, this book surveys the latest research articles, highlighting the new directions and seminal results. It also emphasizes the links the subject has to other areas of mathematics and its applications. In particular, the links between perfect graphs and frequency assignment for telecommunications are discussed.Trade Review"...illuminates the relationships between perfect graph theory and other fields of scientific enquiry..." (SciTech Book News, Vol. 26, No. 2, June 2002)Table of ContentsList of Contributors. Preface. Acknowledgements. 1. Origins and Genesis (C. Berge and J.L. Ramirez Alfonsin). Perfection. Communication Theory. The Perfect Graph Conjecture. Shannon's Capacity. Translation of the Halle-Wittenberg Proceedings. Indian Report. References. 2. From Conjecture to Theorem (Bruce A Reed). Gallai's Graphs. The Perfect Graph Theorem. Some Polyhedral Consequences. A Stronger Theorem. References. 3. A Translation of Gallai's Paper: "Transitiv Orientierbare Graphen" (Frederic Maffray and Myriam Preissmann). Introduction and Results. The Proofs of Theorems (3.12), (3.15) and 3.16). The Proofs of (3.18) and (3.19). The Proofs of (3.1.16). The Proofs of (3.1.17). Determination of all Irreducible Graphs. Determination of the Irreducible Graphs. References. 4. Even Pairs (Hazel Everett et al). Introduction. Even Pairs and Perfect Graphs. Perfectly Contractile Graphs. Quasi-parity Graphs. Recent Progress. Odd Pairs. References. 5. The P_4-Structure of Perfect Graphs (Stefan Hougardy). Introduction. P_4-Stucture: Basics, Isomorphisms and Recognition. Modules, h-Sets, Split Graphs and Unique P_4-Structure. The Semi-Strong perfect Graph Theorem. The Structure of the P_4-Isomorphism Classes. Recognizing P_4-Structure. The P_4-Structure of Minimally Imperfect Graphs. The Partner Structure and Other Generalizations. P_3-Structure. References. 6. Forbidding Holes and Antiholes (Ryan Hayward and Bruce A. Reed). Introduction. Graphs with No Holes. Graphs with No Discs. Graphs with No Long Holes. Balanced Matrices. Bipartitie Graphs with No Hole of Length 4k + 2. Graphs without Even Holes. -Perfect Graphs. Graphs without Odd Holes. References. 7. Perfectly Orderable Graphs: A Survey (Chinh T Hoang). Introduction. Classical Graphs. Minimal Nonperfectly Orderable Graphs. Orientations. Generalizations of Triangulated Graphs. Generalizations of Complements of Chordal Bipartitie Graphs. Other Classes of Perfectly Orderable Graphs. Vertex Orderings. Generalizations of Perfectly Orderable Graphs. Optimizing Perfectly Ordered Graphs. References. 8. Cutsets in Perfect and Minimal Imperfect Graphs (Irena Rusu). Introduction. How Did It Start? Main Results on Minimal Imperfect Graphs. Applications: Star Cutsets. Applications: Clique and Multipartite Cutsets. Applications: Stable Cutsets. Two (Resolved) Conjectures. The Connectivity of Minimal Imperfect Graphs. Some (More) Problems. References. 9. Some Aspects of Minimal Imperfect Graphs (Myriam Preissmann and Andras Sebo). Introduction. Imperfect and Partitionable Graphs. Properties. Constructions. References. 10. Graph Imperfection and Channel Assignment (Colin McDiarmid). Introduction. The Imperfection Ratio. An Alternative Definition. Further Results and Questions. background on Channel Assignment. References. 11. A Gentle Introduction to Semi-definite Programming (Bruce A. Reed). Introduction. The Ellipsoid Method. Solving Semi-definite Programs. Randomized Rounding and Derandomization. Approximating MAXCUT. Approximating Bandwidth. Graph Colouring. 12. The Theta Body. References. The Theta Body and Imperfection (F.B. Shepherd). Background and Overview. Optimization, Convexity and Geometry. The Theta Body. Partitionable Graphs. Perfect Graph Characterizations and a Continuous Perfect Graph Conjecture. References. 13. Perfect Graphs and Graph Entropy (Gabor Simonyi). Introduction. The Information-Theoretic Interpretation. Some Basic Properties. Structural Theorems: Relation to Perfectness. Applications. Generalizations. Graph Capacities and Other Related Functionals. References. 14 A Bibliography on Perfect Graphs (Vaek Chvátal). Index.

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Book SynopsisIn modern society, we are ever more aware of the environmentalissues we face, whether these relate to global warming, depletionof rivers and oceans, despoliation of forests, pollution of land,poor air quality, environmental health issues, etc. At the mostfundamental level it is necessary to monitor what is happening inthe environment - collecting data to describe the changingscene. More importantly, it is crucial to formally describe theenvironment with sound and validated models, and to analyse andinterpret the data we obtain in order to take action. Environmental Statistics provides a broad overview of thestatistical methodology used in the study of the environment,written in an accessible style by a leading authority on thesubject. It serves as both a textbook for students of environmentalstatistics, as well as a comprehensive source of reference foranyone working in statistical investigation of environmentalissues. * Provides broad coverage of the methodology used in tTrade Review"Inspired by the Encyclopedia of Statistical Sciences, SecondEdition (ESS2e), this volume presents a concise, well-rounded focuson the statistical concepts and applications that are essential forunderstanding gathered data in the fields of engineering, qualitycontrol, and the physical sciences. The book successfully upholdsthe goals of ESS2e by combining both previously-published and newlydeveloped contributions written by over 100 leading academics,researchers, and practitioner in a comprehensive, approachableformat. The result is a succinct reference that unveils modern,cutting-edge approaches to acquiring and analyzing data acrossdiverse subject areas within these three disciplines, includingoperations research, chemistry, physics, the earth sciences,electrical engineering, and quality assurance." (Finwin, 7September 2011) "In this book, Vic Barnett, a distinguished environmentalstatistician, provides an overview of statistical methods that havebeen used on such problems in the environmental sciences."(Journal of the American Statistical Association, September2006) "...combines sound fundamentals and their applications."(European Journal of Soil Science, No.56, April 2005) "Many tables, graphs and figures illustrate the environmentalapplications of the statistical methods that are described."(Journal of the Royal Statistical Society, Series A,Vol.168, No.2, March 2005) "...well written...methods are illustrated with interestingexamples...a comprehensive reference source for anyone working onenvironmental issues..." (Short Book Reviews, Vol.24, No.3,December 2004) "Statisticians should enjoy the book. The author is an extremelyknowledgeable statistician, and he is writing about an applicationdomain that he clearly knows." (Technometrics, November2004) "An excellent book. Highly recommended." (Choice, July2004) "...this provides an excellent sketch of the current state ofdevelopment for new statistical methodologies...a valuableresource..." (Statistics in Medicine, 15th August 2005)Table of ContentsPreface. Chapter 1: Introduction. 1.1 Tomorrow is too Late! 1.2 Environmental Statistics. 1.3 Some Examples. 1.3.1 ‘Getting it all together’. 1.3.2 ‘In time and space’. 1.3.3 ‘Keep it simple’. 1.3.4 ‘How much can we take?’ 1.3.5 ‘Over the top’. 1.4 Fundamentals. 1.5 Bibliography. PART I: EXTREMAL STRESSES: EXTREMES, OUTLIERS, ROBUSTNESS. Chapter 2: Ordering and Extremes: Applications, models, inference. 2.1 Ordering the Sample. 2.1.1 Order statistics. 2.2 Order-based Inference. 2.3 Extremes and Extremal Processes. 2.3.1 Practical study and empirical models; generalized extreme-value distributions. 2.4 Peaks over Thresholds and the Generalized Pareto Distribution. Chapter 3: Outliers and Robustness. 3.1 What is an Outlier? 3.2 Outlier Aims and Objectives. 3.3 Outlier-Generating Models. 3.3.1 Discordancy and models for outlier generation. 3.3.2 Tests of discordancy for specific distributions. 3.4 Multiple Outliers: Masking and Swamping. 3.5 Accommodation: Outlier-Robust Methods. 3.6 A Possible New Approach to Outliers. 3.7 Multivariate Outliers. 3.8 Detecting Multivariate Outliers. 3.8.1 Principles. 3.8.2 Informal methods. 3.9 Tests of Discordancy. 3.10 Accommodation. 3.11 Outliers in linear models. 3.12 Robustness in General. PART II: COLLECTING ENVIRONMENTAL DATA: SAMPLING AND MONITORING. Chapter 4: Finite-Population Sampling. 4.1 A Probabilistic Sampling Scheme. 4.2 Simple Random Sampling. 4.2.1 Estimating the mean, &Xmacr;. 4.2.2 Estimating the variance, S2. 4.2.3 Choice of sample size, n. 4.2.4 Estimating the population total, XT. 4.2.5 Estimating a proportion, P. 4.3 Ratios and Ratio Estimators. 4.3.1 The estimation of a ratio. 4.3.2 Ratio estimator of a population total or mean. 4.4 Stratified (simple) Random Sampling. 4.4.1 Comparing the simple random sample mean and the stratified sample mean. 4.4.2 Choice of sample sizes. 4.4.3 Comparison of proportional allocation and optimum allocation. 4.4.4 Optimum allocation for estimating proportions. 4.5 Developments of Survey Sampling. Chapter 5: Inaccessible and Sensitive Data. 5.1 Encountered Data. 5.2 Length-Biased or Size-Biased Sampling and Weighted Distributions. 5.2.1 Weighted distribution methods. 5.3 Composite Sampling. 5.3.1 Attribute Sampling. 5.3.2 Continuous variables. 5.3.3 Estimating mean and variance. 5.4 Ranked-Set Sampling. 5.4.1 The ranked-set sample mean. 5.4.2 Optimal estimation. 5.4.3 Ranked-set sampling for normal and exponential distributions. 5.4.4 Imperfect ordering. Chapter 6: Sampling in the Wild. 6.1 Quadrat Sampling. 6.2 Recapture Sampling. 6.2.1 The Petersen and Chapman estimators. 6.2.2 Capture–recapture methods in open populations. 6.3 Transect Sampling. 6.3.1 The simplest case: strip transects. 6.3.2 Using a detectability function. 6.3.3 Estimating f (y). 6.3.4 Modifications of approach. 6.3.5 Point transects or variable circular plots. 6.4 Adaptive Sampling. 6.4.1 Simple models for adaptive sampling. Part III: EXAMINING ENVIRONMENTAL EFFECTS: STIMULUS–RESPONSE RELATIONSHIPS. Chapter 7: Relationship: regression-type models and methods. 7.1 Linear Models. 7.1.1 The linear model. 7.1.2 The extended linear model. 7.1.3 The normal linear model. 7.2 Transformations. 7.2.1 Looking at the data. 7.2.2 Simple transformations. 7.2.3 General transformations. 7.3 The Generalized Linear Model. Chapter 8: Special Relationship Models, Including Quantal Response and Repeated Measures. 8.1 Toxicology Concerns. 8.2 Quantal Response. 8.3 Bioassay. 8.4 Repeated Measures. Part IV: STANDARDS AND REGULATIONS. Chapter 9: Environmental Standards. 9.1 Introduction. 9.2 The Statistically Verifiable Ideal Standard. 9.2.1 Other sampling methods. 9.3 Guard Point Standards. 9.4 Standards Along the Cause–Effect Chain. Part V: A MANY-DIMENSIONAL ENVIRONMENT: SPATIAL AND TEMPORAL PROCESSES. Chapter 10: Time-Series Methods. 10.1 Space and Time Effects. 10.2 Time Series. 10.3 Basic Issues. 10.4 Descriptive Methods. 10.4.1 Estimating or eliminating trend. 10.4.2 Periodicities. 10.4.3 Stationary time series. 10.5 Time-Domain Models and Methods. 10.6 Frequency-Domain Models and Methods. 10.6.1 Properties of the spectral representation. 10.6.2 Outliers in time series. 10.7 Point Processes. 10.7.1 The Poisson process. 10.7.2 Other point processes. Chapter 11: Spatial Methods for Environmental Processes. 11.1 Spatial Point Process Models and Methods. 11.2 The General Spatial Process. 11.2.1 Predication, interpolation and kriging. 11.2.2 Estimation of the variogram. 11.2.3 Other forms of kriging. 11.3 More about Standards Over Space and Time. 11.4 Relationship. 11.5 More about Spatial Models. 11.5.1 Types of spatial model. 11.5.2 Harmonic analysis of spatial processes. 11.6 Spatial Sampling and Spatial Design. 11.6.1 Spatial sampling. 11.6.2 Spatial design. 11.7 Spatial-Temporal Models and Methods. References. Index.

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Book SynopsisNonlinear Bayesian modelling is a relatively new field, but one that has seen a recent explosion of interest. Nonlinear models offer more flexibility than those with linear assumptions, and their implementation has now become much easier due to increases in computational power. Bayesian methods allow for the incorporation of prior information, allowing the user to make coherent inference. Bayesian Methods for Nonlinear Classification and Regression is the first book to bring together, in a consistent statistical framework, the ideas of nonlinear modelling and Bayesian methods. * Focuses on the problems of classification and regression using flexible, data-driven approaches. * Demonstrates how Bayesian ideas can be used to improve existing statistical methods. * Includes coverage of Bayesian additive models, decision trees, nearest-neighbour, wavelets, regression splines, and neural networks. * Emphasis is placed on sound implementation of nonlinear models. * DiscussTrade Review"The exercises and the excellent presentation style make this book qualified t be a textbook in a graduate level nonlinear regression course." (Journal of Statistical Computation and Simulation, July 2005) "Its in-depth coverage of implementation issues and detailed discussion of pros and cons of different modeling strategies make it attractive for many researchers.” (Technometrics, May 2004) "...a fascinating account of a rapidly evolving area of statistics..." (Short Book Reviews, December 2002) "...will benefit researchers...also suitable for graduate students..." (Mathematical Reviews, 2003m)Table of ContentsPreface Acknowledgements. Introduction Bayesian Modelling Curve Fitting Surface Fitting Classification using Generalised Nonlinear Models Bayesian Tree Models Partition Models Nearest-Neighbour Models Multiple Response Models Appendix A: Probability Distributions Appendix B: Inferential Processes References Index Author Index

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Book SynopsisWith meta-analysis methods playing a crucial role in health research in recent years, this important and clearly-written book provides a much-needed survey of the field. Meta-analysis provides a framework for combining the results of several clinical trials and drawing inferences about the effectiveness of medical treatments.Trade Review“Both books can be recommended for graduate training and are useful additions to the library of those interested in the meta-analytic accumulation of literatures on training, vocational learning, and education in the professions.” (Vocations and Learning, 15 December 2010) "This well-written book offers an exhaustive criticism and up-to-date references, illustrates effectively with real life examples and data…" (Journal of Statistical Computation & Simulation, July 2004) "this is an excellent book..." (Short Book Reviews, April 2001) "...recommended for mathematically skilled readers interested in getting an overview of the various methods and the existing literature..." (Statistics in Medicine, 15 October 2003) Table of ContentsPART A: META-ANALYSIS METHODOLOGY: THE BASICS Introduction: Meta-analysis: Its Development and Uses Defining Outcome Measures used for Combining via Meta-analysis Random Effects Models for Combining Study Estimates Exploring Between Study Heterogeneity Publication Bias Study Quality Sensitivity Analysis Reporting the Results of a Meta-analysis Fixed Effects Methods for Combining Study Estimates PART B: ADVANCED AND SPECIALIZED META-ANALYSIS TOPICS Bayesian Methods in Meta-analysis Meta Regression Meta-analysis of Different Types of Data Incorporating Study Quality into a Meta-analysis Meta-analysis of Multiple and Correlated Outcome Measures Meta-analysis of Epidemiological and other Observational Studies Generalised Synthesis of Evidence - Combining Different Sources of Evidence Meta-analysis of Survival Data Cumulative Meta-analysis Miscellaneous and Developing Areas of Applications in Meta-Analysis Appendix I: Software Used for the Examples in this Book

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Book SynopsisPresents and develops methods from queueing theory in mathematical language and in sufficient depth so that the student may apply the methods to many modern engineering problems and conduct creative research. Step-by-step development of results with careful explanation, and lists of important results make it useful as a handbook and a text.Table of ContentsQueueing Systems. Some Important Random Processes. ELEMENTARY QUEUEING THEORY. Birth-Death Queueing Systems in Equilibrium. Markovian Queues in Equilibrium. INTERMEDIATE QUEUEING THEORY. The Queue M/G/I. The Queue G/M/m. The Method of Collective Marks. ADVANCED MATERIAL. The Queue G/G/1.

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Book SynopsisQueueing Systems Volume 1: Theory Leonard Kleinrock This book presents and develops methods from queueing theory in sufficient depth so that students and professionals may apply these methods to many modern engineering problems, as well as conduct creative research in the field.Table of ContentsA Queueing Theory Primer. Bounds. Inequalities and Approximations. Priority Queueing. Computer Time-Sharing and Multiaccess Systems. Computer-Communication Networks: Analysis and Design. Computer-Communication Networks: Measurement, Flow Control, and ARPANET Traps.

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Book SynopsisMany ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models. * Rapidly expanding area of research for biologists and applied mathematicians * Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models * Provides the reader with the tools needed to construct and interpret models * Offers specific applications of both the models and the methods * Authors have played a dominant role in the field for years Essential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.Trade Review"…particularly attractive and useful for graduate students and other researchers who are interested in studying applications of reaction-diffusion theory to spatial ecology." (Mathematical Reviews, Issue 2007a) "…I would recommend this book to anyone who wants a well supported journey into the modern theory of partial differential equations and dynamic systems…" (The Mathematical Gazette, March 2005)Table of ContentsPreface. Series Preface. 1 Introduction. 1.1 Introductory Remarks. 1.2 Nonspatial Models for a Single Species. 1.3 Nonspatial Models For Interacting Species. 1.4 Spatial Models: A General Overview. 1.5 Reaction-Diffusion Models. 1.6 Mathematical Background. 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues. 2.1 Eigenvalues, Persistence, and Scaling in Simple Models. 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity. 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models. 2.4 Graphical Analysis in One Space Dimension. 2.5 Eigenvalues and Positivity. 2.6 Connections with Other Topics and Models. Appendix. 3 Density Dependent Single-Species Models. 3.1 The Importance of Equilibria in Single Species Models. 3.2 Equilibria and Stability: Sub- and Supersolutions. 3.3 Equilibria and Scaling: One Space Dimension. 3.4 Continuation and Bifurcation of Equilibria. 3.5 Applications and Properties of Single Species Models. 3.6 More General Single Species Models. Appendix. 4 Permanence. 4.1 Introduction. 4.2 Definition of Permanence. 4.3 Techniques for Establishing Permanence. 4.4 Invasibility Implies Coexistence. 4.5 Permanence in Reaction-Diffusion Models for Predation. 4.6 Ecological Permanence and Equilibria. Appendix. 5 Beyond Permanence: More Persistence Theory. 5.1 Introduction. 5.2 Compressivity. 5.3 Practical Persistence. 5.4 Bounding Transient Orbits. 5.5 Persistence in Nonautonomous Systems. 5.6 Conditional Persistence. 5.7 Extinction Results. Appendix. 6 Spatial Heterogeneity in Reaction-Diffusion Models. 6.1 Introduction. 6.2 Spatial Heterogeneity within the Habitat Patch. 6.3 Edge Mediated Effects. 6.4 Estimates and Consequences. Appendix. 7 Nonmonotone Systems. 7.1 Introduction. 7.2 Predator Mediated Coexistence. 7.3 Three Species Competition. 7.4 Three Trophic Level Models. Appendix. References. Index.

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Book SynopsisThis work covers stochastic order relations, which provide insight into the behaviour of complex stochastic (random) systems and enables the user to collect comparative data. Application areas include queuing systems, actuarial and financial risk, decision making, and stochastic simulation.Trade Review"…a noteworthy contribution to applied probability, and I would recommend it to anyone interested in applied stochastic modeling." (Journal of the American Statistical Association, June 2005) “…will replace the excellent but now slightly dated text by Shaked and Shathikumar (1994) as the standard reference on stochastic orders.” (Statistical Papers, Vol.46, No.1, January 2005) "...provides an up-to-date survey of a notable area..." (Mathematical Reviews, 2003d) "...discusses the major concepts related to stochastic orders..." (SciTech Book News, Vol. 26, No. 2, June 2002) "...a very timely and methodically orientated book..." (Zentralblatt Math, Vol.999, No.24, 2002)Table of ContentsPreface. Univariate Stochastic Orders Theory of Integral Stochastic Orders Multivariate Stochastic Orders Stochastic Models, Comparison and Monotonicity Monotonicity and Comparability of Stochastic Processes Monotonicity Properties and Bounds for Queueing Systems Applications to Various Stochastic Models Comparing Risks. List of Symbols. References. Index.

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Book SynopsisThis textbook provides a thorough treatment of standard methods such as linear and quadratic programming, Newton-like methods and the conjugate gradient method. The theoretical aspects of the subject include a treatment of optimality conditions and the significance of Lagrange multipliers.Table of ContentsUNCONSTRAINED OPTIMIZATION. Structure of Methods. Newton-like Methods. Conjugate Direction Methods. Restricted Step Methods. Sums of Squares and Nonlinear Equations. CONSTRAINED OPTIMIZATION. Linear Programming. The Theory of Constrained Optimization. Quadratic Programming. General Linearly Constrained Optimization. Nonlinear Programming. Other Optimization Problems. Non-Smooth Optimization. References. Subject Index.

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Book SynopsisA controversial philosophical approach to statistics following the work of Rev Thomas Bayes (1701). To solve a problem or to make a decision, the Bayesian collects data from all possible theories and assigns a probability to them. This generates a prior distribution from which, workable parameters are determined and complex calculations are made.Trade Review"an excellent primary source for those who wish to learn about thelearning and decision process in a situation of uncertainty..."(Measurement Science Technology, February 2001) "an ideal source for all students and researchers in statisticsmathematics, decision analysis, economic and business studies andall branches of science and engineering who wish to further theirunderstanding of Bayesian statistics." (Zentralblatt Fur Didaktikder Mathematik) "...Bayesians will find it indispensable: non-Bayesians will find,and enjoy, much thought-provoking material to challenge theirorthodoxy...." (The Statistician, Vol.51, No.2, 2002)Table of ContentsFoundations. Generalisations. Modelling. Inference. Remodelling. Appendices. References. Indexes.

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Book SynopsisThis text look at cross-over trials which are experiments in which subjects, whether patients or healthy volunteers, are each given a number of treatments with the object being to study the differences between these treatments. They are used extensively in clinical research.Trade Review"…clearly written…mode of presentation is very effective…I recommend this book as a useful resource…" (Journal of the American Statistical Association, December 2004) "The book by Senn was the very first volume in Wiley's excellent series, "Statistics in Practice". Here, 10 years later, it is now the first of the books in that series to reappear in a second addition.” (Technometrics, May 2004) "...well structured and easy to read...incredibly useful..." (Applied Clinical Trials, December 2002) "...an excellent reference source and is easily readable." (The Statistician) "...explanation are kept as non-technical as possible, although they do not lack statistical rigour...well worth reading..." (Pharmaceutical Statistics, Vol 2, 2003) “…the main additions can be seen as …adding to the arguments for the author’s view on carryover affects...” (Clinical Trials, No.1 2004) Table of ContentsPreface to the Second Edition. Preface to the First Edition. 1. Introduction. 2. Some Basic Considerations Concerning Estimation in Clinical Trials. 3. The AB/BA Design with Normal Data. 4. Other Outcomes and the AB/BA Design. 5. Normal Data from Designs with Three or More Treatments. 6. Other Outcomes from Designs with Three or More Treatments. 7. Some Special Designs. 8. Graphical and Tabular Presentation of Cross-over Trials. 9. Various Design Issues. 10. Mathematical Approaches to Carry-over. References. Author Index. Subject Index.

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Book SynopsisDecision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book: * Provides a rich collection of techniques and procedures. * Discusses the foundational aspects and modern day practice. * Links foundations to practical applications in biostatistics, computer Trade Review“Also anyone interested in learning more about decision theoretic experimental design (a topic of growing interest for example in sequential clinical trials) will find a useful overview and a good starting point for further investigations.” (Stat Papers, 2011) "Decision theory is fundamental to all scientific disciplines., including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book." (Mathematical Reviews, 2011)Table of ContentsPreface. Acknowledgments. 1 Introduction. 1.1 Controversies. 1.2 A guided tour of decision theory. Part One: Foundations. 2 Coherence. 2.1 The "Dutch Book" theorem. 2.2 Temporal coherence. 2.3 Scoring rules and the axioms of probabilities. 2.4 Exercises. 3 Utility. 3.1 St. Petersburg paradox. 3.2 Expected utility theory and the theory of means. 3.3 The expected utility principle. 3.4 The von Neumann-Morgenstern representation theorem. 3.5 Allais' criticism. 3.6 Extensions. 3.7 Exercises. 4 Utility in action. 4.1 The "standard gamble". 4.2 Utility of money. 4.3 Utility functions for medical decisions. 4.4 Exercises. 5 Ramsey and Savage. 5.1 Ramsey's theory. 5.2 Savage's theory. 5.3 Allais revisited. 5.4 Ellsberg paradox. 5.5 Exercises. 6 State independence. 6.1 Horse lotteries. 6.2 State-dependent utilities. 6.3 State-independent utilities. 6.4 Anscombe-Aumann representation theorem. 6.5 Exercises. Part Two Statistical Decision Theory. 7 Decision functions. 7.1 Basic concepts. 7.2 Data-based decisions. 7.3 The travel insurance example. 7.4 Randomized decision rules. 7.5 Classification and hypothesis tests. 7.6 Estimation. 7.7 Minimax-Bayes connections. 7.8 Exercises. 8 Admissibility. 8.1 Admissibility and completeness. 8.2 Admissibility and minimax. 8.3 Admissibility and Bayes. 8.4 Complete classes. 8.5 Using the same ± level across studies with different sample sizes is inadmissible. 8.6 Exercises. 9 Shrinkage. 9.1 The Stein effect. 9.2 Geometric and empirical Bayes heuristics. 9.3 General shrinkage functions. 9.4 Shrinkage with different likelihood and losses. 9.5 Exercises. 10 Scoring rules. 10.1 Betting and forecasting. 10.2 Scoring rules. 10.3 Local scoring rules. 10.4 Calibration and refinement. 10.5 Exercises. 11 Choosing models. 11.1 The "true model" perspective. 11.2 Model elaborations. 11.3 Exercises. Part Three Optimal Design. 12 Dynamic programming. 12.1 History. 12.2 The travel insurance example revisited. 12.3 Dynamic programming. 12.4 Trading off immediate gains and information. 12.5 Sequential clinical trials. 12.6 Variable selection in multiple regression. 12.7 Computing. 12.8 Exercises. 13 Changes in utility as information. 13.1 Measuring the value of information. 13.2 Examples. 13.3 Lindley information. 13.4 Minimax and the value of information. 13.5 Exercises. 14 Sample size. 14.1 Decision-theoretic approaches to sample size. 14.2 Computing. 14.3 Examples. 14.4 Exercises. 15 Stopping. 15.1 Historical note. 15.2 A motivating example. 15.3 Bayesian optimal stopping. 15.4 Examples. 15.5 Sequential sampling to reduce uncertainty. 15.6 The stopping rule principle. 15.7 Exercises. Appendix. A.1 Notation. A.2 Relations. A.3 Probability (density) functions of some distributions. A.4 Conjugate updating. References. Index.

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Book SynopsisAll students and researchers in environmental and biological sciences require statistical methods at some stage of their work. Many have a preconception that statistics are difficult and unpleasant and find that the textbooks available are difficult to understand. Practical Statistics for Environmental and Biological Scientists provides a concise, user-friendly, non-technical introduction to statistics. The book covers planning and designing an experiment, how to analyse and present data, and the limitations and assumptions of each statistical method. The text does not refer to a specific computer package but descriptions of how to carry out the tests and interpret the results are based on the approaches used by most of the commonly used packages, e.g. Excel, MINITAB and SPSS. Formulae are kept to a minimum and relevant examples are included throughout the text.Trade Review"The reassuring tone and straightforward approach of the book would be a useful guide...” (Biochemistry and Molecular Education, July/August 2002) "...covers the basics of designing an experiment/survey, data analysis and presentation, and specific methods." (SciTech Book News, Vol. 26, No. 2, June 2002) "...a good and clear exposition of basic statistical techniques..." (Biometrics, December 2002) "…This no-nonsense approach to elementary statistics should get you or your student started…" (European Journal of Soil Science, March 2003) "...This book provides a concise, userfriendly, non-technical introduction to statistics". (Metrohm Information, Vol.32, No.1, 2003)Table of ContentsPreface ix Part I Statistics Basics 1 1 Introduction 3 1.1 Do you need statistics? 3 1.2 What is statistics? 4 1.3 Some important lessons I have learnt 5 1.4 Statistics is getting easier 6 1.5 Integrity in statistics 7 1.6 About this book 8 2 A Brief Tutorial on Statistics 9 2.1 Introduction 9 2.2 Variability 9 2.3 Samples and populations 10 2.4 Summary statistics 11 2.5 The basis of statistical tests 19 2.6 Limitations of statistical tests 24 3 Before You Start 27 3.1 Introduction 27 3.2 What statistical methods are available? 28 3.3 Surveys and experiments 33 3.4 Designing experiments and surveys — preliminaries 35 3.5 Summary 43 4 Designing an Experiment or Survey 45 4.1 Introduction 45 4.2 Sample size 45 4.3 Sampling 50 4.4 Experimental design 56 4.5 Further reading 60 5 Exploratory Data Analysis and Data Presentation 63 5.1 Introduction 63 5.2 Column graphs 65 5.3 Line graphs 67 5.4 Scatter graphs 69 5.5 General points about graphs 71 5.6 Tables 73 5.7 Standard errors and error bars 74 6 Common Assumptions or Requirements of Data for Statistical Tests 77 6.1 Introduction 77 6.2 Common assumptions 81 6.3 Transforming data 84 Part II Statistical Methods 91 7 t-tests and F-tests 93 7.1 Introduction 93 7.2 Limitations and assumptions 94 7.3 t-tests 95 7.4 F-test 103 7.5 Further reading 105 8 Analysis of Variance 107 8.1 Introduction 107 8.2 Limitations and assumptions 109 8.3 One-way ANOVA 111 8.4 Multiway ANOVA 119 8.5 Further reading 127 9 Correlation and Regression 129 9.1 Introduction 129 9.2 Limitations and assumptions 130 9.3 Pearson’s product moment correlation 131 9.4 Simple linear regression 135 9.5 Correlation or regression? 142 9.6 Multiple linear regression 143 9.7 Comparing two lines 146 9.8 Fitting curves 148 9.9 Further reading 151 10 Multivariate ANOVA 153 10.1 Introduction 153 10.2 Limitations and assumptions 154 10.3 Null hypothesis 156 10.4 Description of the test 156 10.5 Interpreting the results 158 10.6 Further reading 161 11 Repeated Measures 163 11.1 Introduction 163 11.2 Methods for analysing repeated measures data 166 11.3 Designing repeated measures experiments 170 11.4 Further reading 170 12 Chi-square Tests 173 12.1 Introduction 173 12.2 Limitations and assumptions 174 12.3 Goodness of fit test 175 12.4 Test for association between two factors 178 12.5 Comparing proportions 181 12.6 Further reading 184 13 Non-parametric Tests 185 13.1 Introduction 185 13.2 Limitations and assumptions 188 13.3 Mann—Whitney U-test 189 13.4 Two-sample Kolmogorov—Smirnov test 191 13.5 Two-sample sign test 193 13.6 Kruskal—Wallis test 195 13.7 Friedman’s test 198 13.8 Spearman’s rank correlation 200 13.9 Further reading 203 14 Principal Component Analysis 205 14.1 Introduction 205 14.2 Limitations and assumptions 207 14.3 Description of the method 207 14.4 Interpreting the results 209 14.5 Further reading 218 15 Cluster Analysis 221 15.1 Introduction 221 15.2 Limitations and assumptions 222 15.3 Clustering observations 223 15.4 Clustering variables 226 15.5 Further reading 228 Appendices 229 A Calculations for statistical tests 231 B Concentration data for Chapters 14 and 15 247 C Using computer packages 249 D Choosing a test: decision table 261 E List of worked examples 265 Bibliography 271 Index 273

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Book SynopsisThe author presents a well tested approach using real examples taken from bio-medical research. He breaks down each problem into its components and where an unbiased partial test is found to exist, nonparametric combination methodology is used to determine overall solutions.Trade Review"the book is well written. It cand be useful and recommended for researchers and practitioners in a number of scientific disciplines...and for graduate students..." (Zentralblatt MATH, Vol.972, No.12, 2001) "...carefully presents a concise and mathematically rigorous treatment of permutation testing...could be used for a mathematically oriented graduate class...will form a source of recent reference material for research workers..." (Short Book Reviews, Vol. 22, No. 1, April 2002) "This book may herald a new era in biostatistics..." (Psychotherpay and Psychosomatics, September/October 2002) "...graduate and post-graduate students in some areas of physics and chemistry can benefit greatly from reading and using this book..." (The Statistician, Date Unknown)Table of ContentsPreface. Notation and Abbreviations. Introduction. Discussion of a Simple Testing Problem. Theory of Permutation Tests for One-Sample Problems. Examples of Univariate Multi-Sample Problems. Theory of Permutation Tests for Multi-Sample Problems. Nonparametric Combination Methodology. Examples of Nonparametric Combination. Permutation Analysis in Factorial Designs. Permutation Testing with Missing Data. The Behrens--Fisher Permutation Problem. Permutation Testing for Repeated Measurements. Further Applications. References. Index.

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Book SynopsisA guide which uses a problem solving approach and shows how to implement Monte Carlo methods, starting from first principles to advanced techniques.Table of ContentsPreface xi Acknowledgements xiii Mathematical Notation xv 1 Introduction 1 2 The Mathematics Behind Monte Carlo Methods 5 2.1 A Few Basic Terms in Probability and Statistics 5 2.2 Monte Carlo Simulations 7 2.2.1 Monte Carlo Supremacy 8 2.2.2 Multi-dimensional Integration 8 2.3 Some Common Distributions 9 2.4 Kolmogorov’s Strong Law 18 2.5 The Central Limit Theorem 18 2.6 The Continuous Mapping Theorem 19 2.7 Error Estimation for Monte Carlo Methods 20 2.8 The Feynman–Kac Theorem 21 2.9 The Moore–Penrose Pseudo-inverse 21 3 Stochastic Dynamics 23 3.1 Brownian Motion 23 3.2 Itô’s Lemma 24 3.3 Normal Processes 25 3.4 Lognormal Processes 26 3.5 The Markovian Wiener Process Embedding Dimension 26 3.6 Bessel Processes 27 3.7 Constant Elasticity Of Variance Processes 28 3.8 Displaced Diffusion 29 4 Process-driven Sampling 31 4.1 Strong versus Weak Convergence 31 4.2 Numerical Solutions 32 4.2.1 The Euler Scheme 32 4.2.2 The Milstein Scheme 33 4.2.3 Transformations 33 4.2.4 Predictor–Corrector 35 4.3 Spurious Paths 36 4.4 Strong Convergence for Euler and Milstein 37 5 Correlation and Co-movement 41 5.1 Measures for Co-dependence 42 5.2 Copulæ 45 5.2.1 The Gaussian Copula 46 5.2.2 The t-Copula 49 5.2.3 Archimedean Copulae 51 6 Salvaging a Linear Correlation Matrix 59 6.1 Hypersphere Decomposition 60 6.2 Spectral Decomposition 61 6.3 Angular Decomposition of Lower Triangular Form 62 6.4 Examples 63 6.5 Angular Coordinates on a Hypersphere of Unit Radius 65 7 Pseudo-random Numbers 67 7.1 Chaos 68 7.2 The Mid-square Method 72 7.3 Congruential Generation 72 7.4 Ran0 To Ran3 74 7.5 The Mersenne Twister 74 7.6 Which One to Use? 75 8 Low-discrepancy Numbers 77 8.1 Discrepancy 78 8.2 Halton Numbers 79 8.3 Sobol’ Numbers 80 8.3.1 Primitive Polynomials Modulo Two 81 8.3.2 The Construction of Sobol’ Numbers 82 8.3.3 The Gray Code 83 8.3.4 The Initialisation of Sobol’ Numbers 85 8.4 Niederreiter (1988) Numbers 88 8.5 Pairwise Projections 88 8.6 Empirical Discrepancies 91 8.7 The Number of Iterations 96 8.8 Appendix 96 8.8.1 Explicit Formula for the L2-norm Discrepancy on the Unit Hypercube 96 8.8.2 Expected L2-norm Discrepancy of Truly Random Numbers 97 9 Non-uniform Variates 99 9.1 Inversion of the Cumulative Probability Function 99 9.2 Using a Sampler Density 101 9.2.1 Importance Sampling 103 9.2.2 Rejection Sampling 104 9.3 Normal Variates 105 9.3.1 The Box–Muller Method 105 9.3.2 The Neave Effect 106 9.4 Simulating Multivariate Copula Draws 109 10 Variance Reduction Techniques 111 10.1 Antithetic Sampling 111 10.2 Variate Recycling 112 10.3 Control Variates 113 10.4 Stratified Sampling 114 10.5 Importance Sampling 115 10.6 Moment Matching 116 10.7 Latin Hypercube Sampling 119 10.8 Path Construction 120 10.8.1 Incremental 120 10.8.2 Spectral 122 10.8.3 The Brownian Bridge 124 10.8.4 A Comparison of Path Construction Methods 128 10.8.5 Multivariate Path Construction 131 10.9 Appendix 134 10.9.1 Eigenvalues and Eigenvectors of a Discrete-time Covariance Matrix 134 10.9.2 The Conditional Distribution of the Brownian Bridge 137 11 Greeks 139 11.1 Importance Of Greeks 139 11.2 An Up-Out-Call Option 139 11.3 Finite Differencing with Path Recycling 140 11.4 Finite Differencing with Importance Sampling 143 11.5 Pathwise Differentiation 144 11.6 The Likelihood Ratio Method 145 11.7 Comparative Figures 147 11.8 Summary 153 11.9 Appendix 153 11.9.1 The Likelihood Ratio Formula for Vega 153 11.9.2 The Likelihood Ratio Formula for Rho 156 12 Monte Carlo in the BGM/J Framework 159 12.1 The Brace–Gatarek–Musiela/Jamshidian Market Model 159 12.2 Factorisation 161 12.3 Bermudan Swaptions 163 12.4 Calibration to European Swaptions 163 12.5 The Predictor–Corrector Scheme 169 12.6 Heuristics of the Exercise Boundary 171 12.7 Exercise Boundary Parametrisation 174 12.8 The Algorithm 176 12.9 Numerical Results 177 12.10 Summary 182 13 Non-recombining Trees 183 13.1 Introduction 183 13.2 Evolving the Forward Rates 184 13.3 Optimal Simplex Alignment 187 13.4 Implementation 190 13.5 Convergence Performance 191 13.6 Variance Matching 192 13.7 Exact Martingale Conditioning 195 13.8 Clustering 196 13.9 A Simple Example 199 13.10 Summary 200 14 Miscellanea 201 14.1 Interpolation of the Term Structure of Implied Volatility 201 14.2 Watch Your CPU Usage 202 14.3 Numerical Overflow and Underflow 205 14.4 A Single Number or a Convergence Diagram? 205 14.5 Embedded Path Creation 206 14.6 How Slow is Exp()? 207 14.7 Parallel Computing And Multi-threading 209 Bibliography 213 Index 219

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Book SynopsisBased around a conference on financial modeling held in Milan in December 1999, this book brings together the leading names in quantitative finance to discuss the modeling techniques in a variety of areas of financial engineering.Table of ContentsPreface The Quantitative Finance Timeline (Paul Wilmott) Part I. New Directions in Equity Modelling Introduction Asymptotic analysis of stochastic volatility models (Henrik Rasmussen and Paul Wilmott) Passport options, a review (Antony Penaud) Equity Dividend Models (David Bakstein and Paul Wilmott) Isoperimetry, log-concavity and elasticity of option prices (Christer Borell) Part II. New Directions in Interest Rate Modelling Introduction Dynamic, deterministic and static optimal portfolio strategies in a mean-variance framework under stochastic interest rates (Isabelle Bajeux-Besnainou and Roland Portrait) Pricing bond options in a worst-case scenario (David Epstein and Paul Wilmott) Part III. New Directions in Risk Management Introduction Implementing VaR by Historical Simulation (Aldo Nassigh, Andrea Piazzetta and Ferdinando Samaria) CrashMetrics (Philip Hua and Paul Wilmott) Herding in financial markets: a role for psychology in explaining investor behaviour? (Henriëtte Prast) Further Reading Author Biographies Index

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Book SynopsisThis highly instructive, informal text that explains step by step how and why you need to tackle maths within the biological sciences. The skills taught in this informative book are introduced using a problem-solving approach that emphasises the biological background of the book rather than the mathematical theory.Table of ContentsMaths in Biology. Manipulating Numbers. Units and Conversions. Molarities and Dilutions. Areas and Volumes. Exponents and Logs. Introduction to Statistics. Descriptive Statistics. Probability. Inferential Statistics. Correlation and Regression. Appendix 1: Answers to Problems. Appendix 2: Software for Biologists. Appendix 3: Statistical Formulae and Tables. Appendix 4: Glossary. Index.

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Book SynopsisREAD ALL ABOUT IT! David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society.Originating from the Medical Research Council's biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries. Order a copy of this author's comprehensive text TODAY! The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synTrade Review"This is a terrific book and should be on the shelf of every professional that works in clinical trials or health-care evaluation. It gives a thorough pragmatic introduction to Bayesian methods for health-care interventions, provides many example along with data and software to reproduce the analyses, guides readers to areas where Bayesian methods are particularly valuable, and includes an excellent set of exercises." (Journal of the American Statistical Association, June 2009) "Bayesian Approaches to Clinical Trials and Health-Care Evaluation' is a clear and comprehensive text for biostatisticians who want to understand and apply Bayesian statistical methods to clinical research." (Journal of Clinical Best Practices, Nov 2008) "…an indispensable resource for all students and investigators who plan to incorporate Bayesian methods into their research." (The Annals of Pharmacotherapy, January 2005) "...a valuable resource for libraries, and those who are involved in quantitative health care evaluation..." (Royal Statistical Society, Vol.168, No.1, January 2005) "...The technical material is presented in an accessible style, and the examples given clearly illustrate the principles under discussion..." (Short Book Reviews, Vol.24, No.3, December 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...very well laid-out and easy to follow...a very good resource for teaching students..." (Statistical Methods in Medical Research, Vol 14, 2005) "I would use with pleasure and interest this book as a textbook..." (Metron Journal, Vol.63, No.2, 2005) "...I can pay the authors no higher tribute than to say that I would be proud to have written this book. It is elegant and it is destined to becoming a classic in the field." (Statistics in Medicine, 15th July 2005) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004)Table of ContentsPreface. List of examples. 1. Introduction. 1.1 What are Bayesian methods? 1.2 What do we mean by ‘health-care evaluation’? 1.3 A Bayesian approach to evaluation. 1.4 The aim of this book and the intended audience. 1.5 Structure of the book. 2. Basic Concepts from Traditional Statistical Analysis. 2.1 Probability. 2.1.1 What is probability? 2.1.2 Odds and log-odds. 2.1.3 Bayes theorem for simple events. 2.2 Random variables, parameters and likelihood. 2.2.1 Random variables and their distributions. 2.2.2 Expectation, variance, covariance and correlation. 2.2.3 Parametric distributions and conditional independence. 2.2.4 Likelihoods. 2.3 The normal distribution. 2.4 Normal likelihoods. 2.4.1 Normal approximations for binary data. 2.4.2 Normal likelihoods for survival data. 2.4.3 Normal likelihoods for count responses. 2.4.4 Normal likelihoods for continuous responses. 2.5 Classical inference. 2.6 A catalogue of useful distributions*. 2.6.1 Binomial and Bernoulli. 2.6.2 Poisson. 2.6.3 Beta. 2.6.4 Uniform. 2.6.5 Gamma. 2.6.6 Root-inverse-gamma. 2.6.7 Half-normal. 2.6.8 Log-normal. 2.6.9 Student’s t. 2.6.10 Bivariate normal. 2.7 Key points. Exercises. 3. An Overview of the Bayesian Approach. 3.1 Subjectivity and context. 3.2 Bayes theorem for two hypotheses. 3.3 Comparing simple hypotheses: likelihood ratios and Bayes factors. 3.4 Exchangeability and parametric modelling*. 3.5 Bayes theorem for general quantities. 3.6 Bayesian analysis with binary data. 3.6.1 Binary data with a discrete prior distribution. 3.6.2 Conjugate analysis for binary data. 3.7 Bayesian analysis with normal distributions. 3.8 Point estimation, interval estimation and interval hypotheses. 3.9 The prior distribution. 3.10 How to use Bayes theorem to interpret trial results. 3.11 The ‘credibility’ of significant trial results*. 3.12 Sequential use of Bayes theorem*. 3.13 Predictions. 3.13.1 Predictions in the Bayesian framework. 3.13.2 Predictions for binary data*. 3.13.3 Predictions for normal data. 3.14 Decision-making. 3.15 Design. 3.16 Use of historical data. 3.17 Multiplicity, exchangeability and hierarchical models. 3.18 Dealing with nuisance parameters*. 3.18.1 Alternative methods for eliminating nuisance parameters*. 3.18.2 Profile likelihood in a hierarchical model*. 3.19 Computational issues. 3.19.1 Monte Carlo methods. 3.19.2 Markov chain Monte Carlo methods. 3.19.3 WinBUGS. 3.20 Schools of Bayesians. 3.21 A Bayesian checklist. 3.22 Further reading. 3.23 Key points. Exercises. 4. Comparison of Alternative Approaches to Inference. 4.1 A structure for alternative approaches. 4.2 Conventional statistical methods used in health-care evaluation. 4.3 The likelihood principle, sequential analysis and types of error. 4.3.1 The likelihood principle. 4.3.2 Sequential analysis. 4.3.3 Type I and Type II error. 4.4 P-values and Bayes factors*. 4.4.1 Criticism of P-values. 4.4.2 Bayes factors as an alternative to P-values: simple hypotheses. 4.4.3 Bayes factors as an alternative to P-values: composite hypotheses. 4.4.4 Bayes factors in preference studies. 4.4.5 Lindley’s paradox. 4.5 Key points. Exercises. 5. Prior Distributions. 5.1 Introduction. 5.2 Elicitation of opinion: a brief review. 5.2.1 Background to elicitation. 5.2.2 Elicitation techniques. 5.2.3 Elicitation from multiple experts. 5.3 Critique of prior elicitation. 5.4 Summary of external evidence*. 5.5 Default priors. 5.5.1 ‘Non-informative’ or ‘reference’ priors: 5.5.2 ‘Sceptical’ priors. 5.5.3 ‘Enthusiastic’ priors. 5.5.4 Priors with a point mass at the null hypothesis (‘lump-and-smear’ priors)*. 5.6 Sensitivity analysis and ‘robust’ priors. 5.7 Hierarchical priors. 5.7.1 The judgement of exchangeability. 5.7.2 The form for the random-effects distribution. 5.7.3 The prior for the standard deviation of the random effects*. 5.8 Empirical criticism of priors. 5.9 Key points. Exercises. 6. Randomised Controlled Trials. 6.1 Introduction. 6.2 Use of a loss function: is a clinical trial for inference or decision? 6.3 Specification of null hypotheses. 6.4 Ethics and randomisation: a brief review. 6.4.1 Is randomisation necessary? 6.4.2 When is it ethical to randomise? 6.5 Sample size of non-sequential trials. 6.5.1 Alternative approaches to sample-size assessment. 6.5.2 ‘Classical power’: hybrid classical-Bayesian methods assuming normality. 6.5.3 ‘Bayesian power’. 6.5.4 Adjusting formulae for different hypotheses. 6.5.5 Predictive distribution of power and necessary sample size. 6.6 Monitoring of sequential trials. 6.6.1 Introduction. 6.6.2 Monitoring using the posterior distribution. 6.6.3 Monitoring using predictions: ‘interim power’. 6.6.4 Monitoring using a formal loss function. 6.6.5 Frequentist properties of sequential Bayesian methods. 6.6.6 Bayesian methods and data monitoring committees. 6.7 The role of ‘scepticism’ in confirmatory studies. 6.8 Multiplicity in randomised trials. 6.8.1 Subset analysis. 6.8.2 Multi-centre analysis. 6.8.3 Cluster randomization. 6.8.4 Multiple endpoints and treatments. 6.9 Using historical controls*. 6.10 Data-dependent allocation. 6.11 Trial designs other than two parallel groups. 6.12 Other aspects of drug development. 6.13 Further reading. 6.14 Key points. Exercises. 7. Observational Studies. 7.1 Introduction. 7.2 Alternative study designs. 7.3 Explicit modelling of biases. 7.4 Institutional comparisons. 7.5 Key points. Exercises. 8. Evidence Synthesis. 8.1 Introduction. 8.2 ‘Standard’ meta-analysis. 8.2.1 A Bayesian perspective. 8.2.2 Some delicate issues in Bayesian meta-analysis. 8.2.3 The relationship between treatment effect and underlying risk. 8.3 Indirect comparison studies. 8.4 Generalised evidence synthesis. 8.5 Further reading. 8.6 Key points. Exercises. 9. Cost-effectiveness, Policy-Making and Regulation. 9.1 Introduction. 9.2 Contexts. 9.3 ‘Standard’ cost-effectiveness analysis without uncertainty. 9.4 ‘Two-stage’ and integrated approaches to uncertainty in cost-effectiveness modeling. 9.5 Probabilistic analysis of sensitivity to uncertainty about parameters: two-stage approach. 9.6 Cost-effectiveness analyses of a single study: integrated approach. 9.7 Levels of uncertainty in cost-effectiveness models. 9.8 Complex cost-effectiveness models. 9.8.1 Discrete-time, discrete-state Markov models. 9.8.2 Micro-simulation in cost-effectiveness models. 9.8.3 Micro-simulation and probabilistic sensitivity analysis. 9.8.4 Comprehensive decision modeling. 9.9 Simultaneous evidence synthesis and complex cost-effectiveness modeling. 9.9.1 Generalised meta-analysis of evidence. 9.9.2 Comparison of integrated Bayesian and two-stage approach. 9.10 Cost-effectiveness of carrying out research: payback models. 9.10.1 Research planning in the public sector. 9.10.2 Research planning in the pharmaceutical industry. 9.10.3 Value of information. 9.11 Decision theory in cost-effectiveness analysis, regulation and policy. 9.12 Regulation and health policy. 9.12.1 The regulatory context. 9.12.2 Regulation of pharmaceuticals. 9.12.3 Regulation of medical devices. 9.13 Conclusions. 9.14 Key points. Exercises. 10. Conclusions and Implications for Future Research. 10.1 Introduction. 10.2 General advantages and problems of a Bayesian approach. 10.3 Future research and development. Appendix: Websites and Software. A.1 The site for this book. A.2 Bayesian methods in health-care evaluation. A.3 Bayesian software. A.4 General Bayesian sites. References. Index.

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Book SynopsisPraise for the First Edition Anyone interested in getting an introduction to Ramsey theorywill find this illuminating... --MAA Reviews Covering all the major concepts, proofs, and theorems, theSecond Edition of Ramsey Theory is the ultimate guideto understanding every aspect of Shelah''s proof, as well asthe original proof of van der Waerden. The book offers a historicalperspective of Ramsey''s fundamental paper from 1930 andErdos'' and Szekeres'' article from 1935, while placingthe various theorems in the context of T. S. Motzkin''sthought on the subject of Complete Disorder isImpossible. Ramsey Theory, Second Edition includes new and excitingcoverage of Graph Ramsey Theory and Euclidean Ramsey Theory andalso relates Ramsey Theory to other areas in discrete mathematics.In addition, the book features the unprovability results of Parisand Harrington and the methods from topological dynamics pioneeredby Furstenburg. Featuring worked proofs and outsTrade Review"Anyone interested in getting an introduction to Ramsey theory will find this illuminating…" (MAA Reviews, December 17, 2006)Table of ContentsSets. Progressions. Equations. Numbers. Particulars. Beyond Combinatorics. References. Index.

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Book SynopsisDevelops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form.Table of ContentsABELIAN FUNCTIONS. Power Series in Several Variables. The Preparation Theorem. Regular Functions. Meromorphic Functions. The Theorem of Weierstrass and Cousin. The Period Group. Jacobian Functions. Linearization of the Exponent System. The Period Relations. The Reduced Exponent System. Existence Proofs. Picard Varieties. The Addition Theorem. MODULAR FUNCTIONS OF SEVERAL VARIABLES. Automorphic Functions of Several Variables. Algebraic Relations Between Automorphic Functions. Symplectic Geometry. Abelian Functions and Modular Functions. The Fundamental Region of the Modular Group. Modular Forms. The Field of Modular Functions. Algebraic Dependence. Bibliography. Cumulative Index Volumes I, II, and III.

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Book SynopsisThis established introduction to differential geometry aims to make this branch of mathematics accessible to the non-specialist by the use of three different notations: vector algebra and calculus, tensor calculus and the notation devised by Cartan.Table of ContentsChapter I Operations with Vectors. Chapter II Plane Curves. Chapter III Space Curves. Chapter IV The Basic Elements of Surface Theory. Chapter V Some Special Surfaces. Chapter VI The Partial Differential Equations of SurfaceTheory. Chapter VII Inner Differential Geometry in the Small from theExtrinsic Point of View. Chapter VIII Differential Geometry in the Large. Chapter IX Intrinsic Diferential Geometry of Manifolds.Relativity. Chapter X The Wedge Product and the Exterior Derivative ofDifferential Forms, with Applications to Surface Theory. Appendix A Tensor Algebra in Affine, Euclidean, and MinkowskiSpaces. Appendix B Differential Equations. Bibliography. Index.

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Book SynopsisIn this text the authors take the reader from the elements of linear algebra past the frontier of homological algebra. They describe different algebraic domains and then emphasize the similarities and differences between them, employing the terminology of categories and functors.Table of ContentsPartial table of contents: GROUPS. Cosets, Lagrange's Theorem, and Normal Subgroups. Direct and Free Products. ABELIAN GROUPS. Special Features of Commutative Groups. Exact Sequences of Abelian Groups. CATEGORIES AND FUNCTORS. Natural Transformations. Duality Principle. Adjoint Functors. MODULES. Rings. The Functor Hom. INTEGRAL DOMAINS. SEMI-SIMPLE RINGS. The Morita Theorem. THE FUNCTORS EXT AND TOR. List of Symbols. Bibliography. Index.

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Book SynopsisThis classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.Table of ContentsPart I Triangles 3 Regular Polygons 26 Isometry in the Euclidean Plane 39 Two-Dimensional Crystallography 50 Similarity in the Euclidean Plane 67 Circles and Spheres 77 Isometry and Similarity in Euclidean Space 96 Part II Coordinates 107 Complex Numbers 135 The Five Platonic Solids 148 The Golden Section and Phyllotaxis 160 Part III Ordered Geometry 175 Affine Geometry 191 Projective Geometry 229 Absolute Geometry 263 Hyperbolic Geometry 287 Part IV Differential Geometry of Curves 307 The Tensor Notation 328 Differential Geometry of Surfaces 342 Geodesics 366 Topology of Surfaces 379 Four-Dimensional Geometry 396 Tables 413 References 415 Answers to Exercises 419 Index 459

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Book SynopsisThis adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.Table of ContentsBasic Concepts. Trees, Cutsets, and Circuits. Eulerian and Hamiltonian Graphs. Graphs and Vector Spaces. Directed Graphs. Matrices of a Graph. Planarity and Duality. Connectivity and Matching. Covering and Coloring. Matroids. Graph Algorithms. Flows in Networks. Indexes.

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Book SynopsisDevelops an introductory and relatively simple account of the theory and application of the evolutionary type of stochastic process. Professor Bailey adopts the heuristic approach of applied mathematics and develops both theoretical principles and applied techniques simultaneously.Table of ContentsGenerating Functions. Recurrent Events. Random Walk Models. Markov Chains. Discrete Branching Processes. Markov Processes in Continuous Time. Homogeneous Birth and Death Processes. Some Non-Homogeneous Processes. Multi-Dimensional Processes. Queueing Processes. Epidemic Processes. Competition and Predation. Diffusion Processes. Approximations to Stochastic Processes. Some Non-Markovian Processes. References. Solutions to Problems. Indices.

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Book SynopsisA systematic account of the development of stochastic processes over the last 20 years. A supplement contained within the text includes a treatment of the various aspects of measure theory. There is also a chapter on the specialized problem of prediction theory.Table of ContentsIntroduction and Probability Background. Definition of a Stochastic Process--Principal Classes. Processes with Mutually Independent Random Variables. Processes with Mutually Uncorrelated or Orthogonal Random Variables. Markov Processes--Discrete Parameter. Markov Processes--Continuous Parameter. Martingales. Processes with Independent Increments. Processes with Orthogonal Increments. Stationary Processes--Discrete Parameter. Stationary Processes--Continuous Parameter. Linear Least Squares Prediction--Stationary (Wide Sense) Processes. Supplement. Appendix. Bibliography. Index.

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Book SynopsisPresents methods for the design and analysis of surveys, studies, and experiments when the data is qualitative and categorical. This work also covers the delta methods for multinomial frequencies. It discusses topics in misclassification and in reliability assessment.Trade Review"A well written specialized book by Fleiss et al. illustrates in detail the definitions and importance of rates in health and other data analysis." (Journal of Statistical Computation and Simulation, April 2005) "…the definitive text of context, method and application for the efficient analysis of rates and proportions…" (Statistics in Medicine, Vol 24 (17), 15th September 2005) "…well written in a thoroughly readable style. I highly recommend this book…" (Statistical Methods in Medical Research, Vol. 14, 2005) "…persons who regularly encounter this type of data would certainly want this book available as one of their desk-top references." (Technometrics, May 2004)Table of ContentsPreface. Preface to the Second Edition. Preface to the First Edition. 1. An Introduction to Applied Probability. 2. Statistical Inference for a Single Proportion. 3. Assessing Significance in a Fourfold Table. 4. Determining Sample Sizes Needed to Detect a Difference Between Two Proportions. 5. How to Randomize. 6. Comparative Studies: Cross-Sectional, Naturalistic, or Multinomial Sampling. 7. Comparative Studies: Prospective and Retrospective Sampling. 8. Randomized Controlled Trials. 9. The Comparison of Proportions from Several Independent Samples. 10. Combining Evidence from Fourfold Tables. 11. Logistic Regression. 12. Poisson Regression. 13. Analysis of Data from Matched Samples. 14. Regression Models for Matched Samples. 15. Analysis of Correlated Binary Data. 16. Missing Data. 17. Misclassification Errors: Effects, Control, and Adjustment. 18. The Measurement of Interrater Agreement. 19. The Standardization of Rates. Appendix A. Numerical Tables. Appendix B. The Basic Theory of Maximum Likelihood Estimation. Appendix C. Answers to Selected Problems. Author Index. Subject Index.

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Book SynopsisMultivariable Mathematics combines linear algebra and multivariable calculus in a rigorous approach. The material is integrated to emphasize the role of linearity in all of calculus and the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author addresses all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible and also including complete proofs. By emphasizing the theoretical aspects and reviewing the linear algebra material quickly, the book can also be used as a text for an advanced calculus or multivariable analysis course culminating in a treatment of manifolds, differential forms, and the generalized Stokes's Theorem.Table of ContentsPreface. Chapter 1. Vectors and Matrices. 1.1 Vectors in Rn.. 1.2 Dot Product. 1.3 Subspaces of Rn. 1.4 Linear Transformations and Matrix Algebra. 1.5 Introduction to Determinates and the Cross Product. Chapter 2. Functions, Limits, and Continuity. 2.1. Scalar- and Vector-Valued Functions. 2.2. A Bit of Topology in Rn. 2.3. Limits and Continuity. Chapter 3. The Derivative. 3.1. Partial Derivatives and Directional Derivatives. 3.2. Differentiability. 3.3. Differentiation Rules. 3.4. The Gradient. 3.5. Curves. 3.6. Higher-Order Partial Derivatives. Chapter 4. Implicit and Explicit Solutions of Linear Systems. 4.1. Gaussian Elimination and the Theory of Linear Systems. 4.2. Elementary Matrices and Calculating Inverse Matrices. 4.3. Linear Independence, Basis, and Dimension. 4.4. The Four Fundamental Subspaces. 4.5. The Nonlinear Case: Introduction to Manifolds. Chapter 5. Extremum Problems. 5.1. Compactness and the Maximum Value Theorem. 5.2. Maximum/Minimum Problems. 5.3. Quadratic Forms and the Second Derivative Test. 5.4. Lagrange Multipliers. 5.5. Projections, Least Squares, and Inner Product Spaces. Chapter 6. Solving Nonlinear Problems. 6.1. The Contraction Mapping Principle. 6.2. The Inverse and Implicit Function Theorems. 6.3. Manifolds Revisited. Chapter 7. Integration. 7.1. Multiple Integrals. 7.2. Iterated Integrals and Fubini’s Theorem. 7.3. Polar, Cylindrical, and Spherical Coordinates. 7.4. Physical Applications. 7.5. Determinants and n-Dimensional Volume. 7.6. Change of Variables Theorem. Chapter 8. Differential Forms and Integration on Manifolds. 8.1. Motivation. 8.2. Differential Forms. 8.3. Line Integrals and Green’s Theorem. 8.4. Surface Integrals and Flux. 8.5. Stokes’s Theorem. 8.6. Applications to Physics. 8.7. Applications to Topology. 9. Eigenvalues, Eigenvectors, and Applications. 9.1. Linear Transformations and Change of Basis. 9.2. Eigenvalues, Eigenvectors, and Diagonalizability. 9.3. Difference Equations and Ordinary Differential Equations. 9.4. The Spectral Theorem. Glossary of Notations and Results from Single-Variable Calculus. For Further Reading. Answers to Selected Exercises. Index.

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Book SynopsisExplores the application of bootstrap to problems that place unusual demands on the method. The bootstrap method, introduced by Bradley Efron in 1973, is a nonparametric technique for inferring the distribution of a statistic derived from a sample.Table of ContentsPartial table of contents: GENERAL PRINCIPLES OF THE BOOTSTRAP. On the Bootstrap of M-Estimators and Other Statistical Functionals(M. Arcones & E. Gine). Bootstrapping Markov Chains (K. Athreya & C. Fuh). Six Questions Raised by the Bootstrap (B. Efron). Efficient Bootstrap Simulation (P. Hall). Bootstrapping Signs (R. LePage). Bootstrap Bandwidth Selection (J. Marron). APPLICATIONS OF THE BOOTSTRAP. A Generalized Bootstrap (E. Bedrick & J. Hill). Bootstrapping Admissible Linear Model Selection Procedures (D.Brownstone). A Hazard Process for Survival Analysis (J. Hsieh). A Nonparametric Density Estimation Based Resampling Algorithm (M.Taylor & J. Thompson). Nonparametric Rank Estimation Using Bootstrap Resampling andCanonical Correlation Analysis (X. Tu, et al.). Index.

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Book Synopsis"Dunham writes for nonspecialists, and they will enjoy his piquant anecdotes and amusing asides -- Booklist "Artfully, Dunham conducts a tour of the mathematical universe... he believes these ideas to be accessible to the audience he wants to reach, and he writes so that they are.Table of ContentsArithmetic. Bernoulli Trials. Circle. Differential Calculus. Euler. Fermat. Greek Geometry. Hypotenuse. Isoperimetric Problem. Justification. Knighted Newton. Lost Leibniz. Mathematical Personality. Natural Logarithm. Origins. Prime Number Theorem. Quotient. Russell's Paradox. Spherical Surface. Trisection. Utility. Venn Diagram. Where Are the Women? X-Y Plane. Z. Afterword. Notes. Index.

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Book SynopsisMeets the need for a program of short courses involving the essentials of a number of mathematical topics taken by physics and engineering students. Basically applications-oriented, the courses do include selected topics of abstract mathematics. While several courses can be used as practical appendices to conventional mathematics, others serve as introductions, providing motivation for self-study in areas of conceptual math.Table of ContentsDistributions. Spectral Theory of Operators. Asymptotic Methods. Difference Equations. Complex Integration. Symbolic Methods. Probability. Perturbation Theory. Bibliography.

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Book SynopsisThis study deals with the calculations of mathematical expectations, primarily by simulation methods. The authors explore the present state of research and signal the types of problems raised by new methods. Topics discussed include Monte Carlo methods and the simulation of stochastic processes.Table of ContentsPreliminaries. Computation of Expectations in Finite Dimension. Simulation of Random Processes. Deterministic Resolution of Some Markovian Problems. Stochastic Differential Equations and Brownian Functionals. Notes. References. Index.

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Book SynopsisA comprehensive overview of experimental design at the advanced level The development and introduction of new experimental designs in the last fifty years has been quite staggering and was brought about largely by an ever-widening field of applications.Trade Review"…a massively impressive work of scholarship…" (Short Book Reviews, December 2006) "...a broad and in-depth book...covers not only classic but also up-to-date results and references, making it convenient for researchers. It is one of the very few advanced textbooks on experimental design..." (Technometrics, November 2006) "I suspect this excellent book will be used most often by specialists in design...the book's importance is largely as a reference for experts...or as an independent learning tool…" (Journal of the American Statistical Association, June 2006) "I would expect HK to attain essentially the same stature and appeal to virtually the same markets as the 1952 edition." (Journal of Quality Technology, January 2006) "…the authors have done a commendable job in putting together the vast amount of literature that is available on the topics…of great value to students, and also to teachers and researchers." (Mathematical Reviews, 2006b)Table of Contents1. General Incomplete Block Design. 2. Balanced Incomplete Block Designs. 3. Construction of Balanced Incomplete Block Designs. 4. Partially Balanced Incomplete Block Designs. 5. Construction of Partially Balanced Incomplete Block Designs. 6. More Block Designs and Blocking Structures. 7. Two-level Factorial Designs. 8. Confounding In 2¯n Factorial Designs. 9. Partial Confounding In 2¯n Factorial Designs. 10. Designs with Factors at Three Levels. 11. The General Symmetrical Factorial Design. 12. Confounding in Asymmetrical Factorial Designs. 13. Fractional Factorial Designs. 14. Main Effect Plans. 15. Supersaturated Designs. 16. Search Designs. 17. Robust-Design Experiments. 18. Lattice Designs. 19. Cross-Over Designs. Appendix A. Fields and Galois Fields. Appendix B. Finite Geometries. Appendix C. Orthogonal and Balanced Arrays. Appendix D. Selected Asymmetrical Balanced Factorial Designs. References.

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Book SynopsisThe subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accomTable of ContentsMoving Average and Autoregressive Processes. Introduction to Fourier Analysis. Spectral Theory and Filtering. Some Large Sample Theory. Estimation of the Mean and Autocorrelations. The Periodogram, Estimated Spectrum. Parameter Estimation. Regression, Trend, and Seasonality. Unit Root and Explosive Time Series. Bibliography. Index.

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Book SynopsisDesigned to aid readers in gathering the most reliable quantitative information on forests for the least cost.Table of ContentsFocus, Fundamental Concepts, and Theory. Probabilistic Sampling Strategies. Forest Sampling--Single Level. Multi-Information Sources for Sampling. Model-Based Inference. Mensurational Aspects of Forest Inventory. Related Sampling Topics. Related Estimation Topics. Future Directions in Multiresource Sampling in Forestry. References. Answers to the Problems. Index.

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Book SynopsisQueueing theory is an effective tool for studying several performance parameters of computer systems. This book discusses the difficult subject of queuing theory is by working on information processing problems.Table of ContentsA Queueing Theory Primer. Random Processes. Birth-Death Queueing Systems. Markovian Queues. The Queue M/G/1. The Queue G/M/m. The Queue G/G/1. Index.

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Book SynopsisIncludes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.Trade Review"...an excellent source of facts for anyone working in functional analysis or operator theory." (Journal of Operator Theory, Vol.53, No.1, 2005) "For years Lax has been counted among the world's very top people in PDEs, so no serious student can afford to ignore his view of the foundations leading up to that subject." (Choice, Vol. 40, No. 4, December 2002) "...attractive...well suited for graduate courses...and useful for research mathematicians." (Mathematical Reviews, 2003a) "...The book is highly recommended to all students of analysis". (Zentralblatt MATH, Vol.1009, No.9, 2003) "A lot of good material, doled out in short chapters." (American Mathematical Monthly, August/September 2003)Table of ContentsForeword. Linear Spaces. Linear Maps. The Hahn-Banach Theorem. Applications of the Hahn-Banach Theorem. Normed Linear Spaces. Hilbert Space. Applications of Hilbert Space Results. Duals of Normed Linear Space. Applications of Duality. Weak Convergence. Applications of Weak Convergence. The Weak and Weak* Topologies. Locally Convex Topologies and the Krein-Milman Theorem. Examples of Convex Sets and their Extreme Points. Bounded Linear Maps. Examples of Bounded Linear Maps. Banach Algebras and their Elementary Spectral Theory. Gelfand's Theory of Commutative Banach Algebras. Applications of Gelfand's Theory of Commutative Banach Algebras. Examples of Operators and their Spectra. Compact Maps. Examples of Compact Operators. Positive Compact Operators. Fredholm's Theory of Integral Equations. Invariant Subspaces. Harmonic Analysis on a Halfline. Index Theory. Compact Symmetric Operators in Hilbert Space. Examples of Compact Symmetric Operators. Trace Class and Trace Formula. Spectral Theory of Symmetric, Normal and Unitary Operators. Spectral Theory of Self-Adjoint Operators. Examples of Self-Adjoint Operators. Semigroups of Operators. Groups of Unitary Operators. Examples of Strongly Continuous Semigroups. Scattering Theory. A Theorem of Beurling. Appendix A: The Riesz-Kakutani Representation Theorem. Appendix B: Theory of Distributions. Appendix C: Zorn's Lemma. Author Index. Subject Index.

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Book SynopsisA state-of-the-art approach to urban travel demand modeling Currently used travel forecasting methodology was developed almostthree decades ago, primarily to assess the impacts of large-scalecapital improvement projects, and was not designed to deal withcontemporary urban transportation problems. To be effective today,travel demand models must explicitly represent traveler behavior,must be policy-sensitive, and must be operationally reliable. Urban Travel Demand Modeling: From Individual Choices to GeneralEquilibrium presents an integrated system of models which overhaulthe four traditional phases of travel generation, modal split, tripdistribution, and network assignment. This book shows, for thefirst time, how generalized network equilibrium may be rigorouslyforecast from the optimal travel choices of trip consumerswithout the need to resort to heuristic procedures such asfeedbacks. In addition, models for optimal transportation supplydecisions are integrated with tTable of ContentsModeling Travelers' Decisions as Discrete Choices. Route Choice on Uncongested Networks. Combined Travel Demand Modeling Under Uncongested Conditions. Route Choice Modeling Under Congested Conditions. Combined Travel Demand Modeling Under Congested Conditions. Model Parameter Estimation. Joint Equilibrium Modeling of Activity and Travel Systems. Optimal Transportation Supply. Appendices. Bibliography. Indexes.

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Book SynopsisCombines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.Table of ContentsResampling-Based Adjustments: Basic Concepts. Continuous Data Applications: Univariate Analysis. Continuous Data Applications: Multivariate Analysis. Binary Data Applications. Further Topics. Practical Applications. Appendices. References. List of Algorithms. List of Examples. Indexes.

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Book SynopsisThis book discusses adaptive sampling designs which are used in surveys where data collection requires modification as a result of observations made during the process. The strategies detailed in the book offer solutions to the long-standing problem of estimating the abundance of rare, clustered populations.Table of ContentsFixed-Population Sampling Theory. Stochastic Population Sampling Theory. Adaptive Cluster Sampling. Efficiency and Sample Size Issues. Adaptive Cluster Sampling Based on Order Statistics. Adaptive Allocation in Stratified Sampling. Multivariate Aspects of Adaptive Sampling. Detectability in Adaptive Sampling. Optimal Sampling Strategies. References. Index.

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Book SynopsisA complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms.Table of ContentsProblems and Algorithms. Optimal Trees and Paths. Maximum Flow Problems. Minimum-Cost Flow Problems. Optimal Matchings. Integrality of Polyhedra. The Traveling Salesman Problem. Matroids. NP and NP-Completeness. Appendix. Bibliography. Index.

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