Mathematical and statistical software Books

Book SynopsisOffers coverage of basic and advanced statistical methods, concentrating on graphical inspection, and featuring step-by-step instruction to help non-statisticians understand the methodology.Trade Review"...suitable as a reference book for experienced statisticians, a vehicle for learning the S statistical computing language, or a resource for statistics instructors..." (The American Statistician, Vol. 58, No. 1, February 2004) "...especially useful as an introduction to a wide variety of data analysis techniques." (R News) "...The book is well written - there is an air of common sense throughout - and is at a level which ensures its usefulness for a wide range of readers..." (Zentralblatt Math, Vol. 1001, No.01, 2003) "...the book is a useful and practical introduction to many areas of statistical data analysis." (Computational STatistics & Data Analysis) "...surely not the last statistics book you’ll ever need, but it might well be the first you will ever really use." (Basic Applied Ecology, Vol. 4, No. 3) "...recommended...contains a wealth of sage advice..." (Technometrics, Vol. 45, No. 4, November 2003) “...a practical introduction to statistics...does not cover all...sophisticated statistical and graphical features of the S-Plus system, but provides a first class starting point—and, probably, for most readers, a sufficient end point.” (Quarterly of Applied Mathematics, LXI, No. 4, December 2003) “…a valiant and useful first attempt to present both statistics and S-PLUS together…” (Journal of The Royal Statistical Society Vol.167 No.4) Table of ContentsStatistical methods Introduction to S-Plus Experimental design Central tendency Probability Variance The Normal distribution Power calculations Understanding data: graphical analysis Understanding data: tabular analysis Classical tests Bootstrap and jackknife Statistical models in S-Plus Regression Analysis of variance Analysis of covariance Model criticism Contrasts Split-plot Anova Nested designs and variance components analysis Graphs, functions and transformations Curve fitting and piecewise regression Non-linear regression Multiple regression Model simplification Probability distributions Generalised linear models Proportion data: binomial errors Count data: Poisson errors Binary response variables Tree models Non-parametric smoothing Survival analysis Time series analysis Mixed effects models Spatial statistics Bibliography Index

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Book SynopsisLearn statistical methods quickly and easily with the discovery method With its emphasis on the discovery method, this publication encourages readers to discover solutions on their own rather than simply copy answers or apply a formula by rote.Trade Review“…the books have plenty of wise advice for the application of statistics…” (Bulletin of Mathematical Biology,2007)Table of ContentsPreface. 1. Variation (or What Statistics Is All About). 2. Probability. 3. Distributions. 4. Testing Hypotheses. 5. Designing an Experiment or Survey. 6. Analyzing Complex Experiments. 7. Developing Models. 8. Reporting Your Findings. 9. Problem Solving. Appendix: An Microsoft Office Excel Primer. Index to Excel and Excel Add-In Functions. Subject Index.

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Book SynopsisSome probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to geTrade Review"The problems are accessible but still realistic enough to be engaging, and the solutions in the back of the book will get you through any sticky spots. Writing your own versions of a few of these programs will acquaint you with a useful approach to problem solving and a novel style of thinking."--Brian Hayes, American Scientist "Digital Dice will appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder."--Games Magazine "[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets. Digital Dice will appeal to all who like recreational mathematics."--Alan Stevens, Mathematics Today "[T]he book is targeted at teachers and students of probability theory or computer science, as well as aficionados of recreational mathematics, but anyone who is familiar with the basics of probability and is capable of writing simple computer programs will have no problem working their way through this interesting and rewarding book."--Physics World "After the appearance of the author's earlier book on probability problems, [Duelling Idiots And Other Probability Puzzlers], one has high expectations for this book, and one is not disappointed... The book will certainly have great appeal to all three of the targeted audiences."--G A. Hewer, Mathematical Reviews "This well-written entertaining collection of twenty-one probability problems presents their origin and history as well as their computer solutions... These problems could be used in a computer programming course or a probability course that includes Monte Carlo simulations."--Thomas Sonnabend, Mathematics Teacher "All of the books by Nahin and Havil are worth having, including others not listed here. I particularly recommend Digital Dice for the task of teaching undergraduates in mathematics the fundamentals of computation and simulation."--James M. Cargal, The UMAP JournalTable of ContentsPreface to the Paperback Edition xiii Introduction 1 The Problems 35 1. The Clumsy Dishwasher Problem 37 2. Will Lil and Bill Meet at the Malt Shop? 38 3. A Parallel Parking Question 40 4. A Curious Coin-Flipping Game 42 5. The Gamow-Stern Elevator Puzzle 45 6. Steve's Elevator Problem 48 7. The Pipe Smoker's Discovery 51 8. A Toilet Paper Dilemma 53 9. The Forgetful Burglar Problem 59 10. The Umbrella Quandary 61 11. The Case of the Missing Senators 63 12. How Many Runners in a Marathon? 65 13. A Police Patrol Problem 69 14. Parrondo's Paradox 74 15. How Long Is the Wait to Get the Potato Salad? 77 16. The Appeals Court Paradox 81 17. Waiting for Buses 83 18. Waiting for Stoplights 85 19. Electing Emperors and Popes 87 20. An Optimal Stopping Problem 91 21. Chain Reactions, Branching Processes, and Baby Boys 96 MATLAB Solutions To The Problems 101 1. The Clumsy Dishwasher Problem 103 2. Will Lil and Bill Meet at the Malt Shop? 105 3. A Parallel Parking Question 109 4. A Curious Coin-Flipping Game 114 5. The Gamow-Stern Elevator Puzzle 120 6. Steve's Elevator Problem 124 7. The Pipe Smoker's Discovery 129 8. A Toilet Paper Dilemma 140 9. The Forgetful Burglar Problem 144 10. The Umbrella Quandary 148 11. The Case of the Missing Senators 153 12. How Many Runners in a Marathon? 157 13. A Police Patrol Problem 160 14. Parrondo's Paradox 169 15. How Long is the Wait to Get the Potato Salad? 176 16. The Appeals Court Paradox 184 17. Waiting for Buses 187 18. Waiting for Stoplights 191 19. Electing Emperors and Popes 197 20. An Optimal Stopping Problem 204 21. Chain Reactions, Branching Processes, and Baby Boys 213 Appendix 1. One Way to Guess on a Test 221 Appendix 2. An Example of Variance-Reduction in the Monte Carlo Method 223 Appendix 3. Random Harmonic Sums 229 Appendix 4. Solving Montmort's Problem by Recursion 231 Appendix 5. An Illustration of the Inclusion-Exclusion Principle 237 Appendix 6. Solutions to the Spin Game 244 Appendix 7. How to Simulate Kelvin's Fair Coin with a Biased Coin 248 Appendix 8. How to Simulate an Exponential Random Variable 252 Appendix 9. Index to Author-Created MATLAB m-Files in the Book 255 Glossary 257 Acknowledgments 259 Index 261 Also by Paul J. Nahin 265

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Book SynopsisThis introduction to computer-based problem-solving using the MATLAB environment is highly recommended for students wishing to learn the concepts and develop the programming skills that are fundamental to computational science and engineering (CSE). Through a 'teaching by examples' approach, the authors pose strategically chosen problems to help first-time programmers learn these necessary concepts and skills. Each section formulates a problem and then introduces those new MATLAB language features that are necessary to solve it. This approach puts problem-solving and algorithmic thinking first and syntactical details second. Each solution is followed by a 'talking point' that concerns some related, larger issue associated with CSE. Collectively, the worked examples, talking points, and 300+ homework problems build intuition for the process of discretization and an appreciation for dimension, inexactitude, visualization, randomness, and complexity. This sets the stage for further cour

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Book SynopsisA how to guide for applying statistical methods to biomarker data analysis Presenting a solid foundation for the statistical methods that are used to analyze biomarker data, Analysis of Biomarker Data: A Practical Guide features preferred techniques for biomarker validation. The authors provide descriptions of select elementary statistical methods that are traditionally used to analyze biomarker data with a focus on the proper application of each method, including necessary assumptions, software recommendations, and proper interpretation of computer output. In addition, the book discusses frequently encountered challenges in analyzing biomarker data and how to deal with them, methods for the quality assessment of biomarkers, and biomarker study designs. Covering a broad range of statistical methods that have been used to analyze biomarker data in published research studies, Analysis of Biomarker Data: A Practical Guide also features: ATable of ContentsPreface xiii Acknowledgements xvii 1 Introduction 1 1.1 What is a Biomarker? 1 1.2 Biomarkers Versus Surrogate Endpoints 2 1.3 Organization of This Book 3 2 Designing Biomarker Studies 5 2.1 Introduction 5 2.2 Designing the Study 6 2.2.1 The Exposure–Disease Association 6 2.2.2 Cross-sectional Studies 7 2.2.3 Case–Control Studies 7 2.2.4 Retrospective Cohort Studies 9 2.2.5 Prospective Cohort Studies 9 2.2.6 Observational Studies 10 2.2.7 Randomized Controlled Trials 11 2.3 Designing the Analysis 13 2.3.1 Choosing the Appropriate Measure of Association 15 2.3.1.1 Odds Ratio versus Risk Ratio 15 2.3.1.2 Consequences of Not Choosing the Appropriate Measure of Association 16 2.3.2 Choosing the Appropriate Statistical Analysis 16 2.3.3 Choosing the Appropriate Sample Size 17 2.4 Presenting Statistical Results 18 Problems 20 3 Elementary Statistical Methods for Analyzing Biomarker Data 21 3.1 Introduction 21 3.2 Graphical and Tabular Summaries 21 3.3 Descriptive Statistics 26 3.4 Describing the Shape of Distributions 31 3.5 Sampling Distributions 33 3.6 Introduction to Statistical Inference 34 3.6.1 Point Estimation and Confidence Interval Estimation 34 3.6.2 Hypothesis Testing 38 3.7 Comparing Means Across Groups 43 3.7.1 Two Group Comparisons 44 3.7.2 Multiple-Group Comparisons 45 3.8 Correlation Analysis 50 3.9 Regression Analysis 52 3.9.1 Simple Linear Regression 52 3.9.2 Multiple Regression 55 3.9.3 Analysis of Covariance 58 3.10 Analyzing Cross-Classified Data 61 3.10.1 Testing for Independence 61 3.10.2 Comparison of Proportions 65 Problems 69 4 Frequently Encountered Challenges in Analyzing Biomarker Data and How to Deal with Them 72 4.1 Introduction 72 4.2 Non-Normally Distributed Data 73 4.2.1 The Effects of Non-Normality 73 4.2.2 Testing Distributional Assumptions 74 4.2.2.1 Graphical Methods for Assessing Normality 74 4.2.2.2 Measures of Skewness and Kurtosis 81 4.2.2.3 Formal Hypothesis Tests of the Normality Assumption 83 4.2.3 Remedial Measures for Violation of a Distributional Assumption 86 4.2.3.1 Choosing a Transformation 86 4.2.3.2 Using a Robust Statistical Procedure 92 4.2.3.3 Distribution-Free Alternatives 93 4.3 Heterogeneity of Variance 113 4.3.1 The Effects of Heterogeneity 113 4.3.2 The Importance of Heterogeneity in the Comparison of Means 113 4.3.2.1 Comparisons of Two Groups 113 4.3.2.2 Comparisons of More Than Two Groups 116 4.3.2.3 Multiple Comparisons 118 4.4 Dependent Groups 122 4.4.1 The Consequences of Ignoring Dependence Among Groups 122 4.4.2 Comparing Two Dependent Means 124 4.4.2.1 Paired t-test 124 4.4.2.2 Wilcoxon Signed Ranks Test 127 4.4.2.3 Sign Test 128 4.4.3 Tests of Dependent Proportions 134 4.4.3.1 McNemar’s Test 134 4.4.3.2 Cochran’s Q test 138 4.4.3.3 Sample Size and Power Considerations 142 4.5 Correlated Outcomes 144 4.5.1 Choosing the Appropriate Measure of Association 144 4.5.1.1 Spearman’s rho 144 4.5.1.2 Kendall’s tau-b 146 4.5.2 Recommended Methods of Statistical Analysis for Correlation Coefficients 148 4.5.3 Recommended Methods for Interpreting Correlation Coefficient Results 156 4.5.4 Sample Size Issues in Correlation Analysis 157 4.5.5 Comparison of Correlation Coefficients 171 4.5.5.1 Comparison of Independent Correlation Coefficients 172 4.5.5.2 Comparison of Dependent Correlation Coefficients 174 4.5.6 Sample Size Issues When Comparing Two Correlation Coefficients 181 4.5.6.1 Sample Size Issues When Comparing Independent Correlation Coefficients 181 4.5.6.2 Sample Size Issues When Comparing Dependent Correlation Coefficients 183 4.6 Clustered Data 184 4.7 Outliers 199 4.7.1 The Effects of Outliers 199 4.7.2 Detection of Outliers 199 4.7.3 Methods for Accommodating Outliers 207 4.8 Limits of Detection and Non-Detected Observations 208 4.8.1 Statistical Inference When NDs Are Present 210 4.8.2 Maximum Likelihood Estimation of a Correlation Coefficient When Both X and Y Are Subject to Non-Detects 210 4.8.3 Comparison of Confidence Interval Methods for Correlation Coefficients When Both Variables Are Subject to Limits of Detection 212 4.9 The Analysis of Cross-Classified Categorical Data 221 4.9.1 Choosing the Appropriate Measure of Association 221 4.9.1.1 The Odds Ratio 221 4.9.1.2 Risk Ratio 223 4.9.1.3 Risk Difference 224 4.9.1.4 Odds Ratio for Paired Data 225 4.9.2 Choosing the Appropriate Statistical Analysis 225 4.9.3 Choosing the Appropriate Sample Size 226 4.9.4 Choosing a Statistical Method When Both the Predictor and the Outcome Are Dichotomous 226 4.9.4.1 Comparing Two Independent Groups in Terms of a Binomial Proportion 226 4.9.4.2 Exact Test for Independence of Rows and Columns in a 2 × 2 Table 230 4.9.4.3 Exact Inference for Odds Ratios 232 4.9.4.4 Inference for the Odds Ratio for Paired Data 234 4.9.5 Choice of a Statistical Method When the Predictor is Ordinal and the Outcome is Dichotomous 237 4.9.5.1 Tests for a Significant Trend in Proportions 237 4.9.6 Choice of a Statistical Method When Both the Predictor and the Outcome are Ordinal 240 4.9.6.1 Test for Linear-by-Linear Association 240 4.9.7 Choice of a Statistical Method When Both the Predictor and the Outcome are Nominal 243 4.9.7.1 Fisher–Freeman–Halton Test 243 Problems 246 5 Validation of Biomarkers 255 5.1 Overview of Methods for Assessing Characteristics of Biomarkers 255 5.2 General Description of Measures of Agreement 257 5.2.1 Discrete Variables 257 5.2.1.1 Cohen’s Kappa 257 5.2.1.2 Extensions of Coefficient Kappa 265 5.2.1.3 Weighted Kappa 273 5.2.2 Continuous Variables 275 5.2.2.1 Pearson’s Correlation Coefficient 275 5.2.2.2 Alternatives to Pearson’s Correlation Coefficient 277 5.3 Assessing Reliability of a Biomarker 287 5.3.1 General Considerations 287 5.3.2 Assessing Reliability of a Dichotomous Biomarker 287 5.3.2.1 Dichotomous Biomarker, More Than Two Raters 289 5.3.3 Assessing Reliability of a Continuous Biomarker 291 5.3.4 Assessing Inter-Subject, Intra-Subject, and Analytical Measurement Variability 292 5.4 Assessing Validity 294 5.4.1 General Considerations 294 5.4.2 Assessing Validity When a Gold Standard is Available 295 5.4.2.1 Dichotomous Biomarkers 295 5.4.2.2 Comparing Several Dichotomous Biomarkers 302 5.4.2.3 Continuous Biomarkers 304 5.4.3 Assessing Validity When a Gold Standard is Not Available 314 5.4.3.1 Dichotomous Biomarkers 315 5.4.3.2 Continuous Biomarkers 319 5.4.4 Assessing Criterion Validity in Method Comparison Studies 328 5.4.5 Assessing Construct Validity in Method Comparison Studies 329 Problems 329 References 332 Solutions to Problems 348 Index 391

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Book SynopsisNonlinear Parameter Optimization Using R John C.Trade Review"The book chapters are enriched by little anecdotes, and the reader obviously benefits from John C. Nash's experience of more than 30 years in the field of nonlinear optimization. This experience translates into many practical recommendations and tweaks. The book provides plenty of code examples and useful code snippets." (Biometrical Journal, 2016)Table of ContentsPreface xv 1 Optimization problem tasks and how they arise 1 1.1 The general optimization problem 1 1.2 Why the general problem is generally uninteresting 2 1.3 (Non-)Linearity 4 1.4 Objective function properties 4 1.4.1 Sums of squares 4 1.4.2 Minimax approximation 5 1.4.3 Problems with multiple minima 5 1.4.4 Objectives that can only be imprecisely computed 5 1.5 Constraint types 5 1.6 Solving sets of equations 6 1.7 Conditions for optimality 7 1.8 Other classifications 7 References 8 2 Optimization algorithms – an overview 9 2.1 Methods that use the gradient 9 2.2 Newton-like methods 12 2.3 The promise of Newton’s method 13 2.4 Caution: convergence versus termination 14 2.5 Difficulties with Newton’s method 14 2.6 Least squares: Gauss–Newton methods 15 2.7 Quasi-Newton or variable metric method 17 2.8 Conjugate gradient and related methods 18 2.9 Other gradient methods 19 2.10 Derivative-free methods 19 2.10.1 Numerical approximation of gradients 19 2.10.2 Approximate and descend 19 2.10.3 Heuristic search 20 2.11 Stochastic methods 20 2.12 Constraint-based methods – mathematical programming 21 References 22 3 Software structure and interfaces 25 3.1 Perspective 25 3.2 Issues of choice 26 3.3 Software issues 27 3.4 Specifying the objective and constraints to the optimizer 28 3.5 Communicating exogenous data to problem definition functions 28 3.5.1 Use of “global” data and variables 31 3.6 Masked (temporarily fixed) optimization parameters 32 3.7 Dealing with inadmissible results 33 3.8 Providing derivatives for functions 34 3.9 Derivative approximations when there are constraints 36 3.10 Scaling of parameters and function 36 3.11 Normal ending of computations 36 3.12 Termination tests – abnormal ending 37 3.13 Output to monitor progress of calculations 37 3.14 Output of the optimization results 38 3.15 Controls for the optimizer 38 3.16 Default control settings 39 3.17 Measuring performance 39 3.18 The optimization interface 39 References 40 4 One-parameter root-finding problems 41 4.1 Roots 41 4.2 Equations in one variable 42 4.3 Some examples 42 4.3.1 Exponentially speaking 42 4.3.2 A normal concern 44 4.3.3 Little Polly Nomial 46 4.3.4 A hypothequial question 49 4.4 Approaches to solving 1D root-finding problems 51 4.5 What can go wrong? 52 4.6 Being a smart user of root-finding programs 54 4.7 Conclusions and extensions 54 References 55 5 One-parameter minimization problems 56 5.1 The optimize() function 56 5.2 Using a root-finder 57 5.3 But where is the minimum? 58 5.4 Ideas for 1D minimizers 59 5.5 The line-search subproblem 61 References 62 6 Nonlinear least squares 63 6.1 nls() from package stats 63 6.1.1 A simple example 63 6.1.2 Regression versus least squares 65 6.2 A more difficult case 65 6.3 The structure of the nls() solution 72 6.4 Concerns with nls() 73 6.4.1 Small residuals 74 6.4.2 Robustness – “singular gradient” woes 75 6.4.3 Bounds with nls() 77 6.5 Some ancillary tools for nonlinear least squares 79 6.5.1 Starting values and self-starting problems 79 6.5.2 Converting model expressions to sum-of-squares functions 80 6.5.3 Help for nonlinear regression 80 6.6 Minimizing Rfunctions that compute sums of squares 81 6.7 Choosing an approach 82 6.8 Separable sums of squares problems 86 6.9 Strategies for nonlinear least squares 93 References 93 7 Nonlinear equations 95 7.1 Packages and methods for nonlinear equations 95 7.1.1 BB 96 7.1.2 nleqslv 96 7.1.3 Using nonlinear least squares 96 7.1.4 Using function minimization methods 96 7.2 A simple example to compare approaches 97 7.3 A statistical example 103 References 106 8 Function minimization tools in the base R system 108 8.1 optim() 108 8.2 nlm() 110 8.3 nlminb() 111 8.4 Using the base optimization tools 112 References 114 9 Add-in function minimization packages for R 115 9.1 Package optimx 115 9.1.1 Optimizers in optimx 116 9.1.2 Example use of optimx() 117 9.2 Some other function minimization packages 118 9.2.1 nloptr and nloptwrap 118 9.2.2 trust and trustOptim 119 9.3 Should we replace optim() routines? 121 References 122 10 Calculating and using derivatives 123 10.1 Why and how 123 10.2 Analytic derivatives – by hand 124 10.3 Analytic derivatives – tools 125 10.4 Examples of use of R tools for differentiation 125 10.5 Simple numerical derivatives 127 10.6 Improved numerical derivative approximations 128 10.6.1 The Richardson extrapolation 128 10.6.2 Complex-step derivative approximations 128 10.7 Strategy and tactics for derivatives 129 References 131 11 Bounds constraints 132 11.1 Single bound: use of a logarithmic transformation 132 11.2 Interval bounds: Use of a hyperbolic transformation 133 11.2.1 Example of the tanh transformation 134 11.2.2 A fly in the ointment 134 11.3 Setting the objective large when bounds are violated 135 11.4 An active set approach 136 11.5 Checking bounds 138 11.6 The importance of using bounds intelligently 138 11.6.1 Difficulties in applying bounds constraints 139 11.7 Post-solution information for bounded problems 139 Appendix 11.A Function transfinite 141 References 142 12 Using masks 143 12.1 An example 143 12.2 Specifying the objective 143 12.3 Masks for nonlinear least squares 147 12.4 Other approaches to masks 148 References 148 13 Handling general constraints 149 13.1 Equality constraints 149 13.1.1 Parameter elimination 151 13.1.2 Which parameter to eliminate? 153 13.1.3 Scaling and centering? 154 13.1.4 Nonlinear programming packages 154 13.1.5 Sequential application of an increasing penalty 156 13.2 Sumscale problems 158 13.2.1 Using a projection 162 13.3 Inequality constraints 163 13.4 A perspective on penalty function ideas 167 13.5 Assessment 167 References 168 14 Applications of mathematical programming 169 14.1 Statistical applications of math programming 169 14.2 R packages for math programming 170 14.3 Example problem: L1 regression 171 14.4 Example problem: minimax regression 177 14.5 Nonlinear quantile regression 179 14.6 Polynomial approximation 180 References 183 15 Global optimization and stochastic methods 185 15.1 Panorama of methods 185 15.2 R packages for global and stochastic optimization 186 15.3 An example problem 187 15.3.1 Method SANN from optim() 187 15.3.2 Package GenSA 188 15.3.3 Packages DEoptim and RcppDE 189 15.3.4 Package smco 191 15.3.5 Package soma 192 15.3.6 Package Rmalschains 193 15.3.7 Package rgenoud 193 15.3.8 Package GA 194 15.3.9 Package gaoptim 195 15.4 Multiple starting values 196 References 202 16 Scaling and reparameterization 203 16.1 Why scale or reparameterize? 203 16.2 Formalities of scaling and reparameterization 204 16.3 Hobbs’ weed infestation example 205 16.4 The KKT conditions and scaling 210 16.5 Reparameterization of the weeds problem 214 16.6 Scale change across the parameter space 214 16.7 Robustness of methods to starting points 215 16.7.1 Robustness of optimization techniques 218 16.7.2 Robustness of nonlinear least squares methods 220 16.8 Strategies for scaling 222 References 223 17 Finding the right solution 224 17.1 Particular requirements 224 17.1.1 A few integer parameters 225 17.2 Starting values for iterative methods 225 17.3 KKT conditions 226 17.3.1 Unconstrained problems 226 17.3.2 Constrained problems 227 17.4 Search tests 228 References 229 18 Tuning and terminating methods 230 18.1 Timing and profiling 230 18.1.1 rbenchmark 231 18.1.2 microbenchmark 231 18.1.3 Calibrating our timings 232 18.2 Profiling 234 18.2.1 Trying possible improvements 235 18.3 More speedups of R computations 238 18.3.1 Byte-code compiled functions 238 18.3.2 Avoiding loops 238 18.3.3 Package upgrades - an example 239 18.3.4 Specializing codes 241 18.4 External language compiled functions 242 18.4.1 Building an R function using Fortran 244 18.4.2 Summary of Rayleigh quotient timings 246 18.5 Deciding when we are finished 247 18.5.1 Tests for things gone wrong 248 References 249 19 Linking R to external optimization tools 250 19.1 Mechanisms to link R to external software 251 19.1.1 R functions to call external (sub)programs 251 19.1.2 File and system call methods 251 19.1.3 Thin client methods 252 19.2 Prepackaged links to external optimization tools 252 19.2.1 NEOS 252 19.2.2 Automatic Differentiation Model Builder (ADMB) 252 19.2.3 NLopt 253 19.2.4 BUGS and related tools 253 19.3 Strategy for using external tools 253 References 254 20 Differential equation models 255 20.1 The model 255 20.2 Background 256 20.3 The likelihood function 258 20.4 A first try at minimization 258 20.5 Attempts with optimx 259 20.6 Using nonlinear least squares 260 20.7 Commentary 261 Reference 262 21 Miscellaneous nonlinear estimation tools for R 263 21.1 Maximum likelihood 263 21.2 Generalized nonlinear models 266 21.3 Systems of equations 268 21.4 Additional nonlinear least squares tools 268 21.5 Nonnegative least squares 270 21.6 Noisy objective functions 273 21.7 Moving forward 274 References 275 Appendix A R packages used in examples 276 Index 279

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Book SynopsisENGINEERING APPLICATIONS A comprehensive text on the fundamental principles of mechanical engineering Engineering Applications presents the fundamental principles and applications of the statics and mechanics of materials in complex mechanical systems design. Using MATLAB to help solve problems with numerical and analytical calculations, authors and noted experts on the topic Mihai Dupac and Dan B. Marghitu offer an understanding of the static behaviour of engineering structures and components while considering the mechanics of materials knowledge as the most important part of their design. The authors explore the concepts, derivations, and interpretations of general principles and discuss the creation of mathematical models and the formulation of mathematical equations. This practical text also highlights the solutions of problems solved analytically and numerically using MATLAB. The figures generated with MATLAB reinforce visual learning for students andTable of Contents1 Forces 1 1.1 Terminology and Notation 1 1.2 Resolution of Forces 3 1.3 Angle Between Two Forces 3 1.4 Force Vector 4 1.5 Scalar (Dot) Product of Two Forces 5 1.6 Cross Product of Two Forces 5 1.7 Examples 6 2 Moments and Couples 15 2.1 Types of Moments 15 2.2 Moment of a Force About a Point 15 2.3 Moment of a Force About a Line 18 2.4 Couples 20 2.5 Examples 21 3 Equilibrium of Structures 55 3.1 Equilibrium Equations 55 3.2 Supports 57 3.3 Free-Body Diagrams 59 3.4 Two-Force and Three-Force Members 60 3.5 Plane Trusses 61 3.6 Analysis of Simple Trusses 62 3.6.1 Method of Joints 62 3.6.2 Method of Sections 65 3.7 Examples 67 4 Centroids and Moments of Inertia 129 4.1 Centre of the Mass and Centroid 129 4.2 Centroid and Centre of the Mass of a Solid Region, Surface or Curve 130 4.3 Method of Decomposition 134 4.4 First Moment of an Area 134 4.5 The Centre of Gravity 135 4.6 Examples 136 5 Stress, Strain and Deflection 185 5.1 Stress 185 5.2 Elastic Strain 185 5.3 Shear and Moment 186 5.4 Deflections of Beams 189 5.5 Examples 193 6 Friction 211 6.1 Coefficient of Static Friction 212 6.2 Coefficient of Kinetic Friction 213 6.3 Friction Models 213 6.3.1 Coulomb Friction Model 214 6.3.2 Coulomb Model with Viscous Friction 216 6.3.3 Coulomb Model with Stiction 217 6.4 Angle of Friction 218 6.5 Examples 219 7 Work, Energy and Power 255 7.1 Work 255 7.2 Kinetic Energy 256 7.3 Work and Power 258 7.4 Conservative Forces 259 7.5 Work Done by the Gravitational Force 259 7.6 Work Done by the Friction Force 260 7.7 Potential Energy and Conservation of Energy 261 7.8 Work Done and Potential Energy of an Elastic Force 261 7.9 Potential Energy Due to the Gravitational Force 262 7.9.1 Potential Energy Due to the Gravitational Force for a Particle 262 7.9.2 Potential Energy Due to the Gravitational Force for a Rigid Body 263 7.10 Examples 264 8 Simple Machines 295 8.1 Load and Effort, Mechanical Advantage, Velocity Ratio and Efficiency of a Simple Machine 295 8.1.1 Load and Effort 295 8.1.2 Mechanical Advantage 296 8.1.3 Velocity Ratio and Efficiency 296 8.2 Effort and Load of an Ideal Machine 297 8.3 The Lever 297 8.4 Inclined Plane (Wedge) 298 8.5 Screws 299 8.6 Simple Screwjack 299 8.6.1 Motion Impending Upwards 301 8.6.2 Motion Impending Downwards 302 8.6.3 Efficiency While Hoisting Load 303 8.7 Differential Screwjack 303 8.8 Pulleys 304 8.8.1 First-order Pulley System 304 8.8.2 Second-order Pulley System 306 8.8.3 Third-order Pulley System 307 8.9 Differential Pulley 308 8.10 Wheel and Axle 309 8.11 Wheel and Differential Axle 310 8.12 Examples 312 References 353 Index 357

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Book SynopsisStatistics with JMP: Hypothesis Tests, ANOVA and Regression Peter Goos, University of Leuven and University of Antwerp, Belgium David Meintrup, University of Applied Sciences Ingolstadt, Germany A first course on basic statistical methodology using JMP This book provides a first course on parameter estimation (point estimates and confidence interval estimates), hypothesis testing, ANOVA and simple linear regression. The authors approach combines mathematical depth with numerous examples and demonstrations using the JMP software. Key features: Provides a comprehensive and rigorous presentation of introductory statistics that has been extensively classroom tested. Pays attention to the usual parametric hypothesis tests as well as to non-parametric tests (including the calculation of exact p-values). Discusses the power of various statistical tests, along with examples in JMP to Trade Review"Masters and advanced students in applied statistics, industrial engineering, business engineering, civil engineering and bio-science engineering will find this book beneficial. It also provides a useful resource for teachers of statistics particularly in the area of engineering." (Zentralblatt MATH 2016)Table of ContentsDedication iii Preface xiii Acknowledgements xvii Part One Estimators and tests 1 1 Estimating population parameters 3 2 Interval estimators 37 3 Hypothesis tests 71 Part Two One population 103 4 Hypothesis tests for a population mean, proportion or variance 105 5 Two hypothesis tests for the median of a population 149 6 Hypothesis tests for the distribution of a population 175 Part Three Two populations 7 Independent versus paired samples 213 8 Hypothesis tests for means, proportions and variances of two independent samples 219 9 A nonparametric hypothesis test for the medians of two independent samples 263 10 Hypothesis tests for the population mean of two paired samples 285 11 Two nonparametric hypothesis tests for paired samples 305 Part Four More than two populations 325 12 Hypothesis tests for more than two population means: one-way analysis of variance 327 13 Nonparametric alternatives to an analysis of variance 375 14 Hypothesis tests for more than two population variances 401 Part Five More useful tests and procedures 417 15 Design of experiments and data collection 419 16 Testing equivalence 427 17 Estimation and testing of correlation and association 445 18 An introduction to regression modeling 481 19 Simple linear regression 493 A Binomial distribution 589 B Standard normal distribution 593 C X2-distribution 595 D Student’s t-distribution 597 E Wilcoxon signed-rank test 599 F Critical values for the Shapiro-Wilk test 605 G Fisher’s F-distribution 607 H Wilcoxon rank-sum test 615 I Studentized range or Q-distribution 625 J Two-sided Dunnett test 629 K One-sided Dunnett test 633 L Kruskal-Wallis-Test 637 M Rank correlation test 641 Index 643

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Book SynopsisA must have text for risk modelling and portfolio optimization using R. This book introduces the latest techniques advocated for measuring financial market risk and portfolio optimization, and provides a plethora of R code examples that enable the reader to replicate the results featured throughout the book. This edition has been extensively revised to include new topics on risk surfaces and probabilistic utility optimization as well as an extended introduction to R language. Financial Risk Modelling and Portfolio Optimization with R: Demonstrates techniques in modelling financial risks and applying portfolio optimization techniques as well as recent advances in the field. Introduces stylized facts, loss function and risk measures, conditional and unconditional modelling of risk; extreme value theory, generalized hyperbolic distribution, volatility modelling and concepts for capturing dependencies. Explores portfolio risk coTable of ContentsPreface to the Second Edition xi Preface xiii Abbreviations xv About the Companion Website xix PART I MOTIVATION 1 1 Introduction 3 Reference 5 2 A brief course in R 6 2.1 Origin and development 6 2.2 Getting help 7 2.3 Working with R 10 2.4 Classes, methods, and functions 12 2.5 The accompanying package FRAPO 22 References 28 3 Financial market data 29 3.1 Stylized facts of financial market returns 29 3.1.1 Stylized facts for univariate series 29 3.1.2 Stylized facts for multivariate series 32 3.2 Implications for risk models 35 References 36 4 Measuring risks 37 4.1 Introduction 37 4.2 Synopsis of risk measures 37 4.3 Portfolio risk concepts 42 References 44 5 Modern portfolio theory 46 5.1 Introduction 46 5.2 Markowitz portfolios 47 5.3 Empirical mean-variance portfolios 50 References 52 PART II RISK MODELLING 55 6 Suitable distributions for returns 57 6.1 Preliminaries 57 6.2 The generalized hyperbolic distribution 57 6.3 The generalized lambda distribution 60 6.4 Synopsis of R packages for GHD 66 6.4.1 The package fBasics 66 6.4.2 The package GeneralizedHyperbolic 67 6.4.3 The package ghyp 69 6.4.4 The package QRM 70 6.4.5 The package SkewHyperbolic 70 6.4.6 The package VarianceGamma 71 6.5 Synopsis of R packages for GLD 71 6.5.1 The package Davies 71 6.5.2 The package fBasics 72 6.5.3 The package gld 73 6.5.4 The package lmomco 73 6.6 Applications of the GHD to risk modelling 74 6.6.1 Fitting stock returns to the GHD 74 6.6.2 Risk assessment with the GHD 77 6.6.3 Stylized facts revisited 80 6.7 Applications of the GLD to risk modelling and data analysis 82 6.7.1 VaR for a single stock 82 6.7.2 Shape triangle for FTSE 100 constituents 84 References 86 7 Extreme value theory 89 7.1 Preliminaries 89 7.2 Extreme value methods and models 90 7.2.1 The block maxima approach 90 7.2.2 The rth largest order models 91 7.2.3 The peaks-over-threshold approach 92 7.3 Synopsis of R packages 94 7.3.1 The package evd 94 7.3.2 The package evdbayes 95 7.3.3 The package evir 96 7.3.4 The packages extRemes and in2extRemes 98 7.3.5 The package fExtremes 99 7.3.6 The package ismev 101 7.3.7 The package QRM 101 7.3.8 The packages Renext and RenextGUI 102 7.4 Empirical applications of EVT 103 7.4.1 Section outline 103 7.4.2 Block maxima model for Siemens 103 7.4.3 r-block maxima for BMW 107 7.4.4 POT method for Boeing 110 References 115 8 Modelling volatility 116 8.1 Preliminaries 116 8.2 The class of ARCH models 116 8.3 Synopsis of R packages 120 8.3.1 The package bayesGARCH 120 8.3.2 The package ccgarch 121 8.3.3 The package fGarch 122 8.3.4 The package GEVStableGarch 122 8.3.5 The package gogarch 123 8.3.6 The package lgarch 123 8.3.7 The packages rugarch and rmgarch 125 8.3.8 The package tseries 127 8.4 Empirical application of volatility models 128 References 130 9 Modelling dependence 133 9.1 Overview 133 9.2 Correlation, dependence, and distributions 133 9.3 Copulae 136 9.3.1 Motivation 136 9.3.2 Correlations and dependence revisited 137 9.3.3 Classification of copulae 139 9.4 Synopsis of R packages 142 9.4.1 The package BLCOP 142 9.4.2 The package copula 144 9.4.3 The package fCopulae 146 9.4.4 The package gumbel 147 9.4.5 The package QRM 148 9.5 Empirical applications of copulae 148 9.5.1 GARCH–copula model 148 9.5.2 Mixed copula approaches 155 References 157 PART III PORTFOLIO OPTIMIZATION APPROACHES 161 10 Robust portfolio optimization 163 10.1 Overview 163 10.2 Robust statistics 164 10.2.1 Motivation 164 10.2.2 Selected robust estimators 165 10.3 Robust optimization 168 10.3.1 Motivation 168 10.3.2 Uncertainty sets and problem formulation 168 10.4 Synopsis of R packages 174 10.4.1 The package covRobust 174 10.4.2 The package fPortfolio 174 10.4.3 The package MASS 175 10.4.4 The package robustbase 176 10.4.5 The package robust 176 10.4.6 The package rrcov 178 10.4.7 Packages for solving SOCPs 179 10.5 Empirical applications 180 10.5.1 Portfolio simulation: robust versus classical statistics 180 10.5.2 Portfolio back test: robust versus classical statistics 186 10.5.3 Portfolio back-test: robust optimization 190 References 195 11 Diversification reconsidered 198 11.1 Introduction 198 11.2 Most-diversified portfolio 199 11.3 Risk contribution constrained portfolios 201 11.4 Optimal tail-dependent portfolios 204 11.5 Synopsis of R packages 207 11.5.1 The package cccp 207 11.5.2 The packages DEoptim, DEoptimR, and RcppDE 207 11.5.3 The package FRAPO 210 11.5.4 The package PortfolioAnalytics 211 11.6 Empirical applications 212 11.6.1 Comparison of approaches 212 11.6.2 Optimal tail-dependent portfolio against benchmark 216 11.6.3 Limiting contributions to expected shortfall 221 References 226 12 Risk-optimal portfolios 228 12.1 Overview 228 12.2 Mean-VaR portfolios 229 12.3 Optimal CVaR portfolios 234 12.4 Optimal draw-down portfolios 238 12.5 Synopsis of R packages 241 12.5.1 The package fPortfolio 241 12.5.2 The package FRAPO 243 12.5.3 Packages for linear programming 245 12.5.4 The package PerformanceAnalytics 249 12.6 Empirical applications 251 12.6.1 Minimum-CVaR versus minimum-variance portfolios 251 12.6.2 Draw-down constrained portfolios 254 12.6.3 Back-test comparison for stock portfolio 260 12.6.4 Risk surface plots 265 References 272 13 Tactical asset allocation 274 13.1 Overview 274 13.2 Survey of selected time series models 275 13.2.1 Univariate time series models 275 13.2.2 Multivariate time series models 281 13.3 The Black–Litterman approach 289 13.4 Copula opinion and entropy pooling 292 13.4.1 Introduction 292 13.4.2 The COP model 292 13.4.3 The EP model 293 13.5 Synopsis of R packages 295 13.5.1 The package BLCOP 295 13.5.2 The package dse 297 13.5.3 The package fArma 300 13.5.4 The package forecast 301 13.5.5 The package MSBVAR 302 13.5.6 The package PortfolioAnalytics 304 13.5.7 The packages urca and vars 304 13.6 Empirical applications 307 13.6.1 Black–Litterman portfolio optimization 307 13.6.2 Copula opinion pooling 313 13.6.3 Entropy pooling 318 13.6.4 Protection strategies 324 References 334 14 Probabilistic utility 339 14.1 Overview 339 14.2 The concept of probabilistic utility 340 14.3 Markov chain Monte Carlo 342 14.3.1 Introduction 342 14.3.2 Monte Carlo approaches 343 14.3.3 Markov chains 347 14.3.4 Metropolis–Hastings algorithm 349 14.4 Synopsis of R packages 354 14.4.1 Packages for conducting MCMC 354 14.4.2 Packages for analyzing MCMC 358 14.5 Empirical application 362 14.5.1 Exemplary utility function 362 14.5.2 Probabilistic versus maximized expected utility 366 14.5.3 Simulation of asset allocations 369 References 375 Appendix A Package overview 378 A.1 Packages in alphabetical order 378 A.2 Packages ordered by topic 382 References 386 Appendix B Time series data 391 B.1 Date/time classes 391 B.2 The ts class in the base package stats 395 B.3 Irregularly spaced time series 395 B.4 The package timeSeries 397 B.5 The package zoo 399 B.6 The packages tframe and xts 401 References 404 Appendix C Back-testing and reporting of portfolio strategies 406 C.1 R packages for back-testing 406 C.2 R facilities for reporting 407 C.3 Interfacing with databases 407 References 408 Appendix D Technicalities 411 Reference 411 Index 413

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Book SynopsisA step-by-step approach to problem-solving techniques using SPSS in the fields of sports science and physical education Featuring a clear and accessible approach to the methods, processes, and statistical techniques used in sports science and physical education, Sports Research with Analytical Solution using SPSS emphasizes how to conduct and interpret a range of statistical analysis using SPSS. The book also addresses issues faced by research scholars in these fields by providing analytical solutions to various research problems without reliance on mathematical rigor. Logically arranged to cover both fundamental and advanced concepts, the book presents standard univariate and complex multivariate statistical techniques used in sports research such as multiple regression analysis, discriminant analysis, cluster analysis, and factor analysis. The author focuses on the treatment of various parametric and nonparametric statistical tests, which are shown throTable of ContentsPreface xv About the Companion Website xviii Acknowledgments xix 1 Introduction to Data Types and SPSS Operations 1 1.1 Introduction 1 1.2 Types of data 2 1.2.1 Qualitative Data 2 1.2.2 Quantitative Data 3 1.3 Important definitions 4 1.3.1 Variable 4 1.4 Data Cleaning 4 1.5 Detection of Errors 5 1.5.1 Using Frequencies 5 1.5.2 Using Mean and Standard Deviation 5 1.5.3 Logic Checks 5 1.5.4 Outlier Detection 5 1.6 How to Start Spss? 6 1.6.1 Preparing Data File 7 1.7 Exercise 10 1.7.1 Short Answer Questions 10 1.7.2 Multiple Choice Questions 11 2 Descriptive Profile 14 2.1 Introduction 14 2.2 Explanation of Various Descriptive Statistics 16 2.2.1 Mean 16 2.2.2 Variance 16 2.2.3 Standard Error of Mean 17 2.2.4 Skewness 17 2.2.5 Kurtosis 18 2.2.6 Percentiles 19 2.3 Application of Descriptive Statistics 19 2.3.1 Testing Normality of Data and Identifying Outliers 20 2.4 Computation of Descriptive Statistics Using Spss 25 2.4.1 Preparation of Data File 25 2.4.2 Defining Variables 26 2.4.3 Entering Data 26 2.4.4 SPSS Commands 26 2.5 Interpretations of the Results 29 2.6 Developing Profile Chart 31 2.7 Summary of Spss Commands 33 2.8 Exercise 33 2.8.1 Short Answer Questions 33 2.8.2 Multiple Choice Questions 34 2.9 Case Study on Descriptive Analysis 36 3 Correlation Coefficient and Partial Correlation 41 3.1 Introduction 41 3.2 Correlation Matrix and Partial Correlation 43 3.2.1 Product Moment Correlation Coefficient 43 3.2.2 Partial Correlation 45 3.3 Application of Correlation Matrix and Partial Correlation 46 3.4 Correlation Matrix with Spss 46 3.4.1 Computation in Correlation Matrix 46 3.4.2 Interpretations of Findings 51 3.5 Partial Correlation with Spss 51 3.5.1 Computation of Partial Correlations 52 3.5.2 Interpretation of Partial Correlation 55 3.6 Summary of the Spss Commands 56 3.6.1 For Computing Correlation Matrix 56 3.6.2 For Computing Partial Correlations 57 3.7 Exercise 57 3.7.1 Short Answer Questions 57 3.7.2 Multiple Choice Questions 57 3.7.3 Assignment 60 3.8 Case Study on Correlation 60 4 Comparing Means 65 4.1 Introduction 65 4.2 One‐Sample t‐Test 66 4.2.1 Application of One‐Sample t‐Test 67 4.3 Two‐Sample t‐Test for Unrelated Groups 67 4.3.1 Assumptions While Using t‐Test 67 4.3.2 Case I: Two‐Tailed Test 68 4.3.3 Case II: Right Tailed Test 68 4.3.4 Case III: Left Tailed Test 69 4.3.5 Application of Two‐Sample t-Test 70 4.4 Paired t‐Test for Related Groups 70 4.4.1 Case I: Two‐Tailed Test 71 4.4.2 Case II: Right Tailed Test 71 4.4.3 Case III: Left Tailed Test 72 4.4.4 Application of Paired t‐Test 73 4.5 One‐Sample t‐Test with Spss 73 4.5.1 Computation in t‐Test for Single Group 74 4.5.2 Interpretation of Findings 77 4.6 Two‐Sample t‐Test for Independent Groups with Spss 78 4.6.1 Computation in Two‐Sample t‐Test 79 4.6.2 Interpretation of Findings 83 4.7 Paired t‐Test for Related Groups with Spss 85 4.7.1 Computation in Paired t‐Test 86 4.7.2 Interpretation of Findings 89 4.8 Summary of Spss Commands for t‐Tests 90 4.8.1 One‐Sample t‐Test 90 4.8.2 Two‐Sample t‐Test for Independent Groups 90 4.8.3 Paired t‐Test 91 4.9 Exercise 91 4.9.1 Short Answer Questions 91 4.9.2 Multiple Choice Questions 91 4.9.3 Assignment 93 4.10 Case Study 94 5 Independent Measures Anova 100 5.1 Introduction 101 5.2 One‐Way Analysis of Variance 101 5.2.1 One‐Way ANOVA Model 102 5.2.2 Post Hoc Test 102 5.2.3 Application of One‐Way ANOVA 103 5.3 One‐Way Anova with Spss (Equal Sample Size) 103 5.3.1 Computation in One‐Way ANOVA (Equal Sample Size) 104 5.3.2 Interpretation of Findings 107 5.4 One‐Way Anova with Spss (Unequal Sample Size) 110 5.4.1 Computation in One‐Way ANOVA (Unequal Sample Size) 111 5.4.2 Interpretation of Findings 114 5.5 Two‐Way Analysis of Variance 115 5.5.1 Assumptions in Two‐Way Analysis of Variance 116 5.5.2 Hypotheses in Two‐Way ANOVA 116 5.5.3 Factors 117 5.5.4 Treatment Groups 117 5.5.5 Main Effect 117 5.5.6 Interaction Effect 117 5.5.7 Within‐Groups Variation 117 5.5.8 F‐Statistic 117 5.5.9 Two‐Way ANOVA Table 118 5.5.10 Interpretation 118 5.5.11 Application of Two‐Way Analysis of Variance 118 5.6 Two‐Way Anova Using Spss 119 5.6.1 Computation in Two‐Way ANOVA 121 5.6.2 Interpretation of Findings 126 5.7 Summary of the Spss Commands 137 5.7.1 One‐Way ANOVA 137 5.7.2 Two‐Way ANOVA 138 5.8 Exercise 138 5.8.1 Short Answer Questions 138 5.8.2 Multiple Choice Questions 139 5.8.3 Assignment 142 5.9 Case Study on One‐Way Anova Design 143 5.10 Case Study on Two‐Way Anova 147 6 Repeated Measures Anova 153 6.1 Introduction 153 6.2 One‐Way Repeated Measures Anova 154 6.2.1 Assumptions in One‐Way Repeated Measures ANOVA 155 6.2.2 Application in Sports Research 155 6.2.3 Steps in Solving One‐Way Repeated Measures ANOVA 156 6.3 One‐Way Repeated Measures Anova Using Spss 157 6.3.1 Computation in the One‐Way Repeated Measures ANOVA 157 6.3.2 Interpretation of Findings 161 6.3.3 Findings of the Study 165 6.3.4 Inference 166 6.4 Two‐Way Repeated Measures Anova 166 6.4.1 Assumptions in Two‐Way Repeated Measures ANOVA 166 6.4.2 Application in Sports Research 167 6.4.3 Steps in Solving Two‐Way Repeated Measures ANOVA 167 6.5 Two‐Way Repeated Measures Anova Using Spss 168 6.5.1 Computation in Two‐Way Repeated Measures ANOVA 170 6.5.2 Interpretation of Findings 173 6.5.3 Findings of the Study 181 6.5.4 Inference 181 6.6 Summary of the Spss Commands for One‐Way Repeated Measures Anova 182 6.7 Summary of the Spss Commands for Two‐Way Repeated Measures Anova 182 6.8 Exercise 183 6.8.1 Short Answer Questions 183 6.8.2 Multiple Choice Questions 183 6.8.3 Assignment 185 6.9 Case Study on Repeated Measures Design 186 7 Analysis of Covariance 190 7.1 Introduction 190 7.2 Conceptual Framework of Analysis of Covariance 191 7.3 Application of ANCOVA 192 7.4 ANCOVA with Spss 193 7.4.1 Computation in ANCOVA 194 7.5 Summary of the Spss Commands 201 7.6 Exercise 202 7.6.1 Short Answer Questions 202 7.6.2 Multiple Choice Questions 202 7.6.3 Assignment 203 7.7 Case Study on ANCOVA Design 204 8 Nonparametric Tests in Sports Research 209 8.1 Introduction 209 8.2 Chi‐Square Test 211 8.2.1 Testing Goodness of Fit 211 8.2.2 Yates’ Correction 212 8.2.3 Contingency Coefficient 212 8.3 Goodness of Fit with Spss 212 8.3.1 Computation in Goodness of Fit 213 8.3.2 Interpretation of Findings 216 8.4 Testing Independence of Two Attributes 216 8.4.1 Interpretation 218 8.5 Testing Association with Spss 219 8.5.1 Computation in Chi‐Square 219 8.5.2 Interpretation of Findings 223 8.6 Mann–Whitney U Test: Comparing Two Independent Samples 224 8.6.1 Computation in Mann–Whitney U Statistic Using SPSS 224 8.6.2 Interpretation of Findings 226 8.7 Wilcoxon Signed‐Rank Test: For Comparing Two Related Groups 227 8.7.1 Computation in Wilcoxon Signed‐Rank Test Using SPSS 228 8.7.2 Interpretation of Findings 230 8.8 Kruskal–Wallis Test 231 8.8.1 Computation in Kruskal–Wallis Test Using SPSS 232 8.8.2 Interpretation of Findings 234 8.9 Friedman Test 234 8.9.1 Computation in Friedman Test Using SPSS 235 8.9.2 Interpretation of Findings 237 8.10 Summary of the Spss Commands 237 8.10.1 Computing Chi‐Square Statistic (for Testing Goodness of Fit) 237 8.10.2 Computing Chi‐Square Statistic (for Testing Independence) 238 8.10.3 Computation in Mann–Whitney U Test 238 8.10.4 Computation in Wilcoxon Signed‐Rank Test 239 8.10.5 Computation in Kruskal–Wallis Test 239 8.10.6 Computation in Friedman Test 239 8.11 Exercise 240 8.11.1 Short Answer Questions 240 8.11.2 Multiple Choice Questions 241 8.11.3 Assignment 243 8.12 Case Study on Testing Independence of Attributes 243 9 Regression Analysis and Multiple Correlations 246 9.1 Introduction 246 9.2 Understanding Regression Equation 247 9.2.1 Methods of Regression Analysis 247 9.2.2 Multiple Correlation 248 9.3 Application of Regression Analysis 248 9.4 Multiple Regression Analysis with Spss 249 9.4.1 Computation in Regression Analysis 249 9.4.2 Interpretation of Findings 254 9.5 Summary of Spss Commands for Regression Analysis 259 9.6 Exercise 259 9.6.1 Short Answer Questions 259 9.6.2 Multiple Choice Questions 260 9.6.3 Assignment 261 9.7 Case Study on Regression Analysis 263 10 Application of Discriminant Function Analysis 267 10.1 Introduction 268 10.2 Basics of Discriminant Function Analysis 268 10.2.1 Discriminating Variables 268 10.2.2 Dependent Variable 268 10.2.3 Discriminant Function 268 10.2.4 Classification Matrix 269 10.2.5 Stepwise Method of Discriminant Analysis 269 10.2.6 Power of Discriminating Variable 269 10.2.7 Canonical Correlation 269 10.2.8 Wilks’ Lambda 270 10.3 Assumptions in Discriminant Analysis 270 10.4 Why to Use Discriminant Analysis 270 10.5 Steps in Discriminant Analysis 271 10.6 Application of Discriminant Function Analysis 272 10.7 Discriminant Analysis Using Spss 274 10.7.1 Computation in Discriminant Analysis 274 10.7.2 Interpretation of Findings 279 10.8 Summary of the Spss Commands for Discriminant Analysis 284 10.9 Exercise 284 10.9.1 Short Answer Questions 284 10.9.2 Multiple Choice Questions 285 10.9.3 Assignment 286 10.10 Case Study on Discriminant Analysis 288 11 Logistic Regression for Developing Logit Model in Sport 293 11.1 Introduction 293 11.2 Understanding Logistic Regression 294 11.3 Application of Logistic Regression in Sports Research 295 11.4 Assumptions in Logistic Regression 297 11.5 Steps in Developing Logistic Model 297 11.6 Logistic Analysis Using Spss 297 11.6.1 Block 0 299 11.6.2 Block 1 299 11.6.3 Computation in Logistic Regression with SPSS 299 11.7 Interpretation of Findings 304 11.7.1 Case Processing and Coding Summary 304 11.7.2 Analyzing Logistic Models 305 11.8 Summary of the Spss Commands for Logistic Regression 310 11.9 Exercise 310 11.9.1 Short Answer Questions 310 11.9.2 Multiple Choice Questions 311 11.9.3 Assignment 312 11.10 Case Study on Logistic Regression 313 12 Application of Factor Analysis 319 12.1 Introduction 319 12.2 Terminologies Used in Factor Analysis 320 12.2.1 Principal Component Analysis 320 12.2.2 Eigenvalue 320 12.2.3 Kaiser Criterion 321 12.2.4 The Scree Test 321 12.2.5 Communality 321 12.2.6 Factor Loading 322 12.2.7 Varimax Rotation 322 12.3 Assumptions in Factor Analysis 322 12.4 Steps in Factor Analysis 323 12.5 Application of Factor Analysis 323 12.6 Factor Analysis with Spss 324 12.6.1 Computation in Factor Analysis Using SPSS 326 12.7 Summary of the Spss Commands for Factor Analysis 336 12.8 Exercise 336 12.8.1 Short Answer Questions 336 12.8.2 Multiple Choice Questions 337 12.8.3 Assignment 338 12.9 Case Study on Factor Analysis 339 Appendix 346 Bibliography 360 Index 368

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Book SynopsisDemonstrates the simplicity and effectiveness of Mathematica as the solution to practical problems in composite materials. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background.Table of ContentsPreface ix About the Companion Website xi 1 Coordinate Transformation and Tensors 1 1.1 Index Notation 1 1.1.1 Some Examples of Index Notation in 3-D 3 1.1.2 Mathematica Implementation 3 1.1.3 Kronecker Delta 6 1.1.4 Permutation Symbols 9 1.1.5 Product of Matrices 10 1.2 Coordinate Transformations (Cartesian Tensors) 11 1.3 Definition of Tensors 13 1.3.1 Tensor of Rank 0 (Scalar) 13 1.3.2 Tensor of Rank 1 (Vector) 14 1.3.3 Tensor of Rank 2 15 1.3.4 Tensor of Rank 3 17 1.3.5 Tensor of Rank 4 17 1.3.6 Differentiation 19 1.3.7 Differentiation of Cartesian Tensors 20 1.4 Invariance of Tensor Equations 21 1.5 Quotient Rule 22 1.6 Exercises 23 References 24 2 Field Equations 25 2.1 Concept of Stress 25 2.1.1 Properties of Stress 29 2.1.2 (Stress) Boundary Conditions 30 2.1.3 Principal Stresses 31 2.1.4 Stress Deviator 35 2.1.5 Mohr’s Circle 38 2.2 Strain 40 2.2.1 Shear Deformation 47 2.3 Compatibility Condition 49 2.4 Constitutive Relation, Isotropy, Anisotropy 50 2.4.1 Isotropy 52 2.4.2 Elastic Modulus 54 2.4.3 Orthotropy 56 2.4.4 2-D Orthotropic Materials 57 2.4.5 Transverse Isotropy 57 2.5 Constitutive Relation for Fluids 58 2.5.1 Thermal Effect 58 2.6 Derivation of Field Equations 59 2.6.1 Divergence Theorem (Gauss Theorem) 59 2.6.2 Material Derivative 60 2.6.3 Equation of Continuity 62 2.6.4 Equation of Motion 62 2.6.5 Equation of Energy 63 2.6.6 Isotropic Solids 65 2.6.7 Isotropic Fluids 65 2.6.8 Thermal Effects 66 2.7 General Coordinate System 66 2.7.1 Introduction to Tensor Analysis 66 2.7.2 Definition of Tensors in Curvilinear Systems 68 2.7.3 Metric Tensor10, gij 69 2.7.4 Covariant Derivatives 70 2.7.5 Examples 73 2.7.6 Vector Analysis 75 2.8 Exercises 77 References 80 3 Inclusions in Infinite Media 81 3.1 Eshelby’s Solution for an Ellipsoidal Inclusion Problem 82 3.1.1 Eigenstrain Problem 85 3.1.2 Eshelby Tensors for an Ellipsoidal Inclusion 87 3.1.3 Inhomogeneity (Inclusion) Problem 95 3.2 Multilayered Inclusions 104 3.2.1 Background 104 3.2.2 Implementation of Index Manipulation in Mathematica 105 3.2.3 General Formulation 108 3.2.4 Exact Solution for Two-Phase Materials 116 3.2.5 Exact Solution for Three-Phase Materials 123 3.2.6 Exact Solution for Four-Phase Materials 132 3.2.7 Exact Solution for 2-D Multiphase Materials 137 3.3 Thermal Stress 137 3.3.1 Thermal Stress Due to Heat Source 138 3.3.2 Thermal Stress Due to Heat Flow 146 3.4 Airy’s Stress Function Approach 155 3.4.1 Airy’s Stress Function 156 3.4.2 Mathematica Programming of Complex Variables 161 3.4.3 Multiphase Inclusion Problems Using Airy’s Stress Function 163 3.5 Effective Properties 172 3.5.1 Upper and Lower Bounds of Effective Properties 173 3.5.2 Self-Consistent Approximation 175 3.5.3 Source Code for micromech.m 178 3.6 Exercises 188 References 189 4 Inclusions in Finite Matrix 191 4.1 General Approaches for Numerically Solving Boundary Value Problems 192 4.1.1 Method of Weighted Residuals 192 4.1.2 Rayleigh–Ritz Method 203 4.1.3 Sturm–Liouville System 205 4.2 Steady-State Heat Conduction Equations 213 4.2.1 Derivation of Permissible Functions 213 4.2.2 Finding Temperature Field Using Permissible Functions 227 4.3 Elastic Fields with Bounded Boundaries 232 4.4 Numerical Examples 238 4.4.1 Homogeneous Medium 238 4.4.2 Single Inclusion 240 4.5 Exercises 251 References 252 Appendix A Introduction to Mathematica 253 A.1 Essential Commands/Statements 255 A.2 Equations 256 A.3 Differentiation/Integration 260 A.4 Matrices/Vectors/Tensors 260 A.5 Functions 262 A.6 Graphics 263 A.7 Other Useful Functions 265 A.8 Programming in Mathematica 267 A.8.1 Control Statements 268 A.8.2 Tensor Manipulations 270 References 272 Index 273

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Book SynopsisThis introductory text walks readers from the fundamental mechanics of lift to the stage of being able to make practical calculations and predictions of the coefficient of lift for realistic wing profile and platform geometries.Trade Review“This book is a very useful digest of key points from the literature, carefully structured and presented with helpful pointers as to how the successive aerodynamical models can be implemented in the ‘now so readily available interactive matrix computation systems.” (Aeronautical Journal, 1 August 2013)Table of ContentsPreface xvii Series Preface xxiii Part One Plane Ideal Aerodynamics 1 Preliminary Notions 3 1.1 Aerodynamic Force and Moment 3 1.1.1 Motion of the Frame of Reference 3 1.1.2 Orientation of the System of Coordinates 4 1.1.3 Components of the Aerodynamic Force 4 1.1.4 Formulation of the Aerodynamic Problem 4 1.2 Aircraft Geometry 5 1.2.1 Wing Section Geometry 6 1.2.2 Wing Geometry 7 1.3 Velocity 8 1.4 Properties of Air 8 1.4.1 Equation of State: Compressibility and the Speed of Sound 8 1.4.2 Rheology: Viscosity 10 1.4.3 The International Standard Atmosphere 12 1.4.4 Computing Air Properties 12 1.5 Dimensional Theory 13 1.5.1 Alternative methods 16 1.5.2 Example: Using Octave to Solve a Linear System 16 1.6 Example: NACA Report No. 502 18 1.7 Exercises 19 1.8 Further Reading 22 References 22 2 Plane Ideal Flow 25 2.1 Material Properties: The Perfect Fluid 25 2.2 Conservation of Mass 26 2.2.1 Governing Equations: Conservation Laws 26 2.3 The Continuity Equation 26 2.4 Mechanics: The Euler Equations 27 2.4.1 Rate of Change of Momentum 27 2.4.2 Forces Acting on a Fluid Particle 28 2.4.3 The Euler Equations 29 2.4.4 Accounting for Conservative External Forces 29 2.5 Consequences of the Governing Equations 30 2.5.1 The Aerodynamic Force 30 2.5.2 Bernoulli’s Equation 33 2.5.3 Circulation, Vorticity, and Irrotational Flow 33 2.5.4 Plane Ideal Flows 35 2.6 The Complex Velocity 35 2.6.1 Review of Complex Variables 35 2.6.2 Analytic Functions and Plane Ideal Flow 38 2.6.3 Example: the Polar Angle Is Nowhere Analytic 40 2.7 The Complex Potential 41 2.8 Exercises 42 2.9 Further Reading 44 References 45 3 Circulation and Lift 47 3.1 Powers of z 47 3.1.1 Divergence and Vorticity in Polar Coordinates 48 3.1.2 Complex Potentials 48 3.1.3 Drawing Complex Velocity Fields with Octave 49 3.1.4 Example: k = 1, Corner Flow 50 3.1.5 Example: k = 0, Uniform Stream 51 3.1.6 Example: k =−1, Source 51 3.1.7 Example: k =−2, Doublet 52 3.2 Multiplication by a Complex Constant 53 3.2.1 Example: w = const., Uniform Stream with Arbitrary Direction 53 3.2.2 Example: w = i/z, Vortex 54 3.2.3 Example: Polar Components 54 3.3 Linear Combinations of Complex Velocities 54 3.3.1 Example: Circular Obstacle in a Stream 54 3.4 Transforming the Whole Velocity Field 56 3.4.1 Translating the Whole Velocity Field 56 3.4.2 Example: Doublet as the Sum of a Source and Sink 56 3.4.3 Rotating the Whole Velocity Field 56 3.5 Circulation and Outflow 57 3.5.1 Curve-integrals in Plane Ideal Flow 57 3.5.2 Example: Numerical Line-integrals for Circulation and Outflow 58 3.5.3 Closed Circuits 59 3.5.4 Example: Powers of z and Circles around the Origin 60 3.6 More on the Scalar Potential and Stream Function 61 3.6.1 The Scalar Potential and Irrotational Flow 61 3.6.2 The Stream Function and Divergence-free Flow 62 3.7 Lift 62 3.7.1 Blasius’s Theorem 62 3.7.2 The Kutta–Joukowsky Theorem 63 3.8 Exercises 64 3.9 Further Reading 65 References 66 4 Conformal Mapping 67 4.1 Composition of Analytic Functions 67 4.2 Mapping with Powers of ζ 68 4.2.1 Example: Square Mapping 68 4.2.2 Conforming Mapping by Contouring the Stream Function 69 4.2.3 Example: Two-thirds Power Mapping 69 4.2.4 Branch Cuts 70 4.2.5 Other Powers 71 4.3 Joukowsky’s Transformation 71 4.3.1 Unit Circle from a Straight Line Segment 71 4.3.2 Uniform Flow and Flow over a Circle 72 4.3.3 Thin Flat Plate at Nonzero Incidence 73 4.3.4 Flow over the Thin Flat Plate with Circulation 74 4.3.5 Joukowsky Aerofoils 75 4.4 Exercises 75 4.5 Further Reading 78 References 78 5 Flat Plate Aerodynamics 79 5.1 Plane Ideal Flow over a Thin Flat Plate 79 5.1.1 Stagnation Points 80 5.1.2 The Kutta–Joukowsky Condition 80 5.1.3 Lift on a Thin Flat Plate 81 5.1.4 Surface Speed Distribution 82 5.1.5 Pressure Distribution 83 5.1.6 Distribution of Circulation 84 5.1.7 Thin Flat Plate as Vortex Sheet 85 5.2 Application of Thin Aerofoil Theory to the Flat Plate 87 5.2.1 Thin Aerofoil Theory 87 5.2.2 Vortex Sheet along the Chord 87 5.2.3 Changing the Variable of Integration 88 5.2.4 Glauert’s Integral 88 5.2.5 The Kutta–Joukowsky Condition 89 5.2.6 Circulation and Lift 89 5.3 Aerodynamic Moment 89 5.3.1 Centre of Pressure and Aerodynamic Centre 90 5.4 Exercises 90 5.5 Further Reading 91 References 91 6 Thin Wing Sections 93 6.1 Thin Aerofoil Analysis 93 6.1.1 Vortex Sheet along the Camber Line 93 6.1.2 The Boundary Condition 93 6.1.3 Linearization 94 6.1.4 Glauert’s Transformation 95 6.1.5 Glauert’s Expansion 95 6.1.6 Fourier Cosine Decomposition of the Camber Line Slope 97 6.2 Thin Aerofoil Aerodynamics 98 6.2.1 Circulation and Lift 98 6.2.2 Pitching Moment about the Leading Edge 99 6.2.3 Aerodynamic Centre 100 6.2.4 Summary 101 6.3 Analytical Evaluation of Thin Aerofoil Integrals 101 6.3.1 Example: the NACA Four-digit Wing Sections 104 6.4 Numerical Thin Aerofoil Theory 105 6.5 Exercises 109 6.6 Further Reading 109 References 109 7 Lumped Vortex Elements 111 7.1 The Thin Flat Plate at Arbitrary Incidence, Again 111 7.1.1 Single Vortex 111 7.1.2 The Collocation Point 111 7.1.3 Lumped Vortex Model of the Thin Flat Plate 112 7.2 Using Two Lumped Vortices along the Chord 114 7.2.1 Postprocessing 116 7.3 Generalization to Multiple Lumped Vortex Panels 117 7.3.1 Postprocessing 117 7.4 General Considerations on Discrete Singularity Methods 117 7.5 Lumped Vortex Elements for Thin Aerofoils 119 7.5.1 Panel Chains for Camber Lines 119 7.5.2 Implementation in Octave 121 7.5.3 Comparison with Thin Aerofoil Theory 122 7.6 Disconnected Aerofoils 123 7.6.1 Other Applications 124 7.7 Exercises 125 7.8 Further Reading 125 References 126 8 Panel Methods for Plane Flow 127 8.1 Development of the CUSSSP Program 127 8.1.1 The Singularity Elements 127 8.1.2 Discretizing the Geometry 129 8.1.3 The Influence Matrix 131 8.1.4 The Right-hand Side 132 8.1.5 Solving the Linear System 134 8.1.6 Postprocessing 135 8.2 Exercises 137 8.2.1 Projects 138 8.3 Further Reading 139 References 139 8.4 Conclusion to Part I: The Origin of Lift 139 Part Two Three-dimensional Ideal Aerodynamics 9 Finite Wings and Three-Dimensional Flow 143 9.1 Wings of Finite Span 143 9.1.1 Empirical Effect of Finite Span on Lift 143 9.1.2 Finite Wings and Three-dimensional Flow 143 9.2 Three-Dimensional Flow 145 9.2.1 Three-dimensional Cartesian Coordinate System 145 9.2.2 Three-dimensional Governing Equations 145 9.3 Vector Notation and Identities 145 9.3.1 Addition and Scalar Multiplication of Vectors 145 9.3.2 Products of Vectors 146 9.3.3 Vector Derivatives 147 9.3.4 Integral Theorems for Vector Derivatives 148 9.4 The Equations Governing Three-Dimensional Flow 149 9.4.1 Conservation of Mass and the Continuity Equation 149 9.4.2 Newton’s Law and Euler’s Equation 149 9.5 Circulation 150 9.5.1 Definition of Circulation in Three Dimensions 150 9.5.2 The Persistence of Circulation 151 9.5.3 Circulation and Vorticity 151 9.5.4 Rotational Form of Euler’s Equation 153 9.5.5 Steady Irrotational Motion 153 9.6 Exercises 154 9.7 Further Reading 155 References 155 10 Vorticity and Vortices 157 10.1 Streamlines, Stream Tubes, and Stream Filaments 157 10.1.1 Streamlines 157 10.1.2 Stream Tubes and Stream Filaments 158 10.2 Vortex Lines, Vortex Tubes, and Vortex Filaments 159 10.2.1 Strength of Vortex Tubes and Filaments 159 10.2.2 Kinematic Properties of Vortex Tubes 159 10.3 Helmholtz’s Theorems 159 10.3.1 ‘Vortex Tubes Move with the Flow’ 159 10.3.2 ‘The Strength of a Vortex Tube is Constant’ 160 10.4 Line Vortices 160 10.4.1 The Two-dimensional Vortex 160 10.4.2 Arbitrarily Oriented Rectilinear Vortex Filaments 160 10.5 Segmented Vortex Filaments 161 10.5.1 The Biot–Savart Law 161 10.5.2 Rectilinear Vortex Filaments 162 10.5.3 Finite Rectilinear Vortex Filaments 164 10.5.4 Infinite Straight Line Vortices 164 10.5.5 Semi-infinite Straight Line Vortex 164 10.5.6 Truncating Infinite Vortex Segments 165 10.5.7 Implementing Line Vortices in Octave 165 10.6 Exercises 166 10.7 Further Reading 167 References 167 11 Lifting Line Theory 169 11.1 Basic Assumptions of Lifting Line Theory 169 11.2 The Lifting Line, Horseshoe Vortices, and the Wake 169 11.2.1 Deductions from Vortex Theorems 169 11.2.2 Deductions from the Wing Pressure Distribution 170 11.2.3 The Lifting Line Model of Air Flow 170 11.2.4 Horseshoe Vortex 170 11.2.5 Continuous Trailing Vortex Sheet 171 11.2.6 The Form of the Wake 172 11.3 The Effect of Downwash 173 11.3.1 Effect on the Angle of Incidence: Induced Incidence 173 11.3.2 Effect on the Aerodynamic Force: Induced Drag 174 11.4 The Lifting Line Equation 174 11.4.1 Glauert’s Solution of the Lifting Line Equation 175 11.4.2 Wing Properties in Terms of Glauert’s Expansion 176 11.5 The Elliptic Lift Loading 178 11.5.1 Properties of the Elliptic Lift Loading 179 11.6 Lift–Incidence Relation 180 11.6.1 Linear Lift–Incidence Relation 181 11.7 Realizing the Elliptic Lift Loading 182 11.7.1 Corrections to the Elliptic Loading Approximation 182 11.8 Exercises 182 11.9 Further Reading 183 References 183 12 Nonelliptic Lift Loading 185 12.1 Solving the Lifting Line Equation 185 12.1.1 The Sectional Lift–Incidence Relation 185 12.1.2 Linear Sectional Lift–Incidence Relation 185 12.1.3 Finite Approximation: Truncation and Collocation 185 12.1.4 Computer Implementation 187 12.1.5 Example: a Rectangular Wing 187 12.2 Numerical Convergence 188 12.3 Symmetric Spanwise Loading 189 12.3.1 Example: Exploiting Symmetry 191 12.4 Exercises 192 References 192 13 Lumped Horseshoe Elements 193 13.1 A Single Horseshoe Vortex 193 13.1.1 Induced Incidence of the Lumped Horseshoe Element 195 13.2 Multiple Horseshoes along the Span 195 13.2.1 A Finite-step Lifting Line in Octave 197 13.3 An Improved Discrete Horseshoe Model 200 13.4 Implementing Horseshoe Vortices in Octave 203 13.4.1 Example: Yawed Horseshoe Vortex Coefficients 205 13.5 Exercises 206 13.6 Further Reading 207 References 207 14 The Vortex Lattice Method 209 14.1 Meshing the Mean Lifting Surface of a Wing 209 14.1.1 Plotting the Mesh of a Mean Lifting Surface 210 14.2 A Vortex Lattice Method 212 14.2.1 The Vortex Lattice Equations 213 14.2.2 Unit Normals to the Vortex-lattice 215 14.2.3 Spanwise Symmetry 215 14.2.4 Postprocessing Vortex Lattice Methods 215 14.3 Examples of Vortex Lattice Calculations 216 14.3.1 Campbell’s Flat Swept Tapered Wing 216 14.3.2 Bertin’s Flat Swept Untapered Wing 218 14.3.3 Spanwise and Chordwise Refinement 219 14.4 Exercises 220 14.5 Further Reading 221 14.5.1 Three-dimensional Panel Methods 222 References 222 Part Three Nonideal Flow in Aerodynamics 15 Viscous Flow 225 15.1 Cauchy’s First Law of Continuum Mechanics 225 15.2 Rheological Constitutive Equations 227 15.2.1 Perfect Fluid 227 15.2.2 Linearly Viscous Fluid 227 15.3 The Navier–Stokes Equations 228 15.4 The No-Slip Condition and the Viscous Boundary Layer 228 15.5 Unidirectional Flows 229 15.5.1 Plane Couette and Poiseuille Flows 229 15.6 A Suddenly Sliding Plate 230 15.6.1 Solution by Similarity Variable 230 15.6.2 The Diffusion of Vorticity 233 15.7 Exercises 234 15.8 Further Reading 234 References 235 16 Boundary Layer Equations 237 16.1 The Boundary Layer over a Flat Plate 237 16.1.1 Scales in the Conservation of Mass 237 16.1.2 Scales in the Streamwise Momentum Equation 238 16.1.3 The Reynolds Number 239 16.1.4 Pressure in the Boundary Layer 239 16.1.5 The Transverse Momentum Balance 239 16.1.6 The Boundary Layer Momentum Equation 240 16.1.7 Pressure and External Tangential Velocity 241 16.1.8 Application to Curved Surfaces 241 16.2 Momentum Integral Equation 241 16.3 Local Boundary Layer Parameters 243 16.3.1 The Displacement and Momentum Thicknesses 243 16.3.2 The Skin Friction Coefficient 243 16.3.3 Example: Three Boundary Layer Profiles 244 16.4 Exercises 248 16.5 Further Reading 249 References 249 17 Laminar Boundary Layers 251 17.1 Boundary Layer Profile Curvature 251 17.1.1 Pressure Gradient and Boundary Layer Thickness 252 17.2 Pohlhausen’s Quartic Profiles 252 17.3 Thwaites’s Method for Laminar Boundary Layers 254 17.3.1 F(λ) ≈ 0.45 − 6λ 255 17.3.2 Correlations for Shape Factor and Skin Friction 256 17.3.3 Example: Zero Pressure Gradient 256 17.3.4 Example: Laminar Separation from a Circular Cylinder 257 17.4 Exercises 260 17.5 Further Reading 261 References 262 18 Compressibility 263 18.1 Steady-State Conservation of Mass 263 18.2 Longitudinal Variation of Stream Tube Section 265 18.2.1 The Design of Supersonic Nozzles 266 18.3 Perfect Gas Thermodynamics 266 18.3.1 Thermal and Caloric Equations of State 266 18.3.2 The First Law of Thermodynamics 267 18.3.3 The Isochoric and Isobaric Specific Heat Coefficients 267 18.3.4 Isothermal and Adiabatic Processes 267 18.3.5 Adiabatic Expansion 268 18.3.6 The Speed of Sound and Temperature 269 18.3.7 The Speed of Sound and the Speed 269 18.3.8 Thermodynamic Characteristics of Air 270 18.3.9 Example: Stagnation Temperature 270 18.4 Exercises 270 18.5 Further Reading 271 References 271 19 Linearized Compressible Flow 273 19.1 The Nonlinearity of the Equation for the Potential 273 19.2 Small Disturbances to the Free-Stream 274 19.3 The Uniform Free-Stream 275 19.4 The Disturbance Potential 275 19.5 Prandtl–Glauert Transformation 276 19.5.1 Fundamental Linearized Compressible Flows 277 19.5.2 The Speed of Sound 278 19.6 Application of the Prandtl–Glauert Rule 279 19.6.1 Transforming the Geometry 279 19.6.2 Computing Aerodynamical Forces 280 19.6.3 The Prandlt–Glauert Rule in Two Dimensions 282 19.6.4 The Critical Mach Number 284 19.7 Sweep 284 19.8 Exercises 285 19.9 Further Reading 285 References 286 Appendix A Notes on Octave Programming 287 A. 1 Introduction 287 A. 2 Vectorization 287 A.2. 1 Iterating Explicitly 288 A.2. 2 Preallocating Memory 288 A.2. 3 Vectorizing Function Calls 288 A.2. 4 Many Functions Act Elementwise on Arrays 289 A.2. 5 Functions Primarily Defined for Arrays 289 A.2. 6 Elementwise Arithmetic with Single Numbers 289 A.2. 7 Elementwise Arithmetic between Arrays 290 A.2. 8 Vector and Matrix Multiplication 290 A. 3 Generating Arrays 290 A.3. 1 Creating Tables with bsxfun 290 A. 4 Indexing 291 A.4. 1 Indexing by Logical Masks 291 A.4. 2 Indexing Numerically 291 A. 5 Just-in-Time Compilation 291 A. 6 Further Reading 292 References 292 Glossary 293 Nomenclature 305 Index 309

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Book SynopsisA comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration oTable of ContentsAcknowledgements xiii About the Authors xv 1 Introduction and Reading Guide 1 2 Binomial Trees 7 2.1 Equities and Basic Options 7 2.2 The One Period Model 8 2.3 The Multiperiod Binomial Model 9 2.4 Black-Scholes and Trees 10 2.5 Strengths and Weaknesses of Binomial Trees 12 2.5.1 Ease of Implementation 12 2.5.2 Oscillations 12 2.5.3 Non-recombining Trees 14 2.5.4 Exotic Options and Trees 14 2.5.5 Greeks and Binomial Trees 15 2.5.6 Grid Adaptivity and Trees 15 2.6 Conclusion 16 3 Finite Differences and the Black-Scholes PDE 17 3.1 A Continuous Time Model for Equity Prices 17 3.2 Black-Scholes Model: From the SDE to the PDE 19 3.3 Finite Differences 23 3.4 Time Discretization 27 3.5 Stability Considerations 30 3.6 Finite Differences and the Heat Equation 30 3.6.1 Numerical Results 34 3.7 Appendix: Error Analysis 36 4 Mean Reversion and Trinomial Trees 39 4.1 Some Fixed Income Terms 39 4.1.1 Interest Rates and Compounding 39 4.1.2 Libor Rates and Vanilla Interest Rate Swaps 40 4.2 Black76 for Caps and Swaptions 43 4.3 One-Factor Short Rate Models 45 4.3.1 Prominent Short Rate Models 45 4.4 The Hull-White Model in More Detail 46 4.5 Trinomial Trees 47 5 Upwinding Techniques for Short Rate Models 55 5.1 Derivation of a PDE for Short Rate Models 55 5.2 Upwind Schemes 56 5.2.1 Model Equation 57 5.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model 63 5.3.1 Bond Details 64 5.3.2 Model Details 64 5.3.3 Numerical Method 65 5.3.4 An Algorithm in Pseudocode 68 5.3.5 Results 69 6 Boundary, Terminal and Interface Conditions and their Influence 71 6.1 Terminal Conditions for Equity Options 71 6.2 Terminal Conditions for Fixed Income Instruments 72 6.3 Callability and Bermudan Options 74 6.4 Dividends 74 6.5 Snowballs and TARNs 75 6.6 Boundary Conditions 77 6.6.1 Double Barrier Options and Dirichlet Boundary Conditions 77 6.6.2 Artificial Boundary Conditions and the Neumann Case 78 7 Finite Element Methods 81 7.1 Introduction 81 7.1.1 Weighted Residual Methods 81 7.1.2 Basic Steps 82 7.2 Grid Generation 83 7.3 Elements 85 7.3.1 1D Elements 86 7.3.2 2D Elements 88 7.4 The Assembling Process 90 7.4.1 Element Matrices 93 7.4.2 Time Discretization 97 7.4.3 Global Matrices 98 7.4.4 Boundary Conditions 101 7.4.5 Application of the Finite Element Method to Convection-Diffusion-Reaction Problems 103 7.5 A Zero Coupon Bond Under the Two Factor Hull-White Model 105 7.6 Appendix: Higher Order Elements 107 7.6.1 3D Elements 109 7.6.2 Local and Natural Coordinates 111 8 Solving Systems of Linear Equations 117 8.1 Direct Methods 118 8.1.1 Gaussian Elimination 118 8.1.2 Thomas Algorithm 119 8.1.3 LU Decomposition 120 8.1.4 Cholesky Decomposition 121 8.2 Iterative Solvers 122 8.2.1 Matrix Decomposition 123 8.2.2 Krylov Methods 125 8.2.3 Multigrid Solvers 126 8.2.4 Preconditioning 129 9 Monte Carlo Simulation 133 9.1 The Principles of Monte Carlo Integration 133 9.2 Pricing Derivatives with Monte Carlo Methods 134 9.2.1 Discretizing the Stochastic Differential Equation 135 9.2.2 Pricing Formalism 137 9.2.3 Valuation of a Steepener under a Two Factor Hull-White Model 137 9.3 An Introduction to the Libor Market Model 139 9.4 Random Number Generation 146 9.4.1 Properties of a Random Number Generator 147 9.4.2 Uniform Variates 148 9.4.3 Random Vectors 150 9.4.4 Recent Developments in Random Number Generation 151 9.4.5 Transforming Variables 152 9.4.6 Random Number Generation for Commonly Used Distributions 155 10 Advanced Monte Carlo Techniques 161 10.1 Variance Reduction Techniques 161 10.1.1 Antithetic Variates 161 10.1.2 Control Variates 163 10.1.3 Conditioning 166 10.1.4 Additional Techniques for Variance Reduction 168 10.2 Quasi Monte Carlo Method 169 10.2.1 Low-Discrepancy Sequences 169 10.2.2 Randomizing QMC 174 10.3 Brownian Bridge Technique 175 10.3.1 A Steepener under a Libor Market Model 177 11 Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks 179 11.1 Pricing American options using the Longstaff and Schwartz algorithm 179 11.2 A Modified Least Squares Monte Carlo Algorithm for Bermudan Callable Interest Rate Instruments 181 11.2.1 Algorithm: Extended LSMC Method for Bermudan Options 182 11.2.2 Notes on Basis Functions and Regression 185 11.3 Examples 186 11.3.1 A Bermudan Callable Floater under Different Short-rate Models 186 11.3.2 A Bermudan Callable Steepener Swap under a Two Factor Hull-White Model 188 11.3.3 A Bermudan Callable Steepener Cross Currency Swap in a 3D IR/FX Model Framework 189 12 Characteristic Function Methods for Option Pricing 193 12.1 Equity Models 194 12.1.1 Heston Model 196 12.1.2 Jump Diffusion Models 198 12.1.3 Infinite Activity Models 199 12.1.4 Bates Model 200 12.2 Fourier Techniques 201 12.2.1 Fast Fourier Transform Methods 201 12.2.2 Fourier-Cosine Expansion Methods 203 13 Numerical Methods for the Solution of PIDEs 209 13.1 A PIDE for Jump Models 209 13.2 Numerical Solution of the PIDE 210 13.2.1 Discretization of the Spatial Domain 211 13.2.2 Discretization of the Time Domain 211 13.2.3 A European Option under the Kou Jump Diffusion Model 212 13.3 Appendix: Numerical Integration via Newton-Cotes Formulae 214 14 Copulas and the Pitfalls of Correlation 217 14.1 Correlation 218 14.1.1 Pearson’s ρ 218 14.1.2 Spearman’s ρ 218 14.1.3 Kendall’s τ 220 14.1.4 Other Measures 221 14.2 Copulas 221 14.2.1 Basic Concepts 222 14.2.2 Important Copula Functions 222 14.2.3 Parameter estimation and sampling 229 14.2.4 Default Probabilities for Credit Derivatives 234 15 Parameter Calibration and Inverse Problems 239 15.1 Implied Black-Scholes Volatilities 239 15.2 Calibration Problems for Yield Curves 240 15.3 Reversion Speed and Volatility 245 15.4 Local Volatility 245 15.4.1 Dupire’s Inversion Formula 246 15.4.2 Identifying Local Volatility 246 15.4.3 Results 247 15.5 Identifying Parameters in Volatility Models 248 15.5.1 Model Calibration for the FTSE- 100 249 16 Optimization Techniques 253 16.1 Model Calibration and Optimization 255 16.1.1 Gradient-Based Algorithms for Nonlinear Least Squares Problems 256 16.2 Heuristically Inspired Algorithms 258 16.2.1 Simulated Annealing 259 16.2.2 Differential Evolution 260 16.3 A Hybrid Algorithm for Heston Model Calibration 261 16.4 Portfolio Optimization 265 17 Risk Management 269 17.1 Value at Risk and Expected Shortfall 269 17.1.1 Parametric VaR 270 17.1.2 Historical VaR 272 17.1.3 Monte Carlo VaR 273 17.1.4 Individual and Contribution VaR 274 17.2 Principal Component Analysis 276 17.2.1 Principal Component Analysis for Non-scalar Risk Factors 276 17.2.2 Principal Components for Fast Valuation 277 17.3 Extreme Value Theory 278 18 Quantitative Finance on Parallel Architectures 285 18.1 A Short Introduction to Parallel Computing 285 18.2 Different Levels of Parallelization 288 18.3 GPU Programming 288 18.3.1 CUDA and OpenCL 289 18.3.2 Memory 289 18.4 Parallelization of Single Instrument Valuations using (Q)MC 290 18.5 Parallelization of Hybrid Calibration Algorithms 291 18.5.1 Implementation Details 292 18.5.2 Results 295 19 Building Large Software Systems for the Financial Industry 297 Bibliography 301 Index 307

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Book SynopsisEach statistical chapter in the second part relies on one or more real biomedical data sets, kindly made available by the Bordeaux School of Public Health (Institut de Santé Publique, d'Épidémiologie et de Développement - ISPED) and described at the beginning of the book.Trade ReviewFrom the book reviews:“This is a great addition to the chorus of books on R. It is a clear an excellent resource for teaching courses on data analysis and statistical computing using R at the graduate and advanced undergraduate levels. The book can be an asset for data scientists, and even more broadly for a wide variety of users including students, teachers, researchers, software engineers, and others whose work involves statistics, mathematics, and computer science.” (Yousri El Fattah, Computing Reviews, January, 2015)Table of ContentsForeward.- Basic Concepts and Data Organisation.- Importing, Exporting and Producing Data.- Data Manipulation, Functions.- R and its Documentation.- Drawing Curves and Plots.- Programming in R.- Managing Sessions.- Basic Mathematics.- Descriptive Statistics.- A Better Understanding of Random Variables.- Confidence Intervals and Hypothesis Testing.- Simple and Multiple Linear Regression.- Elementary Analysis of Variance.- Installing R and R Packages.- References.- Indices.- Solutions.

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Book SynopsisThis handy reference book detailing the intricacies of R covers version 4.x features, including numerous and significant changes to syntax, strings, reference counting, grid units, and more. Starting with the basic structure of R, the book takes you on a journey through the terminology used in R and the syntax required to make R work. You will find looking up the correct form for an expression quick and easy. Some of the new material includes information on RStudio, S4 syntax, working with character strings, and an example using the Twitter API. With a copy of the R 4 Quick Syntax Reference in hand, you will find that you are able to use the multitude of functions available in R and are even able to write your own functions to explore and analyze data. What You Will LearnDiscover the modes and classes of R objects and how to use themUse both packaged and user-created functions in RImport/export data and create new data objects in RCreate descriptive functions and manipulate objecTable of ContentsPart 1: R Basics1. Downloading R and Setting Up a File System2. The R Prompt3. Assignments and OperatorsPart 2: Kinds of Objects4. Modes of Objects5. Classes of ObjectsPart 3: Functions6. Packaged Functions7. User Created Functions8. How to Use a FunctionPart 4: I/O and Manipulating Objects9. Importing/Creating Data10. Exporting from R11. Descriptive Functions and Manipulating ObjectsPart 5: Flow control12. Flow Control13. Examples of Flow Control14. The Functions ifelse() and switch()Part 6: Some Common Functions, Packages and Techniques15. Some Common Functions16. The Packages base, stats and graphics17. The Tricks of the Trade

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Book SynopsisAnyone who wants to analyze data will find something useful here-even if you don't have a background in mathematics, statistics, or computer programming. If you want to examine data related to your work, this book is the ideal way to start.

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Book SynopsisApplied Predictive Modeling covers the overall predictive modeling process, beginning with the crucial steps of data preprocessing, data splitting and foundations of model tuning.Trade Review“…In teaching a data science course…I use a range of different resources because I need to cover working with data, model evaluation, and machine learning methods. The next time I teach this course, I will use only this book because it covers all of these aspects of the field.” (Louis Luangkesorn, lugerpitt.blogspot.com, June 2015) “There are a wide variety of books available on predictive analytics and data modeling around the web…we’ve carefully selected the following 10 books, based on relevance, popularity, online ratings, and their ability to add value to your business. 1. Applied Predictive Modeling.” (Timothy King, Business Intelligence Solutions Review, solutions-review.com, June 2015) "Applied Predictive Modeling aims to expose many of these techniques in a very readable and self-contained book. This is a very applied and hands-on book. It guides the reader through many examples that serve to illustrate main points, and it raises possible issues and considerations that are oftentimes overlooked or not sufficiently reflected upon. Highly recommended." (Bojan Tunguz, tunguzreview.com, June 2015)“This monograph presents a very friendly practical course on prediction techniques for regression and classification models… It is a well-written book very useful to students and practitioners who need an immediate and helpful way to apply complex statistical techniques.” (Stan Lipovetsky, Technometrics, Vol. 56 (3), August 2014)“In my judgment, Applied Predictive Modeling by Max Kuhn and Kjell Johnson (Springer 2013) ought to be at the very top of the reading list …They come across like coaches who really, really want you to be able to do this…Applied Predictive Modeling is a remarkable text…it is the succinct distillation of years of experience of two expert modelers…” (Joseph Rickert, blog.revolutionanalytics.com, June 2014)Table of ContentsGeneral Strategies.- Regression Models.- Classification Models.- Other Considerations.- Appendix.- References.- Indices.

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Book SynopsisThis third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 25 per cent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox.

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Book Synopsis“If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of the correspondence between quantitative information and mathematical manipulation.” -from the PrefaceFundamentals of Numerical Computation is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking.Professors Driscoll and Braun have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book.

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Book SynopsisThis book presents an introduction to structural equation modeling (SEM) and facilitates the access of students and researchers in various scientific fields to this powerful statistical tool. It offers a didactic initiation to SEM as well as to the open-source software, lavaan, and the rich and comprehensive technical features it offers. Structural Equation Modeling with lavaan thus helps the reader to gain autonomy in the use of SEM to test path models and dyadic models, perform confirmatory factor analyses and estimate more complex models such as general structural models with latent variables and latent growth models. SEM is approached both from the point of view of its process (i.e. the different stages of its use) and from the point of view of its product (i.e. the results it generates and their reading). Table of ContentsPreface ix Introduction xi Chapter 1 Structural Equation Modeling 1 1.1 Basic concepts 2 1.1.1 Covariance and bivariate correlation 2 1.1.2 Partial correlation 5 1.1.3 Linear regression analysis 7 1.1.4 Standard error of the estimate 10 1.1.5 Factor analysis 11 1.1.6 Data distribution normality 18 1.2 Basic principles of SEM 21 1.2.1 Estimation methods (estimators) 27 1.3 Model evaluation of the solution of the estimated model 36 1.3.1 Overall goodness-of-fit indices 36 1.3.2 Local fit indices (parameter estimates) 43 1.3.3 Modification indices 44 1.4 Confirmatory approach in SEM 45 1.5 Basic conventions of SEM 47 1.6 Place and status of variables in a hypothetical model 49 1.7 Conclusion 49 1.8 Further reading 50 Chapter 2 Structural Equation Modeling Software 53 2.1 R environment 54 2.1.1 Installing R software 55 2.1.2 R console 55 2.2 lavaan 58 2.2.1 Installing the lavaan package 58 2.2.2 Launching lavaan 58 2.3 Preparing and importing a dataset 60 2.3.1 Entry and import of raw data 60 2.3.2 What to do in the absence of raw data? 63 2.4 Major operators of lavaan syntax 65 2.5 Main steps in using lavaan 66 2.6 lavaan fitting functions 68 Chapter 3 Steps in Structural Equation Modeling 69 3.1 The theoretical model and its conceptual specification 70 3.2 Model parameters and model identification 71 3.3 Models with observed variables (path models) 73 3.3.1 Identification of a path model 74 3.3.2 Model specification using lavaan (step 2) 76 3.3.3 Direct and indirect effects 78 3.3.4 The statistical significance of indirect effects 80 3.3.5 Model estimation with lavaan (step 3) 81 3.3.6 Model evaluation (step 4) 82 3.3.7 Recursive and non-recursive models 83 3.3.8 Illustration of a path analysis model 85 3.4 Actor-partner interdependence model 90 3.4.1 Specifying and estimating an APIM with lavaan 92 3.4.2 Evaluation of the solution 93 3.4.3 Evaluating the APIM re-specified with equality constraints 94 3.5 Models with latent variables (measurement models and structural models) 95 3.5.1 The measurement model or Confirmatory Factor Analysis 97 3.6 Hybrid models 148 3.7 Measure with a single-item indicator 149 3.8 General structural model including single-item latent variables with a single indicator 151 3.9 Conclusion 152 3.10 Further reading 155 Chapter 4 Advanced Topics: Principles and Applications 157 4.1 Multigroup analysis 157 4.1.1 The steps of MG-CFA 162 4.1.2 Model solutions and model comparison tests 166 4.1.3 Total invariance versus partial invariance 171 4.1.4 Specification of a partial invariance in lavaan syntax 172 4.2 Latent trait-state models 172 4.2.1 The STARTS model 173 4.2.2 The Trait-State-Occasion Model 197 4.2.3 Concluding remarks 211 4.3 Latent growth models 213 4.3.1 General overview 213 4.3.2 Illustration of an univariate linear growth model 223 4.3.3 Illustration of an univariate non-linear (quadratic) latent growth model 228 4.3.4 Conditional latent growth model 232 4.3.5 Second-order latent growth model 240 4.4 Further reading 249 References 251 Index 269

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Book SynopsisData science unifies statistics, data analysis and machine learning to achieve a better understanding of the masses of data which are produced today, and to improve prediction. Special kinds of data (symbolic, network, complex, compositional) are increasingly frequent in data science. These data require specific methodologies, but there is a lack of reference work in this field. Advances in Data Science fills this gap. It presents a collection of up-to-date contributions by eminent scholars following two international workshops held in Beijing and Paris. The 10 chapters are organized into four parts: Symbolic Data, Complex Data, Network Data and Clustering. They include fundamental contributions, as well as applications to several domains, including business and the social sciences. Table of ContentsPreface xi Part 1. Symbolic Data 1 Chapter 1. Explanatory Tools for Machine Learning in the Symbolic Data Analysis Framework 3Edwin DIDAY 1.1. Introduction 4 1.2. Introduction to Symbolic Data Analysis 6 1.2.1. What are complex data? 6 1.2.2. What are “classes” and “class of complex data”? 7 1.2.3. Which kind of class variability? 7 1.2.4. What are “symbolic variables” and “symbolic data tables”? 7 1.2.5. Symbolic Data Analysis (SDA) 9 1.3. Symbolic data tables from Dynamic Clustering Method and EM 10 1.3.1. The “dynamical clustering method” (DCM) 10 1.3.2. Examples of DCM applications 10 1.3.3. Clustering methods by mixture decomposition 12 1.3.4. Symbolic data tables from clustering 13 1.3.5. A general way to compare results of clustering methods by the “explanatory power” of their associated symbolic data table 15 1.3.6. Quality criteria of classes and variables based on the cells of the symbolic data table containing intervals or inferred distributions 15 1.4. Criteria for ranking individuals, classes and their bar chart descriptive symbolic variables 16 1.4.1. A theoretical framework for SDA 16 1.4.2. Characterization of a category and a class by a measure of discordance 18 1.4.3. Link between a characterization by the criteria W and the standard Tf-Idf 19 1.4.4. Ranking the individuals, the symbolic variables and the classes of a bar chart symbolic data table 21 1.5. Two directions of research 23 1.5.1. Parametrization of concordance and discordance criteria 23 1.5.2. Improving the explanatory power of any machine learning tool by a filtering process 25 1.6. Conclusion 27 1.7. References 28 Chapter 2. Likelihood in the Symbolic Context 31Richard EMILION and Edwin DIDAY 2.1. Introduction 31 2.2. Probabilistic setting 32 2.2.1. Description variable and class variable 32 2.2.2. Conditional distributions 33 2.2.3. Symbolic variables 33 2.2.4. Examples 35 2.2.5. Probability measures on (ℂ, C), likelihood 37 2.3. Parametric models for p = 1 38 2.3.1. LDA model 38 2.3.2. BLS method 41 2.3.3. Interval-valued variables 42 2.3.4. Probability vectors and histogram-valued variables 42 2.4. Nonparametric estimation for p = 1 45 2.4.1. Multihistograms and multivariate polygons 45 2.4.2. Dirichlet kernel mixtures 45 2.4.3. Dirichlet Process Mixture (DPM) 45 2.5. Density models for p ≥ 2 46 2.6. Conclusion 46 2.7. References 47 Chapter 3. Dimension Reduction and Visualization of Symbolic Interval-Valued Data Using Sliced Inverse Regression 49Han-Ming WU, Chiun-How KAO and Chun-houh CHEN 3.1. Introduction 49 3.2. PCA for interval-valued data and the sliced inverse regression 51 3.2.1. PCA for interval-valued data 51 3.2.2. Classic SIR 52 3.3. SIR for interval-valued data 53 3.3.1. Quantification approaches 54 3.3.2. Distributional approaches 56 3.4. Projections and visualization in DR subspace 58 3.4.1. Linear combinations of intervals 58 3.4.2. The graphical representation of the projected intervals in the 2D DR subspace 59 3.5. Some computational issues 61 3.5.1. Standardization of interval-valued data 61 3.5.2. The slicing schemes for iSIR 62 3.5.3. The evaluation of DR components 62 3.6. Simulation studies 63 3.6.1. Scenario 1: aggregated data 63 3.6.2. Scenario 2: data based on interval arithmetic 63 3.6.3. Results 64 3.7. A real data example: face recognition data 65 3.8. Conclusion and discussion 73 3.9. References 74 Chapter 4. On the “Complexity” of Social Reality. Some Reflections About the Use of Symbolic Data Analysis in Social Sciences 79Frédéric LEBARON 4.1. Introduction 79 4.2. Social sciences facing “complexity” 80 4.2.1. The total social fact, a designation of “complexity” in social sciences 80 4.2.2. Two families of answers 80 4.2.3. The contemporary deepening of the two approaches, “reductionist” and “encompassing” 81 4.2.4. Issues of scale and heterogeneity 82 4.3. Symbolic data analysis in the social sciences: an example 83 4.3.1. Symbolic data analysis 83 4.3.2. An exploratory case study on European data 83 4.3.3. A sociological interpretation 94 4.4. Conclusion 95 4.5. References 96 Part 2. Complex Data 99 Chapter 5. A Spatial Dependence Measure and Prediction of Georeferenced Data Streams Summarized by Histograms 101Rosanna VERDE and Antonio BALZANELLA 5.1. Introduction 101 5.2. Processing setup 103 5.3. Main definitions 104 5.4. Online summarization of a data stream through CluStream for Histogram data 106 5.5. Spatial dependence monitoring: a variogram for histogram data 107 5.6. Ordinary kriging for histogram data 110 5.7. Experimental results on real data 112 5.8. Conclusion 116 5.9. References 116 Chapter 6. Incremental Calculation Framework for Complex Data 119Huiwen WANG, Yuan WEI and Siyang WANG 6.1. Introduction 119 6.2. Basic data 122 6.2.1. The basic data space 122 6.2.2. Sample covariance matrix 123 6.3. Incremental calculation of complex data 124 6.3.1. Transformation of complex data 124 6.3.2. Online decomposition of covariance matrix 125 6.3.3. Adopted algorithms 128 6.4. Simulation studies 131 6.4.1. Functional linear regression 131 6.4.2. Compositional PCA 133 6.5. Conclusion 135 6.6. Acknowledgment 135 6.7. References 135 Part 3. Network Data 139 Chapter 7. Recommender Systems and Attributed Networks 141Françoise FOGELMAN-SOULIÉ, Lanxiang MEI, Jianyu ZHANG, Yiming LI, Wen GE, Yinglan LI and Qiaofei YE 7.1. Introduction 141 7.2. Recommender systems 142 7.2.1. Data used 143 7.2.2. Model-based collaborative filtering 145 7.2.3. Neighborhood-based collaborative filtering 145 7.2.4. Hybrid models 148 7.3. Social networks 150 7.3.1. Non-independence 150 7.3.2. Definition of a social network 150 7.3.3. Properties of social networks 151 7.3.4. Bipartite networks 152 7.3.5. Multilayer networks 153 7.4. Using social networks for recommendation 154 7.4.1. Social filtering 154 7.4.2. Extension to use attributes 155 7.4.3. Remarks 156 7.5. Experiments 156 7.5.1. Performance evaluation 156 7.5.2. Datasets 157 7.5.3. Analysis of one-mode projected networks 158 7.5.4. Models evaluated 160 7.5.5. Results 160 7.6. Perspectives 163 7.7. References 163 Chapter 8. Attributed Networks Partitioning Based on Modularity Optimization 169David COMBE, Christine LARGERON, Baptiste JEUDY, Françoise FOGELMAN-SOULIÉ and Jing WANG 8.1. Introduction 169 8.2. Related work 171 8.3. Inertia based modularity 172 8.4. I-Louvain 174 8.5. Incremental computation of the modularity gain 176 8.6. Evaluation of I-Louvain method 179 8.6.1. Performance of I-Louvain on artificial datasets 179 8.6.2. Run-time of I-Louvain 180 8.7. Conclusion 181 8.8. References 182 Part 4. Clustering 187 Chapter 9. A Novel Clustering Method with Automatic Weighting of Tables and Variables 189Rodrigo C. DE ARAÚJO, Francisco DE ASSIS TENORIO DE CARVALHO and Yves LECHEVALLIER 9.1. Introduction 189 9.2. Related Work 190 9.3. Definitions, notations and objective 191 9.3.1. Choice of distances 192 9.3.2. Criterion W measures the homogeneity of the partition P on the set of tables 193 9.3.3. Optimization of the criterion W 195 9.4. Hard clustering with automated weighting of tables and variables 196 9.4.1. Clustering algorithms MND–W and MND–WT 196 9.5. Applications: UCI data sets 201 9.5.1. Application I: Iris plant 201 9.5.2. Application II: multi-features dataset 204 9.6. Conclusion 206 9.7. References 206 Chapter 10. Clustering and Generalized ANOVA for Symbolic Data Constructed from Open Data 209Simona KORENJAK-ČERNE, Nataša KEJŽAR and Vladimir BATAGELJ 10.1. Introduction 209 10.2. Data description based on discrete (membership) distributions 210 10.3. Clustering 212 10.3.1. TIMSS – study of teaching approaches 215 10.3.2. Clustering countries based on age–sex distributions of their populations 217 10.4. Generalized ANOVA 221 10.5. Conclusion 225 10.6. References 226 List of Authors 229 Index 233

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Book SynopsisThis revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and consolidate their understanding. The book includes homework, solutions, and Jupyter notebooks. This edition includes new topics such as Boosting, Multi-armed bandits, statistical tests, social networks, queuing networks, and neural networks. For ancillaries related to this book, including examples of Python demos and also Python labs used in Berkeley, please email Mary James at mary.james@springer.com. This is an open access book. Table of ContentsChapter 1. Page Rank - A.- Chapter 2. Page Rank - B.- Chapter 3. Multiplexing - A.- Chapter 4. Multiplexing - B.- Chapter 5. Networks - A.- Chapter 6. Networks - B.- Chapter 7. Digital Link - A.- Chapter 8. Digital Link - B.- Chapter 9. Tracking - A.- Chapter 10. Tracking - B.- Chapter 11. Speech Recognition - A.- Chapter 12. Speech Recognition - B.- Chapter 13. Route planning - A.- Chapter 14. Route Planning - B.- chapter 15. Perspective & Complements.- A. Elementary Probability.- B. Basic Probability.- . Index.

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Book SynopsisThis book shows the capabilities of Microsoft Excel in teaching marketing statistics effectively. It is a step-by-step, exercise-driven guide for students and practitioners who need to master Excel to solve practical marketing problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically inclined, or if you are wary of computers, this is the right book for you.Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in marketing courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. Excel 2019 for Marketing Statistics: A Guide to Solving Practical Problems capitalizes on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work.In this new edition, each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand marketing problems. Practice problems are provided at the end of each chapter with their solutions in an appendix. Separately, there is a full practice test (with answers in an appendix) that allows readers to test what they have learned.Table of ContentsPreface.- Acknowledgements.- 1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean.- 2 Random Number Generator.- 3 Confidence Interval About the Mean Using the TINV Function and Hypothesis Testing.- 4 One-Group t-Test for the Mean.- 5 Two-Group t-Test of the Difference of the Means for Independent Groups.- 6 Correlation and Simple Linear Regression.- 7 Multiple Correlation and Multiple Regression.- 8 One-Way Analysis of Variance (ANOVA).- Appendix A: Answers to End-of-Chapter Practice Problems.- Appendix B: Practice Test.- Appendix C: Answers to Practice Test.- Appendix D: Statistical Formulas.- Appendix E: t-table.- Index.

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Book SynopsisThe main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called “FuzzySTs” which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.Table of Contents- 1. Introduction. - Part I Theoretical Part. - 2. Fundamental Concepts on Fuzzy Sets. - 3. Fuzzy Rule-Based Systems. - 4. Distances Between Fuzzy Sets. - 5. Fuzzy Random Variables and Fuzzy Distributions. - 6. Fuzzy Statistical Inference. - Conclusion Part I. - Part II Applications. - 7. Evaluation of Linguistic Questionnaire. - 8. Fuzzy Analysis of Variance. - Part III An R Package for Fuzzy Statistical Analysis: A DetailedDescription. - 9. FuzzySTs: Fuzzy Statistical Tools: A Detailed Description. - Conclusion.

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Book SynopsisNow in its second edition, this textbook provides an introduction to Python and its use for statistical data analysis. It covers common statistical tests for continuous, discrete and categorical data, as well as linear regression analysis and topics from survival analysis and Bayesian statistics.For this new edition, the introductory chapters on Python, data input and visualization have been reworked and updated. The chapter on experimental design has been expanded, and programs for the determination of confidence intervals commonly used in quality control have been introduced. The book also features a new chapter on finding patterns in data, including time series. A new appendix describes useful programming tools, such as testing tools, code repositories, and GUIs.The provided working code for Python solutions, together with easy-to-follow examples, will reinforce the reader’s immediate understanding of the topic. Accompanying data sets and Python programs are also available online. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis.With examples drawn mainly from the life and medical sciences, this book is intended primarily for masters and PhD students. As it provides the required statistics background, the book can also be used by anyone who wants to perform a statistical data analysis. Table of ContentsI Python and Statistics.- 1 Introduction.- 2 Python.- 3 Data Input.- 4 Data Display.- II Distributions and Hypothesis Tests.- 5 Basic Statistical Concepts.- 6 Distributions of One Variable.- 7 Hypothesis Tests.- 8 Tests of Means of Numerical Data.- 9 Tests on Categorical Data.- 10 Analysis of Survival Times.- III Statistical Modelling.- 11 Finding Patterns in Signals.- 12 Linear Regression Models.- 13 Generalized Linear Models.- 14 Bayesian Statistics.- Appendices.- A Useful Programming Tools.- B Solutions.- C Equations for Confidence Intervals.- D Web Ressources.- Glossary.- Bibliography.- Index.

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Book SynopsisBayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability—keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information—scientific evidence—ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.This book is Open Access.Table of ContentsPart I - Introduction to the Bayes Factor (Likelihood Ratio)Presents the principal statistic discussed throughout this book: the Bayes factor, in the context of forensic science, more often known as the likelihood ratio. Subsections of this part: clarify the different roles (known as, respectively, the ‘investigative’ and ‘evaluative’ role) that forensic scientists may assume in their daily work articulate the reasons why forensic scientists should adhere to a Bayesian framework of inference in order to ensure coherence in their inferential and decision-making tasks formally describe what the Bayes factor is and how it relates to coherent decision analysis describe the advantages that Bayes factors offer in assessing, articulating and communicating the value of scientific evidence in general, and in legal proceedings in particular Part II - Bayes Factor for Investigative PurposesDeals with a peculiar task of the forensic scientist, known as the ‘investigative mode’ (i.e., one of the two main modes of functioning introduced in Part I). That is, in forensic settings, it may well be the case that a potential source (i.e., a suspect) is not available for comparative purposes, in particular in early stages of the legal process. Notwithstanding, data and measurements on recovered material (e.g., seized on a crime scene) can be used for an investigative purpose. In this mode of working, scientists can offer to investigative authorities (or, in a more general perspective, mandating parties) information to help discriminate between general propositions concerning, for instance, the characterizing features of the source that left the recovered material (e.g., gender, externally visible traits such as hair and eye color, handedness, etc.). At this stage in the process, the scientist tries to help answer questions such as ‘what happened?’ in the case under investigation, or ‘what can we infer about the offender?’. In this context, the Bayes factor can be used as a statistic to measure and help decide how to classify, for example, objects and substances on which measurements have been made. This use of the Bayes factor will be explained through practical examples involving topics such as handwriting characteristics, toner from printers in questioned document examination, drugs of abuse, toxicology, forensic anthropology and forensic DNA profiling (listing is not exhaustive and may evolve during the writing of the book). Both univariate and multivariate data will be considered, with or without replicates, and involving different statistical distributions (i.e. Binomial, Poisson, Normal, etc.). The examples refer to realistic forensic applications as they may be encountered in judicial contexts and the forensic practitioner’s own field of activity. Data will be selected from published literature or from the author’s own records. R sample code will be specified and explanations will be included on how to interpret results in context and convey their meaning appropriately.Part III - Bayes Factor for Evaluative PurposesFocuses on the scientist’s role in a more advanced stage of the legal process. That is, situations in which the evaluation of scientific findings will take into account a potential source of the recovered material (e.g., a suspect or an object/tool). This kind of reporting is typically required when scientists need to communicate their results for use at trial. It is of utmost importance at this juncture that scientists express the value of the observed data and findings under competing hypotheses, focusing on a potential (i.e., known) source versus an alternative source (e.g., propositions such as ‘the recovered item comes from the same source as the control material’, and ‘the recovered item is from a source that is different from that of the control material’). The Bayes factor is the central inferential concept for such expressions of weight of evidence. In this part of the book, too, examples will be chosen with the intention to reflect realistic scenarios as they may arise in current judicial practice. In particular, the outline will consider uni- and multi­-variate data from scenarios related to microtraces (e.g., glass and paint fragments), handwriting and drugs of abuse. Besides computational R code, this chapter will also include (i) sensitivity analyses to provide readers with a means to further investigate the properties of the proposed evaluative procedures based on the Bayes factor, and (ii) decision theoretic extensions to outline how to interface expressions of weight of evidence with the broader perspective of coherent decision-making. Part IV - ConclusionSummarizes the key messages developed throughout this book, emphasizing (i) the contribution of an extended use of the Bayes factor in a normative decision framework, and (ii) the role of the Bayes factor as the relevant statistic for both investigative and evaluative tasks that characterize current forensic science.

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Book SynopsisThis open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.Table of ContentsIntroduction.- Locally Refined Splines.- Adaptive surface Fitting with Local Refinement: LR B-spline Surfaces.- A Statistical Criterion to Judge the Goodness of Fit of LR B-splines Surface Approximation.- LR B-splines for Representation of Terrain and Seabed: Data Fusion, Outliers, and Voids.- LR B-spline Surfaces and Volumes for Deformation Analysis of Terrain Data.- Conclusion.

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Book SynopsisThis book is a self-guided tour of MATLAB for engineers and life scientists. It introduces the most commonly used programming techniques through biologically inspired examples. Although the text is written for undergraduates, graduate students and academics, as well as those in industry, will find value in learning MATLAB. The book takes the emphasis off of learning syntax so that the reader can focus more on algorithmic thinking. Although it is not assumed that the reader has taken differential equations or a linear algebra class, there are short introductions to many of these concepts. Following a short history of computing, the MATLAB environment is introduced. Next, vectors and matrices are discussed, followed by matrix-vector operations. The core programming elements of MATLAB are introduced in three successive chapters on scripts, loops, and conditional logic. The last three chapters outline how to manage the input and output of data, create professional quality graphics and find and use MATLAB toolboxes. Throughout, biomedical and life science examples are used to illustrate MATLAB's capabilities.Table of ContentsIntroduction.- MATLAB Programming Environment.- Vectors.- Matrices.- MatrixVector Operations.- Scripts and Functions.- Loops.- Conditional Logic.- Data In/Data Out.- Graphics.- Toolboxes.

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Book SynopsisThis textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.Table of ContentsPreface.- Motivating Introduction.- Linear Models.- Nonlinear Models.- Bayesian Optimal Designs.- Hot Topics.- Real Case Examples.- Appendices.- References.- Index.

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Book SynopsisThis book illustrates the capabilities of Microsoft Excel to teach applied statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical statistical problems in industry. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in statistics courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past.The 2nd edition of Applied Business Statistics for Business and Management capitalizes on these improvements by teaching students and practitioners how to apply Excel to statistical techniques necessary in their courses and workplace. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand business problems. Practice problems are provided at the end of each chapter with their solutions.Table of Contents​Statistics and Data.- Summarizing Data.- Descriptive Statistics and Graphing.- Normal World.- Survey Design.- Sampling.- Inference.- Probability.- Correlation.- Simple Linear Regression.- Multiple Regression.- Significance Tests.- Non Linear Regression.- Survey Reports​.

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Book SynopsisThis guide for practicing statisticians, data scientists, and R users and programmers will teach the essentials of preprocessing: data leveraging the R programming language to easily and quickly turn noisy data into usable pieces of information. Data wrangling, which is also commonly referred to as data munging, transformation, manipulation, janitor work, etc., can be a painstakingly laborious process. Roughly 80% of data analysis is spent on cleaning and preparing data; however, being a prerequisite to the rest of the data analysis workflow (visualization, analysis, reporting), it is essential that one become fluent and efficient in data wrangling techniques.This book will guide the user through the data wrangling process via a step-by-step tutorial approach and provide a solid foundation for working with data in R. The author's goal is to teach the user how to easily wrangle data in order to spend more time on understanding the content of the data. By the end of the book, the user will have learned: How to work with different types of data such as numerics, characters, regular expressions, factors, and dates The difference between different data structures and how to create, add additional components to, and subset each data structure How to acquire and parse data from locations previously inaccessible How to develop functions and use loop control structures to reduce code redundancy How to use pipe operators to simplify code and make it more readable How to reshape the layout of data and manipulate, summarize, and join data sets Table of Contents1. Preface 2. Introduction a. The Role of Data Wrangling i. Introduction to R 1. Open Source 2. Flexibility 3. Community ii. R Basics 1. Assignment & Evaluation 2. Vectorization 3. Getting help 4. Workspace 5. Working with packages 6. Style guide 3. Working with Different Types of Data in R a. Dealing with Numbers i. Integer vs. Double ii. Generating sequence of non-random numbers iii. Generating sequence of random numbers iv. Setting the seed for reproducible random numbers v. Comparing numeric values vi. Rounding numbers b. Dealing with Character Strings i. Character string basics ii. String manipulation with base R iii. String manipulation with stringr iv. Set operatons for character strings c. Dealing with Regular Expressions i. Regex Syntax ii. Regex Functions iii. Additional resources d. Dealing with Factors i. Creating, converting & inspecting factors ii. Ordering levels iii. Revalue levels iv. Dropping levels e. Dealing with Dates i. Getting current date & time ii. Converting strings to dates iii. Extract & manipulate parts of dates iv. Creating date sequences v. Calculations with dates vi. Dealing with time zones & daylight savings vii. Additional resources <4. Managing Data Structures in R a. Data Structure Basics i. Identifying the Structure ii. Attributes b. Managing Vectors i. Creating ii. Adding on to iii. Adding attributes iv. Subsetting c. Managing Lists i. Creating iii. Adding attributes iv. Subsetting d. Managing Matrices i. Creating ii. Adding on to iii. Adding attributes iv. Subsetting e. Managing Data Frames i. Creating ii. Adding on to iii. Adding attributes iv. Subsetting f. Dealing with Missing Values i. Testing for missing values ii. Recoding missing values iii. Excluding missing values 5. Importing, Scraping, and Exporting Data with R a. Importing Data i. Reading data from text files ii. Reading data from Excel files iii. Load data from saved R object file iv. Additional resources b. Scraping Data i. Importing tabular and Excel files stored online ii. Scraping HTML text iii. Scraping HTML table data iv. Working with APIs v. Additional Resources c. Exporting Data i. Writing data to text files ii. Writing data to Excel files iii. Saving data as an R object file iv. Additional resources 6. Creating Efficient & Readable Code in R a. Functions i. Function Components ii. Arguments iii. Scoping Rules iv. Lazy Evaluation v. Returning Multiple Outputs from a Function vi. Dealing with Invalid Parameters vii. Saving and Sourcing Functions viii. Additional Resources b. Loop Control Statements i. Basic control statements (i.e. if, for, while, etc.) ii. Apply family iii. Other useful “loop-like” functions iv. Additional Resources c. Simplify Your Code with %>% i. Pipe (%>%) Operator ii. Additional Functions iii. Additional Pipe Operators iv. Additional Resources 7. Shaping & Transforming Your Data with R a. Reshaping Your Data with tidyr i. Making wide data long ii. Making long data wide iii. Splitting a single column into multiple columns iv. Combining multiple columns into a single column v. Additional tidyr functions vi. Sequencing your tidyr operations vii. Additional resources b. Transforming Your Data with dplyr i. Selecting variables of interest ii. Filtering rows iii. Grouping data by categorical variables iv. Performing summary statistics on variables v. Arranging variables by value vi. Joining datasets vii. Creating new variables viii. Additional resources

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Book SynopsisDieses Lehrbuch enthält in kompakter, übersichtlicher Form die wichtigsten finanzmathematischen Fragestellungen und die dazu passenden Prozeduren von MATLAB (Erklärung der Ein- und Ausgabegrößen, mathematische Darstellung des entsprechenden finanztechnischen Vorgangs, Parameterwahlmöglichkeiten). Damit werden sowohl die numerische als auch die grafische Realisierung von Aufgaben- und Problemstellungen der Finanzmathematik in effektiver Weise ermöglicht. Table of ContentsEinführung in MATLAB - Datumfunktionen - Abschreibungen - Analyse von Cash Flows - Rentenrechnung - Tilgungsrechnung - Analyse festverzinslicher Wertpapiere (Anleihen / Bonds) - Portfolio-Optimierung - Analyse von Finanzderivaten (Optionen) - Finanz-Zeitreihen (Volatilitätsanalyse) - Verzeichnis der MATLAB-Prozeduren

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Book SynopsisDifferentialgleichungen spielen in den Naturwissenschaften und der Technik eine bedeutende Rolle, da viele Modelle mit ihrer Hilfe formuliert werden. Für die exakte Lösung dieser Gleichungen gibt es ausgefeilte mathematische Methoden, die in dem Computeralgebra-System Mathematica verfügbar sind. Das Buch enthält einerseits eine Einführung in die Theorie der gewöhnlichen und partiellen Differentialgleichungen und beschreibt andererseits, wie sich Mathematica zur Lösung dieser Gleichungen einsetzen läßt. Die theoretischen Ergebnisse werden in algorithmischer Form angegeben und mit vielen Beispielen ergänzt, die auch die graphischen Fähigkeiten von Mathematica ausnutzen.Table of ContentsDifferentialgleichungen erster Ordnung - Differentialgleichungssysteme erster Ordnung - Lineare Differentialgleichungen mit konstanten Koeffizienten - Partielle Differentialgleichungen erster Ordnung - Lineare Partielle Differentialgleichungen zweiter Ordnung

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Book SynopsisThis book presents the statistical analysis of compositional data sets, i.e., data in percentages, proportions, concentrations, etc. The subject is covered from its grounding principles to the practical use in descriptive exploratory analysis, robust linear models and advanced multivariate statistical methods, including zeros and missing values, and paying special attention to data visualization and model display issues. Many illustrated examples and code chunks guide the reader into their modeling and interpretation. And, though the book primarily serves as a reference guide for the R package “compositions,” it is also a general introductory text on Compositional Data Analysis. Awareness of their special characteristics spread in the Geosciences in the early sixties, but a strategy for properly dealing with them was not available until the works of Aitchison in the eighties. Since then, research has expanded our understanding of their theoretical principles and the potentials and limitations of their interpretation. This is the first comprehensive textbook addressing these issues, as well as their practical implications with regard to software.The book is intended for scientists interested in statistically analyzing their compositional data. The subject enjoys relatively broad awareness in the geosciences and environmental sciences, but the spectrum of recent applications also covers areas like medicine, official statistics, and economics. Readers should be familiar with basic univariate and multivariate statistics. Knowledge of R is recommended but not required, as the book is self-contained.Trade ReviewFrom the reviews:“This book offers not only the theoretical background to analyse and interpret compositional data, but also the R support and guidance for the compositions package. The book is organised in 7 chapters. … The book is built in an accessible manner for undergraduates and postgraduates alike and offers an all in one overview of the analysis of compositional data in R.” (Irina Ioana Mohorianu, zbMATH, Vol. 1276, 2014)Table of ContentsIntroduction.- Fundamental Concepts of Compositional Data Analysis.- Distributions for Random Compositions.- Descriptive Analysis of Compositional Data.- Linear Models for Compositions.- Multivariate Statistics.- Zeroes, Missings and Outliers.- References.- Index.

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Book SynopsisWie können große und kleine Datenmengen aus Beobachtungen, Messungen, Befragungen, Untersuchungen, Analysen etc. verwaltet, aufbereitet, komprimiert, mit Kennzahlen erklärt und wirksam grafisch dargestellt werden? Wie kann man dazu Hypothesen prüfen, Zusammenhänge aufdecken, Abhängigkeiten finden? Dieses Buch zeigt Ihnen, wie die grundlegenden Methoden der Statistik recht einfach mit Excel umsetzbar sind. Es wurden in einheitlicher, sehr verständlicher Methodik die grundlegenden statistischen Verfahren sowohl der beschreibenden als auch der beurteilenden Statistik zusammengestellt. Umfangreiche Beispiele, didaktisch aufbereitet und stets ausführlich mit Excel umgesetzt, bieten eine umfassende Hilfe für den Umgang mit Datenmengen.Alle Beispiele stehen online für individuelle Übungen bereit. Trade Review“... Die Wahl geeigneter Beispiele und viele Abbildungen ... machen das Buch zu einer Empfehlung für alle, die einen verständlichen Grundkurs Statistik mit Excel suchen ...” (Karl Schäfer, in: Amazon.de, 19. Juli 2016)Table of ContentsWas man über Microsoft Excel wissen sollte.- Excel und große Datenmengen.- Beschreibende Statistik – Auskünfte über eine Da­tenreihe.- Beschreibende Statistik – Auskünfte über mehrere Da­tenreihen.- Zufall, Wahrscheinlichkeit, Verteilungsfunktionen.- Beurteilende Statistik – Prüfen von Verteilungen.- Beurteilende Statistik – Parameterprüfung mit einer Stichprobe.- Beurteilende Statistik – Parametervergleiche zweier verbundener Stichproben.- Beurteilende Statistik – Parametervergleiche zweier nicht verbundener Stichproben.- Einfache Varianzanalyse nicht verbundener Stichproben - Schätzungen.

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Book SynopsisComputeralgebra- Systeme wie MAPLE gehören heute zum Alltag aller, die Mathematik in Schule, Wirtschaft und Hochschule anwenden. Gleichzeitig bieten sie die Möglichkeit, in ganz anderer Weise Beispiele zu untersuchen und zu veranschaulichen, als dies mit Bleistift und Papier möglich ist. Neben einer Einführung in MAPLE hat dieses Buch zum Ziel, durch die Behandlung von Beispielen den Stoff des ersten Studienjahres, wie er in den Vorlesungen zur Analysis und Linearen Algebra behandelt wird, zu vertiefen und zu veranschaulichen. Es besteht aus Aufgaben mit Erläuterungen, anhand derer der Leser den Stoff eigenständig durcharbeiten soll. Mathematische Anwendersysteme als berufsbildende Kompetenz in der Bachelor-Ausbildung: Das Buch eignet sich für ein Modul aufbauend auf den Grundvorlesungen Analysis und Lineare Algebra. Materialien zu diesem Buch für das E-Learning System OKUSON werden für Dozenten unter OnlinePLUS bereitgestellt.Table of ContentsEinführung in MAPLE - Erste Beispiele und Aufgaben - Elementare Operationen mit Matrizen und Vektoren - Das Gauß-Verfahren und die Cramersche Regel - Diagonalisierbarkeit komplexer Matrizen - Matrizen mit positiven Einträgen - Reelle Funktionen einer Variablen - Taylor-Entwicklung - Reelle Funktionen von mehreren Variablen - Quadratische Gleichungen und Quadriken - Hermite-Polynome und Fourier-Reihen - Normalformen - Gewöhnliche Differentialgleichungen - Lösungen

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Book SynopsisIl volume fornisce un'introduzione a teoria e applicazioni dei modelli lineari generalizzati. Si presentano modelli di regressione per risposte continue, binarie, categoriali e di conteggio. Si offre anche un'introduzione ai modelli per risposte correlate. Utilizzando il software statistico R, vengono forniti gli strumenti per l'analisi dei dati tramite i diversi modelli parametrici e semiparametrici. Gli esempi con R alla fine di ciascun capitolo rappresentano una guida ad esercitazioni con il computer e richiedono una partecipazione attiva nello svolgere le analisi proposte. Numerosi esercizi concludono ogni capitolo. Il taglio adottato è funzionale ad approfondire in modo integrato aspetti teorici e applicativi. Unico nel suo genere, è rivolto agli studenti di Scienze Statistiche. Table of Contents1. Modelli lineari e lineari generalizzati.- 2. Modelli lineari generalizzati.- 3. Modelli per dati bancari.- 4. Modelli per risposte politomiche.- 5. Modelli per dati di conteggio.- 6. Quasi-verosimiglianza.- Modelli per risposte correlate.- A Dati utilizzati nel testo.- B Distribuzioni di probabilità.- C Eguaglianza tra stime OLS e GLS.- D Il metodo delta.- E Funzioni generatrici.- F Codice R per l’esempio 2.9.- G Equivalenza tra residui di Pearson e di devianza.- H Modelli per la sovradispersione: schema.

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Book SynopsisIl libro contiene in forma compatta il programma svolto negli insegnamenti introduttivi di Statistica e tratta alcuni argomenti indispensabili per l'attività di ricerca, come le tecniche di simulazione Monte Carlo, i metodi di inferenza statistica, di best fit e di analisi dei dati di laboratorio. Gli argomenti vengono sviluppati partendo dai fondamenti, evidenziandone gli aspetti applicativi, fino alla descrizione dettagliata di molti casi di particolare rilevanza in ambito scientifico e tecnico. Il testo è rivolto agli studenti universitari dei corsi ad indirizzo scientifico e a tutti quei ricercatori che devono risolvere problemi concreti che coinvolgono l’analisi dei dati e le tecniche di simulazione. In questa edizione, completamente rivista e corretta, sono stati aggiunti alcuni importanti argomenti sul test d’ipotesi (a cui è stato dedicato un capitolo interamente nuovo) e sul trattamento degli errori sistematici. Per la prima volta è stato adottato il software R, con una ricca libreria di programmi originali accessibile al lettore.Table of Contents1 La probabilità.- 2 Rappresentazione dei fenomeni aleatori.- 3 Calcolo elementare delle probabilità.- 4 Calcolo delle probabilità per più variabili.- 5 Funzioni di variabili aleatorie.- 6 Statistica di base: stime.- 7 Statistica di base: verifica di ipotesi.- 8 Il metodo Monte Carlo.- 9 Applicazioni del metodo Monte Carlo.- 10 Inferenza statistica e verosimiglianza.- 11 Minimi quadrati.- 12 Analisi dei dati sperimentali.

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Book SynopsisThis book discusses all major topics on survey sampling and estimation. It covers traditional as well as advanced sampling methods related to the spatial populations. The book presents real-world applications of major sampling methods and illustrates them with the R software. As a large sample size is not cost-efficient, this book introduces a new method by using the domain knowledge of the negative correlation between the variable of interest and the auxiliary variable in order to control the size of a sample. In addition, the book focuses on adaptive cluster sampling, rank-set sampling and their applications in real life. Advance methods discussed in the book have tremendous applications in ecology, environmental science, health science, forestry, bio-sciences, and humanities. This book is targeted as a text for undergraduate and graduate students of statistics, as well as researchers in various disciplines.Table of Contents-1. Introduction.- 2. Simple Random Sampling.- 3. Stratied Random Sampling.- 4. Cluster Sampling.- 5. Double Sampling.- 6. Probability Proportional to Size Sampling.- 7. Systematic Sampling.- 8. Resampling Techniques.- 9. Adaptive Cluster Sampling.- 10. Two-Stage Adaptive Cluster Sampling.- 11. Adaptive Cluster Double Sampling.- 12. Inverse Adaptive Cluster Sampling.- 13. Two Stage Inverse Adaptive Cluster Sampling.- 14. Stratified Inverse Adaptive Cluster Sampling.- 15. Negative Adaptive Cluster Sampling.- 16. Negative Adaptive Cluster Double Sampling.- 17. Two- Stage Negative Adaptive Cluster Sampling.- 18. Balanced and Unbalanced Ranked Set Sampling.- 19. Ranked Set Sampling in Other Parameter Estimation and Non-Parametric Inference.- 20. Important Versions of Ranked Set Sampling.- 21. Sampling Errors.

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Book SynopsisThis book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language.The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines.Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.Table of ContentsPrefacePart I: Introduction Chapter 1: Overview of Statistical Modeling and StanChapter 2: Review of Bayesian InferenceChapter 3: Before Starting Statistical ModelingPart II: Introduction of StanChapter 4: Start with Stan, RStan and PyStanChapter 5: Elementary Regression and Model CheckPart III: Essential Components and Techniques for ExpertsChapter 6: Introduction of Distributions from Modeling ViewpointsChapter 7: Issues of RegressionChapter 8: Nonlinear ModelChapter 9: Hierarchical ModelChapter 10: Advanced GrammarsChapter 11: How to Lead ConvergenceChapter 12: Discrete ParametersChapter 13: Usage of MCMC SamplesPart IV: Advanced Topics for Real-world DataChapter 14: Longitudinal Data Analysis with State Space Model Chapter 15: Spatial Data Analysis with Markov Field ModelChapter 16: Survival AnalysisChapter 17: Causal InferenceChapter 18: Model selectionAppendix: Differences between Stan and BUGSReferenceIndex

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Book SynopsisThis book provides a design and development perspective MPC for micro-grid control, emphasizing step-by-step conversion of a nonlinear MPC to linear MPC preserving critical aspects of nonlinear MPC. The book discusses centralized and decentralized MPC control algorithms for a generic modern-day micro-grid consisting of vital essential constituents. It starts with the nonlinear MPC formulation for micro-grids. It also moves towards the linear time-invariant and linear time-variant approximations of the MPC for micro-grid control. The contents also discuss how the application of orthonormal special functions can improve computational complexity of MPC algorithms. It also highlights various auxiliary requirements like state estimator, disturbance compensator for robustness, selective harmonic eliminator for eliminating harmonics in the micro-grid, etc. These additional requirements are crucial for the successful online implementation of the MPC. In the end, the book shows how a well-designed MPC is superior in performance compared to the conventional micro-grid primary controllers discussed above. The key topics discussed in this book include – the detailed modeling of micro-grid components; operational modes in micro-grid and their control objectives; conventional micro-grid primary controllers; the importance of MPC as a micro-grid primary controller; understanding of MPC operation; nonlinear MPC formulation; linear approximations of MPC; application of special functions in the MPC formulation; and other online requirements for the MPC implementation. The examples in the book are available both from a calculation point of view and as MATLAB codes. This helps the students get acquainted with the subject first and then allows them to implement the subject they learn in software for further understanding and research.Table of ContentsChapter 1. Micro-grid Introduction and Overview.- Chapter 2. An Overview of Micro-grid Control.- Chapter 3. Mathematical Modelling of a Micro-grid.- Chapter 4. Introduction to Model Predictive Control.- Chapter 5. LTI-MPC for the Micro-grid Control.- Chapter 6. LTV-MPC with Extended “TAIL”.- Chapter 7. Special functions in the MPC formulation.- Chapter 8. Auxiliary Requirements for Real-time Implementation.- Chapter 9. Conclusion and Future Scope.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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