Probability and statistics Books

Book SynopsisThis text is an ideal introduction to the use of quantitative methods in archaeology. Statistical techniques are presented in a clear and straightforward manner throughout, and the careful balance between introduction of key concepts and their application to archaeological data is perfectly suited for both students and professionals in the field.Table of ContentsList of Tables. List of Figures. List of Equations. Acknowledgments. 1 Quantifying Archaeology. 2 Data. Scales of Measurement. Nominal level measurement. Ordinal level measurement. Interval level measurement. Ratio level measurement. The relationship among the scales of measurement. Validity. Accuracy and Precision. Populations and Samples. 3 Characterizing Data Visually. Frequency Distributions. Histograms. Stem and Leaf Diagrams. Ogives (Cumulative Frequency Distributions). Describing a Distribution. Bar Charts. Displaying Data like a Pro. Archaeology and Exploratory Data Analysis. 4 Characterizing Data Numerically: Descriptive Statistics. Measures of Central Tendency. Mean. Median. Mode. Which measure of location is best? Measures of Dispersion. Range. Interquartile range. Variance and standard deviation. Calculating Estimates of the Mean and Standard Deviation. Coefficients of Variation. Box Plots. Characterizing Nominal and Ordinal Scale Data. Index of dispersion for nominal data and the index of qualitative variation. 5 An Introduction to Probability. Theoretical Determinations of Probability. Empirical Determinations of Probability. Complex Events. Using Probability to Determine Likelihood. The Binomial Distribution. The psychic's trick. Simplifying the binomial. Probability in Archaeological Contexts. 6 Putting Statistics to Work: The Normal Distribution. 7 Hypothesis Testing I: An Introduction. Hypotheses of Interest. Formal Hypothesis Testing and the Null Hypothesis. Errors in Hypothesis Testing. 8 Hypothesis Testing II: Confi dence Limits, the t-Distribution, and One-Tailed Tests. Standard Error. Comparing Sample Means to m. Statistical Inference and Confidence Limits. The t-Distribution. Degrees of freedom and the t-distribution. Hypothesis Testing Using the t-Distribution. Testing One-Tailed Null Hypotheses. 9 Hypothesis Testing III: Power. Calculating. Statistical Power. Increasing the power of a test. Calculating Power: An Archaeological Example. Power Curves. Putting it all Together: A Final Overview of Hypothesis Testing. Steps to hypothesis testing. Evaluating common hypotheses. 10 Analysis of Variance and the F-Distribution. Model II ANOVA: Identifying the Impacts of Random Effects. Model I ANOVA: The Analysis of Treatment Effects. A Final Summary of Model I and Model II ANOVA. ANOVA Calculation Procedure. Identifying the Sources of Signifi cant Variation in Model I and Model II ANOVA. Comparing Variances. 11 Linear Regression and Multivariate Analysis. Constructing a Regression Equation. Evaluating the Statistical Significance of Regression. Using Regression Analysis to Predict Values. Placing confi dence intervals around the regression coefficient. Confidence Limits around Y for a Given Xi. Estimating X from Y. The Analysis of Residuals. Some Final Thoughts about Regression. Selecting the right regression model. Do not extrapolate beyond the boundaries of the observed data. Use the right methods when creating reverse predictions. Be aware of the assumptions for regression analysis. You may be able to transform your data to create a linear relationship from a curvilinear relationship. Use the right confi dence limits. 12 Correlation. Pearson’s Product-Moment Correlation Coefficient. The assumptions of Pearson's product-moment correlation coeffi cient. Spearman's Rank Order Correlation Coeffi cient. Some Final Thoughts (and Warnings) about Correlation. 13 Analysis of Frequencies. Determining the Source of Variation in a Chi-Square Matrix. Assumptions of Chi-Square Analysis. The Analysis of Small Samples Using Fisher’s Exact Test and Yate's Continuity Correction. The Median Test. 14 An Abbreviated Introduction to Nonparametric and Multivariate Analysis. Nonparametric Tests Comparing Groups. Wilcoxon two-sample test. Kruskal–Wallis nonparametric ANOVA. Multivariate Analysis and the Comparison of Means. A review of pertinent conceptual issues. Two-way ANOVA. Nested ANOVA. 15 Factor Analysis and Principal Component Analysis. Objectives of Principal Component and Factor Analysis. Designing the Principal Component/Factor Analysis. Assumptions and Conceptual Considerations of Factor Analysis. An Example of Factor Analysis. Factor Analysis vs. Principal Component Analysis. 16 Sampling, Research Designs, and the Archaeological Record. How to Select a Sample. How Big a Sample is Necessary? Some Concluding Thoughts. References. Appendix A Areas under a Standardized Normal Distribution. Appendix B Critical Values for the Student's t-Distribution. Appendix C Critical Values for the F-Distribution. Appendix D Critical Values for the Chi-Square Distribution. Appendix E Critical Values for the Wilcoxon Two-Sample U-Test. Index.

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Book SynopsisChoosing and Using Statistics remains an invaluable guide for students using a computer package to analyse data from research projects and practical class work. The text takes a pragmatic approach to statistics with a strong focus on what is actually needed. There are chapters giving useful advice on the basics of statistics and guidance on the presentation of data. The book is built around a key to selecting the correct statistical test and then gives clear guidance on how to carry out the test and interpret the output from four commonly used computer packages: SPSS, Minitab, Excel, and (new to this edition) the free program, R. Only the basics of formal statistics are described and the emphasis is on jargon-free English but any unfamiliar words can be looked up in the extensive glossary. This new 3rd edition of Choosing and Using Statistics is a must for all students who use a computer package to apply statistics in practical and project work. Features neTrade Review"Written in a concise and direct style, this book presents a selection of some of the most widely used statistical tests and data exploration techniques." (Biological Conservation, 1 March 2012) "Written in a concise and direct style, this book presents a selection of some of the most widely used statistical tests and data exploration techniques ... In general, this book is a very good primer for students with no statistical expertise." (Biological Conservation Reviews, 2011) "This book makes everything so easy. Complicated tests are effortlessly condensed, and the instructions are almost too easy to follow. Diagrams and sample data sets are used frequently so you can practise using tests before applying them to your own data sets, whilst the logical layout guides you toward the correct test for both your data, and what you want to prove (or disprove)." (Animals & Men, February 2011)Table of ContentsPreface xiii The third edition xiv How to use this book xiv Packages used xv Example data xv Acknowledgements for the first edition xv Acknowledgements for the second edition xv Acknowledgements for the third edition xvi 1 Eight steps to successful data analysis 1 2 The basics 2 Observations 2 Hypothesis testing 2 P-values 3 Sampling 3 Experiments 4 Statistics 4 Descriptive statistics 5 Tests of difference 5 Tests of relationships 5 Tests for data investigation 6 3 Choosing a test: a key 7 Remember: eight steps to successful data analysis 7 The art of choosing a test 7 A key to assist in your choice of statistical test 8 4 Hypothesis testing, sampling and experimental design 23 Hypothesis testing 23 Acceptable errors 23 P-values 24 Sampling 25 Choice of sample unit 25 Number of sample units 26 Positioning of sample units to achieve a random sample 26 Timing of sampling 27 Experimental design 27 Control 28 Procedural controls 28 Temporal control 28 Experimental control 29 Statistical control 29 Some standard experimental designs 29 5 Statistics, variables and distributions 32 What are statistics? 32 Types of statistics 33 Descriptive statistics 33 Parametric statistics 33 Non-parametric statistics 33 What is a variable? 33 Types of variables or scales of measurement 34 Measurement variables 34 Continuous variables 34 Discrete variables 35 How accurate do I need to be? 35 Ranked variables 35 Attributes 35 Derived variables 36 Types of distribution 36 Discrete distributions 36 The Poisson distribution 36 The binomial distribution 37 The negative binomial distribution 39 The hypergeometric distribution 39 Continuous distributions 40 The rectangular distribution 40 The normal distribution 40 The standardized normal distribution 40 Convergence of a Poisson distribution to a normal distribution 41 Sampling distributions and the 'central limit theorem' 41 Describing the normal distribution further 41 Skewness 41 Kurtosis 43 Is a distribution normal? 43 Transformations 43 An example 44 The angular transformation 44 The logit transformation 45 The t-distribution 46 Confidence intervals 47 The chi-square distribution 47 The exponential distribution 47 Non-parametric 'distributions' 48 Ranking, quartiles and the interquartile range 48 Box and whisker plots 48 6 Descriptive and presentational techniques 49 General advice 49 Displaying data: summarizing a single variable 49 Box and whisker plot (box plot) 49 Displaying data: showing the distribution of a single variable 50 Bar chart: for discrete data 50 Histogram: for continuous data 51 Pie chart: for categorical data or attribute data 52 Descriptive statistics 52 Statistics of location or position 52 Arithmetic mean 53 Geometric mean 53 Harmonic mean 53 Median 53 Mode 53 Statistics of distribution, dispersion or spread 55 Range 55 Interquartile range 55 Variance 55 Standard deviation (SD) 55 Standard error (SE) 56 Confidence intervals (CI) or confidence limits 56 Coefficient of variation 56 Other summary statistics 56 Skewness 57 Kurtosis 57 Using the computer packages 57 General 57 Displaying data: summarizing two or more variables 62 Box and whisker plots (box plots) 62 Error bars and confidence intervals 63 Displaying data: comparing two variables 63 Associations 63 Scatterplots 64 Multiple scatterplots 64 Trends, predictions and time series 65 Lines 65 Fitted lines 67 Confidence intervals 67 Displaying data: comparing more than two variables 68 Associations 68 Three-dimensional scatterplots 68 Multiple trends, time series and predictions 69 Multiple fitted lines 69 Surfaces 70 7 The tests 1: tests to look at differences 72 Do frequency distributions differ? 72 Questions 72 G-test 72 An example 73 Chi-square test 75 An example 76 Kolmogorov–Smirnov test 86 An example 87 Anderson–Darling test 89 Shapiro–Wilk test 90 Graphical tests for normality 90 Do the observations from two groups differ? 92 Paired data 92 Paired t-test 92 Wilcoxon signed ranks test 96 Sign test 99 Unpaired data 103 t-test 103 One-way ANOVA 111 Mann–Whitney U 119 Do the observations from more than two groups differ? 123 Repeated measures 123 Friedman test (for repeated measures) 123 Repeated-measures ANOVA 127 Independent samples 128 One-way ANOVA 129 Post hoc testing: after one-way ANOVA 138 Kruskal–Wallis test 142 Post hoc testing: after the Kruskal–Wallis test 145 There are two independent ways of classifying the data 145 One observation for each factor combination (no replication) 146 Friedman test 146 Two-way ANOVA (without replication) 152 More than one observation for each factor combination (with replication) 160 Interaction 160 Two-way ANOVA (with replication) 163 An example 164 Scheirer–Ray–Hare test 175 An example 175 There are more than two independent ways to classify the data 182 Multifactorial testing 182 Three-way ANOVA (without replication) 183 Three-way ANOVA (with replication) 184 An example 184 Multiway ANOVA 191 Not all classifications are independent 192 Non-independent factors 192 Nested factors 192 Random or fixed factors 193 Nested or hierarchical designs 193 Two-level nested-design ANOVA 193 An example 193 8 The tests 2: tests to look at relationships 199 Is there a correlation or association between two variables? 199 Observations assigned to categories 199 Chi-square test of association 199 An example 200 Cramér coefficient of association 208 Phi coefficient of association 209 Observations assigned a value 209 'Standard' correlation (Pearson's product-moment correlation) 210 An example 210 Spearman's rank-order correlation 214 An example 215 Kendall rank-order correlation 218 An example 218 Regression 219 An example 220 Is there a cause-and-effect relationship between two variables? 220 Questions 220 'Standard' linear regression 221 Prediction 221 Interpreting r2 222 Comparison of regression and correlation 222 Residuals 222 Confidence intervals 222 Prediction interval 223 An example 223 Kendall robust line-fit method 230 Logistic regression 230 An example 231 Model II regression 235 Polynomial, cubic and quadratic regression 235 Tests for more than two variables 236 Tests of association 236 Questions 236 Correlation 236 Partial correlation 237 Kendall partial rank-order correlation 237 Cause(s) and effect(s) 237 Questions 237 Regression 237 Analysis of covariance (ANCOVA) 238 Multiple regression 242 Stepwise regression 242 Path analysis 243 9 The tests 3: tests for data exploration 244 Types of data 244 Observation, inspection and plotting 244 Principal component analysis (PCA) and factor analysis 244 An example 245 Canonical variate analysis 251 Discriminant function analysis 251 An example 251 Multivariate analysis of variance (MANOVA) 256 An example 256 Multivariate analysis of covariance (MANCOVA) 259 Cluster analysis 259 DECORANA and TWINSPAN 263 Symbols and letters used in statistics 264 Greek letters 264 Symbols 264 Upper-case letters 265 Lower-case letters 266 Glossary 267 Assumptions of the tests 282 What if the assumptions are violated? 284 Hints and tips 285 Using a computer 285 Sampling 286 Statistics 286 Displaying the data 287 A table of statistical tests 289 Index 291

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Book SynopsisMeasuring baseball will never be the same.Trade ReviewA deeply old-fashioned treatise in which a statistic of Mr. Taylor's devising (potential runs per game) is used to rate the top hitters in history by era, position and role... Charming. -- Tim Marchman Wall Street Journal 2011Table of ContentsPrefaceList of AbbreviationsPregame AnalysisPart I: Every Era Has Its Greats1. The Era of Constant Change, 1876-1892: The Age of Dan Brouthers2. The Live Ball Interval, 1893-1900: The Age of Ed Delahanty3. The Dead Ball Era, 1901-1920: The Age of Ty Cobb4. The Live Ball Ea, 1921-1941: The Age of Babe Ruth5. The Live Ball Continued Era, 1942-1962: The Age of Ted Williams6. The Dead Ball Interval, 1963-1976: The Age of Hank Aaron7. The Live Ball Revived Era, 1977-1992: The Age of Mike Schmidt8. The Live Ball Enhanced Era, 1993-2009: The Age of UncertaintyPart II: The Ultimate Lineup Card9. Fielding a Team of Great Hitters10. The Table Setters11. The Table ClearersPart III: Hot Stove League Favorites Revisted12. Left on Base13. Whatever Happened to the Triple Crown?Postgame ReportAppendix: Using the BPPA Formula in Fantasy Baseball LeaguesNotesIndex

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Book SynopsisHis mathematical morsels are not only enjoyable to read-they may even help you improve your game.Table of ContentsPrefacePart I: General Golf Analysis1. The Shape of Golf2. Golfer's Spread: Variation in Golf3. Good Luck Putting: Randomness on the Greens4. The Rivalry: Cautious and Risky Strategies5. Handicap Systems and Other HustlesPart II: Analysis of PGA Tour Statistics6. The ShotLink Revolution: Golf Statistics7. Lags and Gags: Putting Statistics8. Chips and Flops: Short Game Statistics9. Iron Byron: Approach Shot Statistics10. The Big Dog: Driving Statistics11. Tigermetrics: Player Rankings12. More Rating Systems and Tiger TalesAppendix A: Supplementary TablesAppendix B: Player ProfilesNotesGlossaryReferences

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Book SynopsisThis book presents models and statistical methods for the analysis of recurrent event data. More general intensity-based models are also considered, as well as simpler models that focus on rate or mean functions.Trade ReviewFrom the Reviews: "The book provides many good real life examples to demonstrate application of the methods discussed....[it] is excellent for teaching an advanced class in statistics on this topic as it also contains many good exercises at the end of each chapter, some being extensions of the discussions." (Journal of Biopharmaceutical Statistics (JBS), Issue #5, 2008) "This book provides a timely and comprehensive review of methodologies for recurrent event data analysis and should be beneficial to Biometrics readers who are interested in recurrent events." "The strength of this book is its scope. It covers most of the methodology that is readily available for general use. ...Overall, we think this is a very good reference for recurrent event data analysis, especially because no other books provide a similar degree of coverage, and it would provide a nice textbook for a graduate-level course on the topic." (Biometrics, September 2008) "This book deals with processes generating multiple events over time. … The book comprises eight chapters, four appendices and a useful notational glossary. … it is directed to a much broader target readership, like social scientists, economists and industrial statisticians as well. … Many examples are used to illustrate and discuss the models and statistical methods in great detail. Techniques for estimation, testing and model checking are lucidly described … for a graduate course." (Harald Heinzl, Zentralblatt MATH, Vol. 1159, 2009) “…Every aspiring statistical researcher interested in recurrent events should have this book on his/her shelf as a great guide for learning the state-of-the-art stochastic models, frequentist (mostly estimating equation and asymptotic based) methods, and computational tools (including popular programs and routines). This is a very well-organized and comprehensive book on a very rapidly expanding area of research. As a mentor of PhD students, I myself will definitely recommend every graduate student interested in mastering recurrent events to read this book thoroughly to understand the current state of the literature as well as areas of future research and further development.” ( Journal of the American Statistical Association, Dec. 2009, Vol. 104, No. 488)Table of ContentsModels and Frameworks for Analysis of Recurrent Events.- Methods Based on Counts and Rate Functions.- Analysis of Gap Times.- General Intensity-Based Models.- Multitype Recurrent Events.- Observation Schemes Giving Incomplete or Selective Data.- OtherTopics.

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Book SynopsisProvides a comprehensive resource on what has become the dominant paradigm in designing novel interaction methods, involving gestures, speech, text, touch and brain-controlled interaction, embedded in innovative and emerging human-computer interfaces.

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Book SynopsisProvides a comprehensive resource on what has become the dominant paradigm in designing novel interaction methods, involving gestures, speech, text, touch and brain-controlled interaction, embedded in innovative and emerging human-computer interfaces.

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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 SynopsisProvides a lively development of the mathematics needed to answer the question, ‘How many times should a deck of cards be shuffled to mix it up?’ The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table.Table of Contents Shuffling cards: An introduction Practice and history of shuffling cards Convergence rates for riffle shuffles Features Eigenvectors and Hopf algebras Shuffling and carries Different models for riffle shuffling Move to front shuffling and variations Shuffling and geometry Shuffling and algebraic topology Type B shuffles and shelf shuffling machines Descent algebras, $P$-partitions, and quasisymmetric functions Overhand shuffling ``Smoosh'' shuffle How to shuffle perfectly (randomly) Applications to magic tricks, traffic merging, and statistics Shuffling and multiple zeta values Bibliography Index

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Book SynopsisDevelops a mathematical theory for finance, based on an intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics.Table of Contents The market Numeraires and market viability Financing optimization maximality Ramifications and extensions Elements of functional and convex analysis Bibliography Index

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Book SynopsisProvides a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.Table of Contents Preliminaries Independent random variables with independent sum and difference Characterization of probability distributions through the independence of linear forms Characterization of probability distributions through the symmetry of the conditional distribution of one linear form given another Characterization theorems on the field of $p$-adic numbers Miscellaneous characterization theorems Bibliography Index Index of symbols

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Book SynopsisIntroduces the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. By avoiding extreme technicalities and elaborate proof techniques, this is an accessible resource for students and researchers.Table of Contents Introductory remarks: Constituents of the univariate antenna problem Regularization tools: Functional and Fourier analytic auxiliaries Regularization methodologies: Matricial methodologies of resolution Compact operator methodologies of resolution Example realizations light: Univariate differentiation Reconstruction and regularization methods Regularization examples: Regularization methodologies in geotechnology Sampling tools: Lattice point and special function theoretic auxiliaries Sampling methodologies: Sampling over continuously connected pointsets Sampling over discretely given pointsets Polyharmonic finite bandwidth sampling Polyharmonic infinite bandwidth sampling Polymetaharmonic finite bandwidth sampling Polymetaharmonic infinite bandwidth sampling Sampling examples: Sampling methodologies in technology Concluding remarks: Recovery as interconnecting whole List of symbols Bibliography Index

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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 SynopsisThe Canadian Political Science Association's 1964 Conference on Statistics was held in Charlottetown on June 13 and 14. The general theme of the Conference was Regional Statistical Studies. Twelve papers were presented and of these nine are included in this volume.

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Book SynopsisThis book throws new light on the origins of probability and statistics. Heretofore these were thought to be entirely the creation of recent centuries, but it is demonstrated here that probability has a much longer history, reaching back to biblical times. Study of the Talmudic sources, with frequent reference to selected commentaries, as well as post-Talmudic sources, reveals that such reasoning was used by Talmudic rabbis from the first centuries of the Christian era in dealing with juridical problems. The Talmudic rabbis even formulated the rudimentary rules of the arithmetic of probabilities and later also the mathematical theory of combinations and permutations. It is shown that almost all the conceptions of probability which are entertained today, as well as some of the enigmas which beset contemporary philosophers of probability and induction, are described in the rabbinic writings. Readers interested in the history of ideas and the philosophy of science, the developme

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Book SynopsisStatistics in Kinesiology, Fifth Edition, introduces basic statistical concepts, with an emphasis on those commonly used in the exercise sciences. Examples drawn from kinesiology fields and extensive problem sets facilitate a deeper understanding of statistical methods and their applications.Table of ContentsChapter 1. Measurement, Statistics, and Research What Is Measurement? Process of Measurement Variables and Constants Research Design and Statistical Analysis Statistical Inference SummaryChapter 2. Organizing and Displaying Data Organizing Data Displaying Data SummaryChapter 3. Percentiles Common Percentile Divisions Calculations Using Percentiles SummaryChapter 4. Measures of Central Tendency Mode Median Mean Relationships Among the Mode, Median, and Mean SummaryChapter 5. Measures of Variability Range Interquartile Range Variance Standard Deviation Definition Method of Hand Calculations Calculating Standard Deviation for a Sample Coefficient of Variation Standard Deviation and Normal Distribution SummaryChapter 6. The Normal Curve Z Scores Standard Scores Probability and Odds Calculating Skewness and Kurtosis SummaryChapter 7. Fundamentals of Statistical Inference Predicting Population Parameters Using Statistical Inference Estimating Sampling Error Levels of Confidence, Confidence Intervals, and Probability of Error An Example Using Statistical Inference Statistical Hypothesis Testing Type I and Type II Error Degrees of Freedom Living With Uncertainty Two- and One-Tailed Tests Applying Confidence Intervals SummaryChapter 8. Correlation and Bivariate Regression Correlation Calculating the Correlation Coefficient Bivariate Regression Homoscedasticity SummaryChapter 9. Multiple Correlation and Multiple Regression Multiple Correlation Partial Correlation Multiple Regression SummaryChapter 10. The t Test: Comparing Means From Two Sets of Data The t Tests Types of t Tests Magnitude of the Difference (Size of Effect) Determining Power and Sample Size The t Test for Proportions SummaryChapter 11. Simple Analysis of Variance: Comparing the Means Among Three or More Sets of Data Assumptions in ANOVA Sources of Variance Calculating F: The Definition Method Determining the Significance of F Post Hoc Tests Magnitude of the Treatment (Size of Effect) SummaryChapter 12. Analysis of Variance With Repeated Measures Assumptions in Repeated Measures ANOVA Calculating Repeated Measures ANOVA Correcting for Violations of the Assumption of Sphericity Post Hoc Tests Interpreting the Results An Example From Leisure Studies and Recreation SummaryChapter 13. Quantifying Reliability Intraclass Correlation Coefficient Standard Error of Measurement SummaryChapter 14. Factorial Analysis of Variance A Between–Between Example A Between–Within Example A Within–Within Example SummaryChapter 15. Analysis of Covariance Relationship Between ANOVA and Regression ANCOVA and Statistical Power Assumptions in ANCOVA The Pretest–Posttest Control Group Design Pairwise Comparisons SummaryChapter 16. Analysis of Nonparametric Data Chi-Square (Single Classification) Chi-Square (Two or More Classifications) Rank Order Correlation Mann-Whitney U Test Kruskal-Wallis ANOVA for Ranked Data Friedman’s Two-Way ANOVA by Ranks SummaryChapter 17. Clinical Measures of Association Relative Risk Odds Ratio Diagnostic Testing SummaryChapter 18. Advanced Statistical Procedures Multilevel Modeling Meta-Analysis Multiple Analysis of Variance Factor Analysis Discriminant Analysis Summary Appendix: Statistical Tables

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Book SynopsisThe papers collected here focus on probabilistic causality, addressing topics such as the search for causal mechanisms, epistemic and metaphysical views of causality, Bayesian nets and causal dependence, and causation in the special sciences. Some papers stress the statistical analysis of probabilistic data; others address causal issues in physics, with an emphasis on physical processes that are also probabilistic—i.e., stochastic processes.

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Book SynopsisThe 1964 publication of "Inference and Disputed Authorship" made the cover of "Time" magazine and drew the attention of academics and the public alike for its use of statistical methodology to solve one of American history's most notorious questions: the disputed authorship of the "Federalist Papers". Back in print for a new generation of readers, this classic volume applies mathematics, including the once-controversial Bayesian analysis, to the heart of a literary and historical problem by studying frequently used words in the texts. The reissue of this landmark book will be welcomed by anyone interested in the juncture of history, political science, and authorship.

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Book SynopsisThis is a reprint of the orginal book released in 1968. Our primary goal in this book is to sharpen the skill, sophistication, and in- tuition of the reader in the interpretation of mental test data, and in the construction and use of mental tests both as instruments of psychological theory and as tools in the practical problems of selection, evaluation, and guidance. We seek to do this by exposing the reader to some psychologically meaningful statistical theories of mental test scores. Although this book is organized in terms of test-score theories and models, the practical applications and limitations of each model studied receive substantial emphasis, and these discussions are presented in as nontechnical a manner as we have found possible. Since this book catalogues a host of test theory models and formulas, it may serve as a reference handbook. Also, for a limited group of specialists, this book aims to provide a more rigorous foundation for further theoretical research than has heretofore been available.One aim of this book is to present statements of the assumptions, together with derivations of the implications, of a selected group of statistical models that the authors believe to be useful as guides in the practices of test construction and utilization. With few exceptions we have given a complete proof for each major result presented in the book. In many cases these proofs are simpler, more complete, and more illuminating than those originally offered. When we have omitted proofs or parts of proofs, we have generally provided a reference containing the omitted argument. We have left some proofs as exercises for the reader, but only when the general method of proof has already been demonstrated. At times we have proved only special cases of more generally stated theorems, when the general proof affords no additional insight into the problem and yet is substantially more complex mathematically.Trade ReviewThis comprehensive and authoritative work is a major contribution to the literature of test theory. Without doubt it is destined to become a classic in the field. Maurice Tatsuoka (1971)

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Book SynopsisProbability Theory is a classic topic in any course of exact sciences, that evolved from the amalgamation of different areas of mathematics, including set and measure theory. An axiomatic treatment of probability is presented in the book. Probability Theory is fundamental to several areas of knowledge, including engineering, computer science, mathematics, physics, sciences, economics, biology, medicine, social sciences and social communication. This book targets graduate students who may not have taken basic courses in these specific topics, and can provide a quick and concise way to obtain the knowledge they need to succeed in advanced courses.

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Book SynopsisLinear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships.The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including: the fundamentals of stochastic processes and the construction of stochastic systems; an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and a presentation of stochastic adaptive control theory. Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.Table of Contents Contents Preface to the Classics Edition; Preface; Chapter 0: Introduction; Chapter 1: Stochastic Processes; Chapter 2: Linear Stochastic Systems; Chapter 3: Estimation Theory; Chapter 4: Stochastic Realization Theory; Chapter 5: System Identification: Foundations and Basic Concepts; Chapter 6: Least Squares Parameter Estimation; Chapter 7: Maximum Likelihood Estimation of Gaussian ARMAX and State-Space Systems; Chapter 8: Minimum Prediction Error Identification Methods; Chapter 9: Nonstationary System Identification; Chapter 10: Feedback, Causality, and Closed Loop System Identification; Chapter 11: Linear-Quadratic Stochastic Control; Chapter 12: Stochastic Adaptive Control; Appendices; Appendix 1: Probability Theory; Appendix 2: System Theory; Appendix 3: Harmonic and Related Analysis; References; Index.

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Book SynopsisThis book develops the theory of probability and mathematical statistics with the goal of analyzing real-world data. Throughout the text, the R package is used to compute probabilities, check analytically computed answers, simulate probability distributions, illustrate answers with appropriate graphics, and help students develop intuition surrounding probability and statistics. Examples, demonstrations, and exercises in the R programming language serve to reinforce ideas and facilitate understanding and confidence. The book’s Chapter Highlights provide a summary of key concepts, while the examples utilizing R within the chapters are instructive and practical. Exercises that focus on real-world applications without sacrificing mathematical rigor are included, along with more than 200 figures that help clarify both concepts and applications. In addition, the book features two helpful appendices: annotated solutions to 700 exercises and a Review of Useful Math.

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Book SynopsisCompressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing.An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate.The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.

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Book SynopsisThe mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents: a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century, important connections between the moment problem and many branches of analysis, a unified exposition of important classical results, which are difficult to read in the original journals, and a strong foundation for many areas in modern applied mathematics.

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Book SynopsisStarting with the fundamentals of classical smooth optimization and building on established convex programming techniques, this research monograph presents a foundation and methodology for modern nonconvex nondifferentiable optimization. It provides readers with theory, methods, and applications of nonconvex and nondifferentiable optimization in statistical estimation, operations research, machine learning, and decision making. A comprehensive and rigorous treatment of this emergent mathematical topic is urgently needed in today's complex world of big data and machine learning. This book takes a thorough approach to the subject and includes examples and exercises to enrich the main themes, making it suitable for classroom instruction. Modern Nonconvex Nondifferentiable Optimization is intended for applied and computational mathematicians, optimizers, operations researchers, statisticians, computer scientists, engineers, economists, and machine learners. It could be used in advanced courses on optimization/operations research and nonconvex and nonsmooth optimization.

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Book SynopsisCollecting a set of classical and emerging methods that otherwise would not be available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book is designed to bring together an eclectic group of researchers with a wide variety of applications and disciplines including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods. Inside, readers will find: Basic techniques of model-based image processing. A comprehensive treatment of Bayesian and regularized image reconstruction methods. An integrated treatment of advanced reconstruction techniques such as majorization, constrained optimization, ADMM, and Plug-and-Play methods for model integration. Foundations of Computational Imaging can be used in courses on Model-Based or Computational Imaging, Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. It is also for researchers or practitioners in medical imaging, scientific imaging, commercial imaging, or industrial imaging.

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Book SynopsisAmong the many branches of applied mathematics, options pricing theory occupies a unique position: it utilizes a wide range of advanced mathematical concepts, making it appealing to mathematicians, and it is regularly applied at financial institutions, making it indispensable to practitioners. The emergence of artificial intelligence in the financial industry has led to further interest in mathematical finance and has increased the demand for literature on this subject that is accessible to a large audience.This book presents a self-contained introduction to options pricing theory and includes a complete discussion of the required concepts in finance and probability theory; an introduction to basic models, emphasizing both critical thinking and practical applications; and over 200 exercises, several Python codes for the analysis and application of the options pricing models, and numerical projects intended to help close the gap between theory and practice. A First Course in Options Pricing Theory is suitable for an advanced undergraduate course on financial mathematics and options pricing theory in engineering, computer science, and applied mathematics programs. The reader is assumed to be familiar with the standard material in calculus and linear algebra. Stochastic calculus is not used in the book.

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Book SynopsisThe series, Contemporary Perspectives in Data Mining, is composed of blind refereed scholarly research methods and applications of data mining. This series will be targeted both at the academic community, as well as the business practitioner.Data mining seeks to discover knowledge from vast amounts of data with the use of statistical and mathematical techniques. The knowledge is extracted from this data by examining the patterns of the data, whether they be associations of groups or things, predictions, sequential relationships between time order events or natural groups.Data mining applications are seen in finance (banking, brokerage, insurance), marketing (customer relationships, retailing, logistics, travel), as well as in manufacturing, health care, fraud detection, home-land security, and law enforcement.

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Book SynopsisThe series, Contemporary Perspectives in Data Mining, is composed of blind refereed scholarly research methods and applications of data mining. This series will be targeted both at the academic community, as well as the business practitioner.Data mining seeks to discover knowledge from vast amounts of data with the use of statistical and mathematical techniques. The knowledge is extracted from this data by examining the patterns of the data, whether they be associations of groups or things, predictions, sequential relationships between time order events or natural groups.Data mining applications are seen in finance (banking, brokerage, insurance), marketing (customer relationships, retailing, logistics, travel), as well as in manufacturing, health care, fraud detection, home-land security, and law enforcement.

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Book SynopsisEarly in her extraordinary career, Deborah Stone wrote Policy Paradox, a landmark work on politics. Now, in Counting, she revolutionises how we approach numbers and shows how counting shapes the way we see the world. Most of us think of counting as a skill so basic that we see numbers as objective, indisputable facts. Not so, says Stone. In this playful-yet-probing work, Stone reveals the inescapable link between quantifying and classifying, and explains how counting determines almost every facet of our lives—from how we are evaluated at work to how our political opinions are polled to whether we get into higher education or even out of prison. But numbers, Stone insists, need not rule our lives. Especially in this age of big data, Stone’s work is a pressing and spirited call to reclaim our authority over numbers, and to take responsibility for how we use them.

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Book SynopsisProbability and statistics are essential tools for nearly every field of analysis.This volume presents the basic principles and applications of probability and statistics, as well as methods of data collection, proper interpretation of data, and many other topics, allowing readers to acquire a sound knowledge base for their understanding of probability and statistics in the real world.

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Book SynopsisWhat is latent class analysis? If you asked that question thirty or forty years ago you would have gotten a different answer than you would today. Closer to its time of inception, latent class analysis was viewed primarily as a categorical data analysis technique, often framed as a factor analysis model where both the measured variable indicators and underlying latent variables are categorical. Today, however, it rests within much broader mixture and diagnostic modeling framework, integrating measured and latent variables that may be categorical and/or continuous, and where latent classes serve to define the subpopulations for whom many aspects of the focal measured and latent variable model may differ.For latent class analysis to take these developmental leaps required contributions that were methodological, certainly, as well as didactic. Among the leaders on both fronts was C. Mitchell “Chan” Dayton, at the University of Maryland, whose work in latent class analysis spanning several decades helped the method to expand and reach its current potential. The current volume in the Center for Integrated Latent Variable Research (CILVR) series reflects the diversity that is latent class analysis today, celebrating work related to, made possible by, and inspired by Chan’s noted contributions, and signaling the even more exciting future yet to come.

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Book SynopsisMultilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation.In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs.Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

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Book SynopsisMultilevel Modeling Methods with Introductory and Advanced Applications provides a cogent and comprehensive introduction to the area of multilevel modeling for methodological and applied researchers as well as advanced graduate students. The book is designed to be able to serve as a textbook for a one or two semester course in multilevel modeling. The topics of the seventeen chapters range from basic to advanced, yet each chapter is designed to be able to stand alone as an instructional unit on its respective topic, with an emphasis on application and interpretation.In addition to covering foundational topics on the use of multilevel models for organizational and longitudinal research, the book includes chapters on more advanced extensions and applications, such as cross-classified random effects models, non-linear growth models, mixed effects location scale models, logistic, ordinal, and Poisson models, and multilevel mediation. In addition, the volume includes chapters addressing some of the most important design and analytic issues including missing data, power analyses, causal inference, model fit, and measurement issues. Finally, the volume includes chapters addressing special topics such as using large-scale complex sample datasets, and reporting the results of multilevel designs.Each chapter contains a section called Try This!, which poses a structured data problem for the reader. We have linked our book to a website (http://modeling.uconn.edu) containing data for the Try This! section, creating an opportunity for readers to learn by doing. The inclusion of the Try This! problems, data, and sample code eases the burden for instructors, who must continually search for class examples and homework problems. In addition, each chapter provides recommendations for additional methodological and applied readings.

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Book SynopsisThis book covers the use of R programming language for data visualization. The large real-world datasets can be quickly visualized to gain several insights from it using R. Whether the data is already clean or needs some preliminary steps before data visualization like data cleaning and wrangling, all these can be done using R to produce elegant, publication-ready, and exciting plots. This book covers different plot types from simple ones like univariate and bivariate plots (histograms, box plots, violin plots, scatter plots, density plots, bar graphs, pie charts, tree maps, beeswarm plots, Cleveland dot charts, line plots, etc) to more complex ones like mapping and visualizing patterns of missing data (upset plots, different Stamen map types with different zoom levels). All these were shown using free real-world data sets to illustrate the diverse capability of R for data visualization.Table of Contents Volume 1 Chapter 1 Installing R and RStudio Chapter 2 Getting Started with R and RStudio Chapter 3 Univariate Plots for Continuous Data Chapter 4 Univariate Plots for Categorical Data Chapter 5 Bivariate Plots for Continuous DataVolume 2 Chapter 6 Bivariate Plots for Continuous Categorical Data Chapter 7 Bivariate Plots for Categorical Data Chapter 8 More Than 2 Dimensions Chapter 9 Visualizing Missing Data Chapter 10 Mapping

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Book SynopsisThis book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in practice this assumption is often forgotten. In this book, we consider modified chi-squared tests, which do not suffer from such a drawback. The authors provide examples of chi-squared tests for various distributions widely used in practice, and also consider chi-squared tests for the parametric proportional hazards model and accelerated failure time model, which are widely used in reliability and survival analysis. Particular attention is paid to the choice of grouping intervals and simulations. This book covers recent innovations in the field as well as important results previously only published in Russian. Chi-squared tests are compared with other goodness-of-fit tests (such as the Cramer-von Mises-Smirnov, Anderson-Darling and Zhang tests) in terms of power when testing close competing hypotheses.Table of ContentsIntroduction ix Chapter 1. Chi-squared Goodness-of-fit Tests for Complete Data 1 1.1. Classical Pearson’s chi-squared test 1 1.2. Joint distribution of Xn(θ∗n)and√n(θ∗n−θ) 3 1.3. Parameter estimation based on complete data Lemma of Chernoff and Lehmann 5 1.4. Parameter estimation based on grouped data. Theorem of Fisher 10 1.5. Nikulin-Rao-Robson chi-squared test 12 1.6. Other modifications 18 1.7. The choice of grouping intervals 20 Chapter 2. Chi-squared Test for Censored Data 31 2.1. Generalized Pearson-Fisher chi-squared test 32 2.2. Maximum likelihood estimators for censored data 34 2.3. Nikulin-Rao-Robson chi-squared test for censored data 38 2.4. The choice of grouping intervals 45 2.4.1. Equifrequent grouping (EFG) 45 2.4.2. Intervals with equal expected numbers of failures (EENFG) 46 2.4.3. Optimal grouping (OptG) 48 2.5. Chi-squared tests for specific families of distributions 51 2.5.1. Exponential distribution 51 2.5.2. Weibull distribution 55 2.5.3. Lognormal distribution 60 2.5.4. Loglogistic distribution 63 2.5.5. Gompertz distribution 67 Chapter 3. Comparison of the Chi-squared Goodness-of-fit Test with Other Tests 71 3.1. Tests based on the difference between non-parametric and parametric estimators 71 3.2. Comparison of goodness-of-fit tests for complete data 76 3.3. Comparison of goodness-of-fit tests for censored data 79 3.3.1. Lognormal-generalized Weibull pair of competing hypotheses 80 3.3.2. Exponential-Weibull pair of competing hypotheses 82 3.3.3. Weibull-generalized Weibull pairs of competing hypotheses 84 Chapter 4. Chi-squared Goodness-of-fit Tests for Regression Models 87 4.1. Data and the idea of chi-squared test construction 89 4.2. Asymptotic distribution of the random vector Z 91 4.3. Test statistic 96 4.4. Choice of random grouping intervals 97 4.4.1. Test for the exponential AFT model 99 4.4.2. Tests for the scale-shape AFT models with constant covariates 101 4.4.3. Test for the Weibull AFT model with step-stresses 108 Appendices 111 Appendix 1 113 Appendix 2 125 Bibliography 131 Index 141

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Book SynopsisThe purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.Table of ContentsForeword ix Preface xi Chapter 1 Classical Branching Models 1 1.1 Bienaymé–Galton–Watson process 1 1.1.1 Moments and probability of extinction 4 1.1.2 Limit theorems 9 1.2 Processes with unrestricted immigration 17 1.2.1 Limit theorems 21 1.2.2 Critical process with decreasing to zero immigration 25 1.3 Processes with immigration after empty generation only 29 1.3.1 Limit theorems 31 1.3.2 Critical process with decreasing to zero immigration 36 1.4 Background and bibliographical notes 40 Chapter 2 Branching Processes with Migration 43 2.1 Galton–Watson process with migration 43 2.2 Limit theorems 47 2.2.1 Non-critical processes 47 2.2.2 Critical processes with non-negative migration mean 49 2.2.3 Critical processes with negative migration mean 52 2.3 Regeneration and migration 55 2.3.1 Alternating regenerative processes 56 2.3.2 An extension of Galton–Watson processes with migration 58 2.4 Background and bibliographical notes 62 Chapter 3 CB Processes: Extinction 65 3.1 Definition of processes and basic properties 65 3.1.1 Basic properties 69 3.1.2 Probability generating functions and moments 73 3.2 Extinction probability 75 3.2.1 Subcritical processes 76 3.2.2 Supercritical processes 78 3.2.3 Critical processes 84 3.3 Background and bibliographical notes 91 Chapter 4 CB Processes: Limit Theorems 95 4.1 Subcritical processes 95 4.2 Critical processes 100 4.2.1 Extinction is not certain 101 4.2.2 Extinction is certain 109 4.2.3 Feller diffusion approximation 110 4.3 Supercritical processes 115 4.3.1 Almost sure convergence 117 4.3.2 L1–convergence 118 4.3.3 L2–convergence 121 4.4 Background and bibliographical notes 125 Chapter 5 Statistics of CB Processes 127 5.1 Maximum likelihood estimation 127 5.1.1 MLE based on entire family tree up to nth generation 130 5.1.2 EM algorithms for incomplete data 146 5.1.3 Simulated example 152 5.2 Conditional weighted least squares estimation 158 5.2.1 Subcritical processes 159 5.2.2 Critical processes 161 5.2.3 Supercritical processes 166 5.3 Minimum disparity estimation 169 5.4 Bayesian inference 171 5.4.1 Estimation based on entire family tree up to nth generation 172 5.4.2 MCMC algorithms for incomplete data 173 5.5 Background and bibliographical notes 176 Appendices 179 Appendix 1 181 Appendix 2 185 Appendix 3 191 Appendix 4 195 Bibliography 197 Index 209

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Book Synopsis Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps. Table of ContentsPreface xiRomain AZAÏS and Florian BOUGUET List of Acronyms xiii Introduction xvRomain AZAÏS and Florian BOUGUET Chapter 1. Statistical Analysis for Structured Models on Trees 1Marc HOFFMANN and Adelaide OLIVIER 1.1. Introduction 1 1.1.1. Motivation 1 1.1.2. Genealogical versus temporal data 2 1.2. Size-dependent division rate 4 1.2.1. From partial differential equation to stochastic models 4 1.2.2. Non-parametric estimation: the Markov tree approach 6 1.2.3. Sketch of proof of Theorem 1.1 10 1.3. Estimating the age-dependent division rate 16 1.3.1. Heuristics and convergence of empirical measures 17 1.3.2. Estimation results 20 1.3.3. Sketch of proof of Theorem 1.4 24 1.4. Bibliography 37 Chapter 2. Regularity of the Invariant Measure and Non-parametric Estimation of the Jump Rate 39Pierre HODARA, Nathalie KRELL and Eva LOCHERBACH 2.1. Introduction 39 2.2. Absolute continuity of the invariant measure 43 2.2.1. The dynamics 43 2.2.2. An associated Markov chain and its invariant measure 45 2.2.3. Smoothness of the invariant density of a single particle 47 2.2.4. Lebesgue density in dimension N 50 2.3. Estimation of the spiking rate in systems of interacting neurons 51 2.3.1. Harris recurrence 55 2.3.2. Properties of the estimator 56 2.3.3. Simulation results 58 2.4. Bibliography 61 Chapter 3. Level Crossings and Absorption of an Insurance Model 65Romain AZAÏS and Alexandre GENADOT 3.1. An insurance model 65 3.2. Some results about the crossing and absorption features 70 3.2.1. Transition density of the post-jump locations 70 3.2.2. Absorption time and probability 71 3.2.3. Kac–Rice formula 74 3.3. Inference for the absorption features of the process 77 3.3.1. Semi-parametric framework 77 3.3.2. Estimators and convergence results 79 3.3.3. Numerical illustration 81 3.4. Inference for the average number of crossings 89 3.4.1. Estimation procedures 89 3.4.2. Numerical application 90 3.5. Some additional proofs 92 3.5.1. Technical lemmas 92 3.5.2. Proof of Proposition 3.3 97 3.5.3. Proof of Corollary 3.2 98 3.5.4. Proof of Theorem 3.5 100 3.5.5. Proof of Theorem 3.6 102 3.5.6. Discussion on the condition (C2G) 103 3.6. Bibliography 104 Chapter 4. Robust Estimation for Markov Chains with Applications to Piecewise-deterministic Markov Processes 107Patrice BERTAIL, Gabriela CIOŁEK and Charles TILLIER 4.1. Introduction 107 4.2. (Pseudo)-regenerative Markov chains 109 4.2.1. General Harris Markov chains and the splitting technique 110 4.2.2. Regenerative blocks for dominated families 111 4.2.3. Construction of regeneration blocks 112 4.3. Robust functional parameter estimation for Markov chains 114 4.3.1. The influence function on the torus 115 4.3.2. Example 1: sample means 116 4.3.3. Example 2: M-estimators 117 4.3.4. Example 3: quantiles 118 4.4. Central limit theorem for functionals of Markov chains and robustness 118 4.5. A Markov view for estimators in PDMPs 121 4.5.1. Example 1: Sparre Andersen model with barrier 122 4.5.2. Example 2: kinetic dietary exposure model 125 4.6. Robustness for risk PDMP models 127 4.6.1. Stationary measure 127 4.6.2. Ruin probability 132 4.6.3. Extremal index 136 4.6.4. Expected shortfall 138 4.7. Simulations 140 4.8. Bibliography 144 Chapter 5. Numerical Method for Control of Piecewise-deterministic Markov Processes . 147Benoite DE SAPORTA and Francois DUFOUR 5.1. Introduction 147 5.2. Simulation of piecewise-deterministic Markov processes 149 5.3. Optimal stopping 150 5.3.1. Assumptions and notations 150 5.3.2. Dynamic programming 153 5.3.3. Quantized approximation 154 5.4. Exit time 158 5.4.1. Problem setting and assumptions 158 5.4.2. Recursive formulation 159 5.4.3. Numerical approximation 161 5.5. Numerical example 162 5.5.1. Piecewise-deterministic Markov model 162 5.5.2. Deterministic time to reach the boundary 164 5.5.3. Quantization 166 5.5.4. Optimal stopping 167 5.5.5. Exit time 169 5.6. Conclusion 170 5.7. Bibliography 171 Chapter 6. Rupture Detection in Fatigue Crack Propagation 173Romain AZAIS, Anne GEGOUT-PETIT and Florine GRECIET 6.1. Phenomenon of crack propagation 173 6.1.1. Virkler’s data 174 6.2. Modeling crack propagation 175 6.2.1. Deterministic models 175 6.2.2. Sources of uncertainties 177 6.2.3. Stochastic models 178 6.3. PDMP models of propagation 183 6.3.1. Relevance of PDMP models 183 6.3.2. Multiplicative model 185 6.3.3. One-jump models 186 6.4. Rupture detection 193 6.4.1. Length at versus time t . 193 6.4.2. Growth rate dat /dt versus ΔKt in log scale 194 6.5. Conclusion and perspectives 203 6.6. Bibliography 204 Chapter 7. Piecewise-deterministic Markov Processes for Spatio-temporal Population Dynamics . 209Candy ABBOUD, Rachid SENOUSSI and Samuel SOUBEYRAND 7.1. Introduction 209 7.1.1. Models of population dynamics 209 7.1.2. Spatio-temporal PDMP for population dynamics 210 7.1.3. Chapter contents 212 7.2. Stratified dispersal models 212 7.2.1. Reaction–diffusion equations for modeling short-distance dispersal 212 7.2.2. Stratified diffusion 215 7.2.3. Coalescing colony model with Allee effect 216 7.2.4. A PDMP based on reaction–diffusion for modeling invasions with multiple introductions 221 7.3. Metapopulation epidemic model 223 7.3.1. Spatially realistic Levins model 223 7.3.2. A colonization PDMP 224 7.3.3. Bayesian inference approach 229 7.3.4. Markov chain Monte Carlo algorithm 235 7.3.5. Examples of results 236 7.4. Stochastic approaches for modeling spatial trajectories 237 7.4.1. Conditioning a Brownian motion by punctual observations 239 7.4.2. Movements with jumps 242 7.4.3. The Doléans–Dade exponential semi-martingales 247 7.4.4. Statistical issues 249 7.5. Conclusion 252 7.6. Bibliography 252 List of Authors 257 Index 259

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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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