Probability and statistics Books

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Book SynopsisLearning Data Science is the first book to cover foundational skills in both programming and statistics that encompass the entire data science lifecycle: the process of collecting, wrangling, analyzing, and drawing conclusions from data.

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Book SynopsisProbabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector field. In other words, they infer a latent quantity from data. This book shows that it is thus formally possible to think of computational routines as learning machines, and to use the notion of Bayesian inference to build more flexible, efficient, or customised algorithms for computation. The text caters for Masters'' and PhD students, as well as postgraduate researchers in artificial intelligence, computer science, statistics, and applied mathematics. Extensive background material is provided along with a wealth of figures, worked examples, and exercises (with solutions) to develop intuition.Trade Review'Computational methods for solving numerical problems lie at the heart of many of the technological advances in science and engineering over the last five decades, and underpin fields as diverse as artificial intelligence, climate modelling, and epidemiology. This impressive text rethinks numerical problems through the lens of probabilistic inference and decision making. This fresh perspective opens up a new chapter in this field, and suggests new and highly efficient methods. A landmark achievement!' Zoubin Ghahramani, University of Cambridge'This beautiful book is both timely and important with deep roots in powerful early exposition in numerical analysis. In this stunning and comprehensive new book, early developments from Kac and Larkin have been comprehensively built upon, formalised and extended by including modern day machine learning, numerical analysis and the formal Bayesian statistical methodology. Probabilistic Numerical methodology is of enormous importance for this age of data-centric science and Hennig, Osborne and Kersting are to be congratulated in providing us with this definitive volume.' Mark Girolami, University of Cambridge and The Alan Turing Institute'Numerical analysis is at the very heart of digital computing: every result of a computation on a digital computer is a only finite-precision representation of the true mathematical quantity where the precision is the tradeoff between computation time and accuracy. This book presents an in-depth overview of both the past and present of the newly emerging area of probabilistic numerics, where recent advances in probabilistic machine learning are used to develop principled improvements which are both faster and more accurate than classical numerical analysis algorithms. A must-read for every algorithm developer and practitioner in optimization!' Ralf Herbrich, Hasso Plattner Institute'Probabilistic Numerics spans from the intellectual fireworks of the dawn of a new field to its practical algorithmic consequences. It is precise but accessible and rich in wide-ranging, principled examples. This convergence of ideas from diverse fields in lucid style is the very fabric of good science.' Carl Edward Rasmussen, University of Cambridge'An important read for anyone who has thought about uncertainty in numerical methods; an essential read for anyone who hasn't …' John Cunningham, Columbia University'This is a rare example of a textbook that essentially founds a new field, re-casting numerics on stronger, more general foundations. A tour de force.' David Duvenaud, University of Toronto'The idea of applying probabilistic inference to the problem of numerical analysis must appear bold, possibly outrageous, even to an entrenched Bayesian statistician. Many in machine learning are now familiar with the application of Bayesian methods to problems that involve randomness, say, the estimation of quantities from noisy data. But to apply the 'calculus of uncertainty' to unknown mathematical facts, where the uncertainty arises only from our lack of knowledge, opens up a universe of new possibilities. This elegant idea is at the core of Probabilistic Numerics, and the authors succeed in demonstrating its potential to transform the way we think about computation itself. And that's not even considering what would happen if we were to apply probabilistic numerics to the numerical problems that arise from probabilistic numerics itself!' Thore Graepel, Senior Vice President, Altos Labs'… the machine learning background of the authors comes through clearly in the book … I thoroughly recommend it.' Chris J. Oates, SIAM ReviewTable of ContentsIntroduction; 1. Mathematical background; 2. Integration; 3. Linear algebra; 4. Local optimisation; 5. Global optimisation; 6. Solving ordinary differential equations; 7. The frontier; Solutions to exercises; References; Index.

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Book SynopsisTable of ContentsIntroduction 1 About This Book 1 About the Fourth Edition 2 Foolish Assumptions 2 Icons Used in This Book 3 Beyond the Book 3 Where to Go from Here 3 Part 1: Getting Started with SPSS 5 Chapter 1: Introducing SPSS 7 SPSS’s Job, Our Job, and Your Job 7 SPSS’s job 8 Our job 8 Your job 9 Garbage In, Garbage Out: Recognizing the Importance of Good Data 9 Talking to SPSS: Can You Hear Me Now? 12 The graphical user interface 12 Syntax 12 Programmability 13 How SPSS works 13 Getting Help When You Need It 15 Chapter 2: Finding the Best SPSS for You 17 Campus Editions 19 Subscription Plans 20 Commercial Editions 22 What’s New in Version 27 24 Chapter 3: Getting to Know SPSS by Running a Simple Session 25 Opening a Dataset 25 Running an Analysis 27 Interpreting Results 30 Creating Graphs 33 Investigating Data 37 Part 2: Getting Data into and out of SPSS 43 Chapter 4: Understanding SPSS Data: Defining Metadata 45 Entering Variable Definitions on the Variable View Tab 46 Name 47 Type 47 Width 51 Decimals 52 Label 52 Values 53 Missing 54 Columns 55 Align 55 Measure 55 Role 56 Entering and Viewing Data Items on the Data View Tab 56 Chapter 5: Opening Data Files 59 Getting Acquainted with the SPSS File Format 59 Reading Simple Data from a Text File 60 Transferring Data from Another Program 65 Reading an Excel file 67 Reading from an unknown program type 68 Saving Data 69 Chapter 6: Getting Data and Results from SPSS 71 Exporting Data to Another Program 71 Navigating SPSS Statistics Viewer 72 Moving SPSS Output to Other Applications 74 Copying and pasting output 74 Exporting output 75 Printing Data 80 Chapter 7: More about Defining Your Data 81 Working with Dates and Times 82 Using the Date and Time Wizard 84 Creating and Using a Multiple-Response Set 86 Copying Data Properties 90 Part 3: Messing with Data in SPSS 95 Chapter 8: The Transform and Data Menus 97 Sorting Cases 97 Selecting the Data You Want to Look At 100 Splitting Data for Easier Analysis 103 Counting Case Occurrences 104 Recoding Variables 107 Recoding into different variables 107 Automatic recoding 110 Binning 113 Optimal Binning 117 Chapter 9: Computing New Variables 119 Calculating a New Variable with a Formula 120 Calculating a New Variable with a Condition 122 Using System Variables 124 Contrasting $Sysmis with SYSMIS 125 Understanding Missing Data in Formulas 127 Efficiently Calculating with Multiple Formulas 129 Chapter 10: Some Useful Functions 133 The LENGTH Function 134 The ANY Function 137 The MEAN Function and Missing Data 139 RND, TRUNC, and MOD 141 Logicals, the MISSING Function, and the NOT Function 143 String Parsing and Nesting Functions 144 Calculating Lags 146 Chapter 11: Combining Files 147 Merging Files by Adding Cases 147 Merging Files by Adding Variables 152 Part 4: Graphing Data 161 Chapter 12: On the Menu: Graphing Choices in SPSS 163 Building Graphs the Chart Builder Way 164 The Gallery tab 164 The Basic Elements tab 168 The Groups/Point ID tab 169 The Titles/Footnotes tab 170 The Element Properties tab 170 The Chart Appearance tab 176 The Options tab 177 Building Graphs with Graphboard Template Chooser 178 Chapter 13: Building Graphs Using Chart Builder 183 Simple Graphs 184 Simple scatterplots 184 Simple dot plots 185 Simple bar graphs 186 Simple error bars 187 Simple histograms 189 Population pyramids 191 Stacked area charts 192 Fancy Graphs 194 Charts with multiple lines 194 Colored scatterplots 196 Scatterplot matrices 198 Stacked bar charts 199 Pie charts 200 Clustered range bar graphs 202 Differenced area graphs 202 Dual-axis graph 204 Fancy Maps Using Graphboard Template Chooser 205 Heat map 206 Choropleth of values 206 Coordinates on a reference map 209 Part 5: Analyzing Data 211 Chapter 14: Using Descriptive Statistics 213 Looking at Levels of Measurement 213 Defining the four levels of measurement 214 Defining summary statistics 215 Focusing on Frequencies for Categorical Variables 217 Understanding Frequencies for Continuous Variables 221 Summarizing Continuous Variables with the Descriptives Procedure 224 Chapter 15: Knowing When Not to Trust Your Data 227 Sampling 227 Understanding Sample Size 228 Testing Hypotheses 229 Calculating Confidence Intervals 231 Conducting In-Depth Hypothesis Testing 232 Using the Normal Distribution 235 Working with Z-Scores 236 Chapter 16: Testing One Group 239 Conducting Inferential Tests 239 Running the Chi-Square Goodness of Fit Test 240 Running the One-Sample T-Test Procedure 246 Chapter 17: Showing Relationships between Categorical Variables 251 Running the Crosstabs Procedure 252 Running the Chi-Square Test of Independence 256 Comparing Column Proportions 260 Adding Control Variables 261 Creating a Clustered Bar Chart 264 Chapter 18: Showing Relationships between Continuous Dependent and Categorical Independent Variables 267 Conducting Inferential Tests 268 Using the Compare Means Dialog 268 Running the Independent-Samples T-Test Procedure 269 Comparing the Means Graphically 275 Running the Summary Independent-Samples T-Test Procedure 277 Running the Paired-Samples T-Test Procedure 280 Chapter 19: Showing Relationships between Continuous Variables 285 Viewing Relationships 286 Running the Bivariate Procedure 288 Running the Simple Linear Regression Procedure 292 Part 6: Getting More Advanced with Analyzing Data 301 Chapter 20: Doing More Advanced Analyses 303 Running the One-Way ANOVA Procedure 303 Conducting Post Hoc Tests 311 Comparing Means Graphically 314 Running the Multiple Linear Regression Procedure 315 Viewing Relationships 325 Chapter 21: What Is Normal Anyway? 327 Understanding Nonparametric Tests 328 Understanding Distributions 328 Running a Nonparametric Independent Samples Test 331 Running a Nonparametric Related Samples Test 338 Chapter 22: When to Do What 345 Determining Which Statistical Test to Perform 346 Using Advanced Techniques 350 Part 7: Making SPSS Your Own 351 Chapter 23: Changing Settings 353 General Options 354 Language Options 356 Viewer Options 357 Data Options 358 Currency Options 360 Output Options 361 Chart Options 362 Pivot Tables Options 364 File Locations Options 365 Scripts Options 366 Multiple Imputations Options 368 Syntax Editor Options 369 Privacy Options 370 Chapter 24: Editing Charts and Chart Templates 371 Changing and Editing Axes 372 Changing the axis range 372 Scaling the axis range 373 Changing Style: Lines and Symbols 376 Editing chart lines 376 Editing data points 378 Applying Templates 380 Chapter 25: Editing Tables 383 Working with TableLooks 384 Style Output 387 Pivoting Trays 390 Part 8: Programming SPSS with Command Syntax 393 Chapter 26: Getting Acquainted with Syntax 395 Pasting 396 Performing a Series of Related Compute Statements 399 Labeling 400 Repeatedly Generating the Same Report 400 Chapter 27: Adding Syntax to Your Toolkit 403 Your Wish Is My Command 404 Understanding Keywords 405 Declaring Data 406 Commenting Your Way to Clarity 407 Running Your Code 408 Controlling Flow and Executing Conditionals 410 IF 410 DO IF 411 SELECT IF 412 Part 9: The Part of Tens 413 Chapter 28: Ten (or So) Modules You Can Add to SPSS 415 The Advanced Statistics Module 416 The Custom Tables Module 416 The Regression Module 418 The Categories Module 418 The Data Preparation Module 419 The Decision Trees Module 419 The Forecasting Module 420 The Missing Values Module 421 The Bootstrapping Module 421 The Complex Samples Module 422 The Conjoint Module 422 The Direct Marketing Module 422 The Exact Tests Module 423 The Neural Networks Module 424 Chapter 29: Ten Useful SPSS Resources 425 Supporting Websites for This Book 425 LinkedIn and LinkedIn Groups 426 IBM SPSS Statistics Certification 427 IBM Data Science Community 427 SPSSX-L 427 Online Videos 428 Twitter 429 Live Instruction 430 Asynchronous Instruction and Tutorials 431 SPSS Statistics for Data Analysis and Visualization 432 Chapter 30: Ten SPSS Statistics Gotchas 433 Failing to Declare Level of Measurement 433 Conflating String Values with Labels 434 Failing to Declare Missing Data 435 Failing to Find Add-on Modules and Plug-Ins 435 Failing to Meet Statistical and Software Assumptions 437 Confusing Pasting Syntax with Copy and Paste 438 Thinking You Create Variables in SPSS as You Do in Excel 438 Getting Confused by Listwise Deletion 439 Losing Track of Your Active Dataset 440 Forgetting to Turn Off Select and Split and Weight 441 Index 443

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Book SynopsisAbout our author The late Neil A. Weiss received his Ph.D. from UCLA and subsequently accepted an assistant professor position at Arizona State University (ASU), where he was ultimately promoted to the rank of full professor. Dr. Weiss taught statistics, probability, and mathematics, from the freshman level to the advanced graduate level, for more than 30 years. In recognition of his excellence in teaching, Dr. Weiss received the Dean's Quality Teaching Award from the ASU College of Liberal Arts and Sciences. He also was runner-up twice for the Charles Wexler Teaching Award in the ASU School of Mathematical and Statistical Sciences. Dr. Weiss's comprehensive knowledge and experience ensure that his texts are mathematically and statistically accurate, as well as pedagogically sound. In addition to his numerous research publications, Dr. Weiss was the author of A Course in Probability (Addison-Wesley, 2006). He alsoTable of Contents PART I: Introduction 1. The Nature of Statistics PART II: Descriptive Statistics 2. Organizing Data 3. Descriptive Measures PART III: Probability, Random Variables, and Sampling Distributions 4. Probability Concepts 5. Discrete Random Variables 6. The Normal Distribution 7. The Sampling Distribution of the Sample Mean PART IV: Inferential Statistics 8. Confidence Intervals for One Population Mean 9. Hypothesis Tests for One Population Mean 10. Inferences for Two Population Means 11. Inferences for Population Standard Deviations 12. Inferences for Population Proportions 13. Chi-Square Procedures PART V: Regression, Correlation, and ANOVA 14. Descriptive Methods in Regression and Correlation 15. Inferential Methods in Regression and Correlation 16. Analysis of Variance (ANOVA) PART VI: Multiple Regression and Model Building; Experimental Design and ANOVA MODULE A: Multiple Regression Analysis MODULE B: Model Building in Regression MODULE C: Design of Experiments and Analysis of Variance Answers to Selected Exercises Index Appendix A: Statistical Tables Appendix B: Answers to Selected Exercises

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Book SynopsisTable of Contents1. Introduction to Statistics and Data Analysis 1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability 1.2 Sampling Procedures; Collection of Data 1.3 Measures of Location: The Sample Mean and Median Exercises 1.4 Measures of Variability Exercises 1.5 Discrete and Continuous Data 1.6 Statistical Modeling, Scientific Inspection, and Graphical Methods 1.7 General Types of Statistical Studies: Designed Experiment, Observational Study, and Retrospective Study Exercises 2. Probability 2.1 Sample Space 2.2 Events Exercises 2.3 Counting Sample Points Exercises 2.4 Probability of an Event 2.5 Additive Rules Exercises 2.6 Conditional Probability, Independence and Product Rules Exercises 2.7 Bayes' Rule Exercises Review Exercises 2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 3. Random Variables and Probability Distributions 3.1 Concept of a Random Variable 3.2 Discrete Probability Distributions 3.3 Continuous Probability Distributions Exercises 3.4 Joint Probability Distributions Exercises Review Exercises 3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 4. Mathematical Expectation 4.1 Mean of a Random Variable Exercises 4.2 Variance and Covariance of Random Variables Exercises 4.3 Means and Variances of Linear Combinations of Random Variables 4.4 Chebyshev's Theorem Exercises Review Exercises 4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 5. Some Discrete Probability Distributions 5.1 Introduction and Motivation 5.2 Binomial and Multinomial Distributions Exercises 5.3 Hypergeometric Distribution Exercises 5.4 Negative Binomial and Geometric Distributions 5.5 Poisson Distribution and the Poisson Process Exercises Review Exercises 5.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 6. Some Continuous Probability Distributions 6.1 Continuous Uniform Distribution 6.2 Normal Distribution 6.3 Areas under the Normal Curve 6.4 Applications of the Normal Distribution Exercises 6.5 Normal Approximation to the Binomial Exercises 6.6 Gamma and Exponential Distributions 6.7 Chi-Squared Distribution 6.8 Beta Distribution 6.9 Lognormal Distribution (Optional) 6.10 Weibull Distribution (Optional) Exercises Review Exercises 6.11 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 7. Functions of Random Variables (Optional) 7.1 Introduction 7.2 Transformations of Variables 7.3 Moments and Moment-Generating Functions Exercises 8. Sampling Distributions and More Graphical Tools 8.1 Random Sampling and Sampling Distributions 8.2 Some Important Statistics Exercises 8.3 Sampling Distributions 8.4 Sampling Distribution of Means and the Central Limit Theorem Exercises 8.5 Sampling Distribution of S2 8.6 t-Distribution 8.8 Quantile and Probability Plots Exercises Review Exercises 8.9 Potential Misconceptions and Hazards; Relationship to Mate

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Book SynopsisAbout our authors Richard D. De?Veaux? is an internationally known educator and consultant. He has taught at the Wharton School and the Princeton University School of Engineering, where he won a Lifetime Award for Dedication and Excellence in Teaching. He is the C. Carlisle and M. Tippit Professor of Statistics at Williams College, where he has taught since 1994. Dick has won both the Wilcoxon and Shewell awards from the American Society for Quality. He is a fellow of the American Statistical Association (ASA) and an elected member of the International Statistical Institute (ISI). In 2008, he was named Statistician of the Year by the Boston Chapter of the ASA, and was the 2018-2021 Vice-President of the ASA. Dick is also well known in industry, where for more than 30 years he has consulted for such Fortune 500 companies as American Express, Hewlett-Packard, Alcoa, DuPont, Pillsbury, General Electric, and Chemical Bank. Because he consulted with Mickey Hart

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Book SynopsisHighly praised for its broad, practical coverage, the second edition of this popular text incorporated the major statistical models and issues relevant to epidemiological studies. Epidemiology: Study Design and Data Analysis, Third Edition continues to focus on the quantitative aspects of epidemiological research. Updated and expanded, this edition shows students how statistical principles and techniques can help solve epidemiological problems.New to the Third Edition New chapter on risk scores and clinical decision rules New chapter on computer-intensive methods, including the bootstrap, permutation tests, and missing value imputation New sections on binomial regression models, competing risk, information criteria, propensity scoring, and splines Many more exercises and examples using both Stata and SAS More than 60 new figures After introducing study design and reviewTrade Review"This text, like its predecessors, hits the mark. … The author writes extremely well and the text is resplendent with exercises. It would be a crime if Epidemiology: Study Design and Data Analysis were never used as a text! … I wish a text like this had been available for my coursework. Enhancing its value as a text, it will be extremely useful as a reference book for its intended audience—researchers and applied statisticians. … the only excuse for an epidemiologist or applied statistician not to have it on his or her bookshelf is that he or she has not seen or heard of it. Make this book your next purchase!"—Gregory E. Gilbert, The American Statistician, November 2014Praise for Previous Editions:"As a text in quantitative epidemiology, this book also works nicely as a text in biostatistics…The presentation style is relaxed, the examples are helpful, and the level of technical difficulty makes the material approachable without oversimplification…It is sufficiently broad and deep in coverage to compete with standard texts in the field and has the added bonus of emphasizing study design. Methods and issues related to designs commonly used in a wide variety of health sciences are included…"-Ken Hess, Department of Biomathematics and Biostatistics, Anderson Cancer Center"The second edition of this epidemiology text is strengthened to cater to the two audiences the author has in mind: applied statisticians wishing to learn how their statistical expertise can be used in the epidemiology field and statistic-curious researchers who want to understand how statistical techniques can be used to solve epidemiological problems. …The result is a book that will invariably appeal to the intended audience, one with practical applications of techniques and interpretations of results in an epidemiological context. …The book is most certainly an ambitious attempt at covering a broad array of the most important epidemiologic study designs and analytical methods. This is further enforced by the addition of the meta-analysis chapter. …This book will be valuable to statisticians in applying their discipline to epidemiology. Mark Woodward's excellent second edition will effectively serve post-graduate or advanced undergraduate students studying epidemiology, as well as statisticians or researchers who are regularly confronted with epidemiological questions."-Journal of the American Statistical Association"This book provides very good coverage of major issues in the design of epidemiological studies, and a decent, but very quick, tour of commonly used statistical models for such studies."-Short Book Reviews Publication of the International Statistical Institute, K.S. Brown, University of Waterloo, Canada"Amazingly, Woodward manages to describe quite sophisticated models and analysis with nothing more complicated than summation signs. …I highly recommend it."-Statistics in Medicine, 2006"The second edition of this concisely written book covers all statistical methods being of relevance for the planning and analysis of epidemiological studies where the author avoids unnecessary mathematical details for the sake of comprehensibility. The presented statistical principles are always carefully discussed in the context of epidemiological concepts, for instance depending on the different study designs. Detailed practical examples coming from real studies as far as possible illustrate their application. …The book can be highly recommended to researchers in epidemiology who want to understand better the statistical principles being typically applied in this field and to statisticians who want to understand more about statistics in epidemiology, but also to graduate students in epidemiology, public health, medical research and statistics."-Biometrics, Sept. 2005"I think anyone with an interest in both biostatistics and epidemiology will want a copy this book on their bookshelf … it is a first-rate reference book." "I find Professor Woodward's text the most complete and practical introduction to the design and analysis of epidemiological studies I've encountered… an excellent text for either a course introducing epidemiologists to statistical thought and methods or a course introducing statisticians to epidemiological thought and methods… students appreciate having a readable textbook replete with understandable examples and worked exercises…offers a complete introduction to statistical and epidemiological methods in the study of disease in human populations. All of the standard topics are included, and the second edition even has a chapter on meta-analysis. …This book can be used as a text to introduce epidemiological methods to graduate students in statistics who have no background in epidemiology, or vice versa…Professor Woodward is to be congratulated on a job well done."-Dan McGee, Dept of Statistics, Florida State UniversityTable of ContentsFundamental Issues. Basic Analytical Procedures. Assessing Risk Factors. Confounding and Interaction. Cohort Studies. Case-Control Studies. Intervention Studies. Sample Size Determination. Modeling Quantitative Outcome Data. Modeling Binary Outcome Data. Modeling Follow-Up Data. Meta-Analysis. Risk Scores and Clinical Decision Rules. Computer-Intensive Methods. Appendices. Index.

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Book SynopsisThis affordable student study guide and workbook to accompany Wendy J. Steinberg and Matthew Price’s Statistics Alive!, Third Edition, helps students get the added review and practice they need to improve their skills and master their Introduction to Statistics course. Bundle and SAVE! Student Study Guide to Accompany Statistics Alive!, Third Edition + Main Text ISBN: 978-1-0718-3088-8Table of ContentsModule 1. Math Review, Vocabulary, and Symbols Module 2. Measurement Scales Module 3. Frequency and Percentile Tables Module 4. Graphs and Plots Module 5. Mode, Median, and Mean Module 6. Range, Variance, and Standard Deviation Module 7. Percent Area and the Normal Curve Module 8. z Scores Module 9. Score Transformations and Their Effects Module 10. Probability Definitions and Theorems Module 11. The Binomial Distribution Module 12. Sampling, Variables, and Hypotheses Module 13. Errors and Significance Module 14. The z Score as a Hypothesis Test Module 15. Standard Error of the Mean Module 16. Normal Deviate Z Test Module 17. One-Sample t Test Module 18. Interpreting and Reporting One-Sample t: Error, Confidence, and Parameter Estimates Module 19. Standard Error of the Difference Between the Means Module 20. t Test With Independent Samples and Equal Sample Sizes Module 21. t Test With Unequal Sample Sizes Module 22. t Test With Related Samples Module 23. Interpreting and Reporting Two-Sample t: Error, Confidence, and Parameter Estimates Module 24. ANOVA Logic: Sums of Squares, Partitioning, and Mean Squares Module 25. One-Way ANOVA: Independent Samples and Equal Sample Sizes Module 26. Tukey HSD Test Module 27. Scheffé Test Module 28. Main Effects and Interaction Effects Module 29. Factorial ANOVA Module 30. One-Variable Chi-Square: Goodness of Fit Module 31. Two-Variable Chi-Square: Test of Independence Module 32. Measures of Effect Size Module 33. Power and the Factors Affecting It Module 34. Relationship Strength and Direction Module 35. Pearson r Module 36. Correlation Pitfalls Module 37. Linear Prediction Module 38. Standard Error of Prediction Module 39. Introduction to Multiple Regression Module 40. Selecting the Appropriate Analysis

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Book SynopsisSuitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books Trade ReviewFrom the reviews: "[the material is] superbly motivated with interest-grabbing examples... exercises excellent and plentiful." Edward Williams, University of Michigan-Dearborn, USA "... it is a notoriously hard task to introduce probability and statistics with a mix of intuition and mathematics to keep students motivated. Therefore, I very much welcome this book and recommend it as course material." Sara van de Geer, Leiden University, The Netherlands "This textbook provides a well-written first course in probability and statistics...It is a book that has been written based on the long teaching experience of the authors and I would certainly recommend it for university coursework." Short Book Reviews of the International Statistical Institute, December 2005 "This book has numerous quick exercises to give direct feedback to the students. … A website at www.springeronline.com/978-1-85233-896-1 gives access to the data files used in the text … . This will be a key text for undergraduates in computer science, physics, mathematics, chemistry, biology and business studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects." (Rainer Beedgen, Zentralblatt MATH, Vol. 1079, 2006) "The book is designed for a one-semester introductory course in probability and statistics basics for engineering students. … It can also be used by students in other more mathematically oriented majors such as applied mathematics with more emphasis on the mathematics and additional coverage in topics such as combinatorics, conditional expectation, and generating functions. … More elaborate exercises and real datasets are given at the end of each chapter." (Arthur B. Yeh, Technometrics, Vol. 49 (3), August, 2007)Table of ContentsWhy probability and statistics?.- Outcomes, events, and probability.- Conditional probability and independence.- Discrete random variables.- Continuous random variables.- Simulation.- Expectation and variance.- Computations with random variables.- Joint distributions and independence.- Covariance and correlation.- More computations with more random variables.- The Poisson process.- The law of large numbers.- The central limit theorem.- Exploratory data analysis: graphical summaries.- Exploratory data analysis: numerical summaries.- Basic statistical models.- The bootstrap.- Unbiased estimators.- Efficiency and mean squared error.- Maximum likelihood.- The method of least squares.- Confidence intervals for the mean.- More on confidence intervals.- Testing hypotheses: essentials.- Testing hypotheses: elaboration.- The t-test.- Comparing two samples.

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Book SynopsisThis book provides hands-on guidance for researchers and practitioners in criminal justice and criminology to perform statistical analyses and data visualization in the free and open-source software R. It offers a step-by-step guide for beginners to become familiar with the RStudio platform and tidyverse set of packages. This volume will help users master the fundamentals of the R programming language, providing tutorials in each chapter that lay out research questions and hypotheses centering around a real criminal justice dataset, such as data from the National Survey on Drug Use and Health, National Crime Victimization Survey, Youth Risk Behavior Surveillance System, The Monitoring the Future Study, and The National Youth Survey. Users will also learn how to manipulate common sources of agency data, such as calls-for-service (CFS) data. The end of each chapter includes exercises that reinforce the R tutorial examples, designed to help master the software as well as to provide practice on statistical concepts, data analysis, and interpretation of results. The text can be used as a stand-alone guide to learning R or it can be used as a companion guide to an introductory statistics textbook, such as Basic Statistics in Criminal Justice (2020).Table of Contents1. Getting started.2. Managing your data.3. Data visualization.4. Spatiotemporal data visualization and basic crime analysis.5. Descriptive statistics: measures of central tendency.6. Descriptive statistics: measures of dispersion.7. Statistical inference in criminal justice research.8. Defining the observed significance level of a test.9. Hypothesis testing using the binomial distribution.10. Chi-square: a test commonly used for nominal-level measures.11. The normal distribution and its application to tests of statistical significance.12. Comparing means in two samples.13. Analysis of variance.14. Measures of association for nominal and ordinal variables.15. Measuring association for interval data.16. Introduction to regression analysis.

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Book SynopsisIntroduction to Statistics.- Types of Data.- Data Collection Methods (Sampling Theory).- Measures of Central Tendency.- Measures of Dispersion.- Measures of Positions.- Outliers.- Introduction to Distributions.- Skewness, Kurtosis and Modality.- Data Visualisation.- Confidence Intervals.- Hypothesis Testing.- Correlation and Linear Regression.- Statistical Project - Steps and Process.- Appendix A - Partioning of the Ordinary Least Square Variance.- Appendix B - Big-O and Little-o Notation.

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Book SynopsisThe second edition represents an ongoing effort to make probability accessible to students in a wide range of fields such as mathematics, statistics and data science, engineering, computer science, and business analytics. The book is written for those learning about probability for the first time. Revised and updated, the book is aimed specifically at statistics and data science students who need a solid introduction to the basics of probability.While retaining its focus on basic probability, including Bayesian probability and the interface between probability and computer simulation, this edition's significant revisions are as follows:The approach followed in the book is to develop probabilistic intuition before diving into details. The best way to learn probability is by practising on a lot of problems. Many instructive problems together with problem-solving strategies are given. Answers to all problems and worked-out solutions to selected problems are also provided.Henk Tijms is the author of several textbooks in the area of applied probability. In 2008, he had received the prestigious INFORMS Expository Writing Award for his work. He is active in popularizing probability at Dutch high schools.Table of ContentsCombinatorics and Calculus for Probability; Basics of Probability; Useful Probability Distributions; Real-Life Examples of Poisson Probabilities; Monte Carlo Simulation and Probability; A Primer on Markov Chains; Solutions to Selected Problems;

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Book SynopsisA Waterstones Best Popular Science Book of 2023'Delightfully clear and vivid to read...A splendid book! Philip Pullman'Absolutely fascinating' James O'Brien'An exceptional book - readable, funny and more needed than ever' Dr Chris van Tulleken, bestselling author of Ultra-Processed PeopleAre you more likely to become a professional footballer if your surname is Ball?· How can you be one hundred per cent sure you will win a bet?· Why did so many Pompeiians stay put while Mount Vesuvius was erupting?· How do you prevent a nuclear war?Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?). For just as long, we have been getting it wrong. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Our job is to separate the good from the bad. Unfortunately, the foibles of our own biology - the biases that ultimately make us human - can let us down when it comes to making rational inferences about the world around us. And that can have disastrous consequences.How to Expect the Unexpected will teach you how and why predictions go wrong, help you to spot phony forecasts and give you a better chance of getting your own predictions correct.Trade ReviewA vivid, wide-ranging and delightful guide to the light and the dark side of prediction * Tim Harford, bestselling author of How to Make the World Add Up *Kit Yates presents maths as it should be taught to everyone: accessible, fun, stimulating, and deeply relevant to our lives. Spend some time with this book and you're likely to make better judgements and decisions, to see through the charlatans and snake-oil salespeople - and perhaps even to fool yourself a little less. * Philip Ball, author of the award-winning Critical Mass *Fascinating and fun. From the everyday to global challenges, Kit Yates explores how changing your mind - so often thought to be a weakness - is the best life skill we can all acquire. A brilliant book * Professor Alice Roberts *Yates' writing is a beacon of clarity sorely needed in a complicated and confusing world. How do we overcome our biases, understand coincidences or tackle the unreliability of our intuition? With bountiful familiar examples, he effortlessly overturns so many of our deep-rooted wrong-headed notions gently and persuasively. I'll be quoting from this book * Jim Al-Khalili *I'm a Yates fan. His style is all-clarity-no-bullshit * Aperiodical *Seriously good * Caroline Lucas MP *Absolutely fascinating * James O'Brien *An exceptional book - readable, funny and more needed than ever * Dr Chris van Tulleken, bestselling author of Ultra-Processed People *Yates' writing style imbues the subjects covered with an infectious enthusiasm, artfully dispelling the dry, stuffy perceptions many people have of maths * Physics World *HOW TO EXPECT THE UNEXPECTED is fascinating and (very much to the point) delightfully clear and vivid to read. Like many people, I like reading about maths without actually knowing how to do it, and part of the pleasure of reading this came from its many examples from everyday life. A splendid book! * Philip Pullman *

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Book SynopsisTable of ContentsPreface.- 1 Introduction.- 2 Statistical Learning.- 3 Linear Regression.- 4 Classification.- 5 Resampling Methods.- 6 Linear Model Selection and Regularization.- 7 Moving Beyond Linearity.- 8 Tree-Based Methods.- 9 Support Vector Machines.- 10 Deep Learning.- 11 Survival Analysis and Censored Data.- 12 Unsupervised Learning.- 13 Multiple Testing.- Index.

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Book SynopsisThis Brief provides a roadmap for the R language and programming environment with signposts to further resources and documentation.Table of ContentsIntroduction to R.- Data Structures.- Tables and Graphs.- Hypothesis Tests.- Linear Models.

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Book SynopsisThis book provides in-depth coverage of Probability & Statistics 1 for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study.Exam Board: Cambridge Assessment International EducationFirst teaching: 2018 First examination: 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 and examination from 2020. This title is endorsed by Cambridge Assessment International Education.Written by expert authors, this Student Book: covers the complete content of Probability & Statistics 1 with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus set

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Book SynopsisThis series has been developed specifically for the Cambridge International AS & A Level Mathematics (9709) syllabus to be examined from 2020.Table of ContentsIntroduction; 1. Representation of data; 2. Measures of central tendency; 3. Measures of variation; 4. Probability; 5. Permutations and combinations; 6. Probability distributions; 7. The binomial and geometric distributions; 8. The normal distribution; Answers

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Book SynopsisEveryone wants to succeed in life. But what causes some of us to be more successful than others? Is it really down to skill and strategy - or something altogether more unpredictable? This book intends to change the way you think about business and the world.

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Book SynopsisThis series has been developed specifically for the Cambridge International AS & A Level Mathematics (9709) syllabus to be examined from 2020. Cambridge International AS & A Level Mathematics: Probability & Statistics 2 matches the corresponding unit of the syllabus, with a clear and logical progression through. It contains materials on topics such as hypothesis testing, Poisson distribution, linear combinations and continuous random variables, and sampling. This coursebook contains a variety of features including recap sections for students to check their prior knowledge, detailed explanations and worked examples, end-of-chapter and cross-topic review exercises and ''Explore'' tasks to encourage deeper thinking around mathematical concepts. Answers to coursebook questions are at the back of the book.Table of Contents1. Hypothesis testing; 2. Poisson distribution; 3. Linear combinations of random variables; Cross-topic revision exercise 1; 4. Continuous random variables; 5. Sampling; 6. Interpretation of sample data; Cross-topic revision exercise 2; Practice paper; Answers; Glossary; Index.

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Book SynopsisA guide to critical thinking in the ''post-truth'' era, from the author of Sunday Times best-seller The Organized Mind We live in a world of information overload. Facts and figures on absolutely everything are at our fingertips, but are too often biased, distorted, or outright lies. From unemployment figures to voting polls, IQ tests to divorce rates, we''re bombarded by seemingly plausible statistics on how people live and what they think. Daniel Levitin teaches us how to effectively ask ourselves: can we really know that? And how do they know that? In this eye-opening, accessible guide filled with fascinating examples and practical takeaways, acclaimed neuroscientist Daniel Levitin shows us how learning to understand statistics will enable you to make better, smarter judgements on the world around you.Trade ReviewIn a post-truth world, Levitin's book is an invaluable primer on how to sort the fact from the fiction * Sunday Times *The world is awash with data, but not always with accurate information. [Levitin] does a terrific job of illustrating the difference between the two with precision and delightful good humour -- Charles Wheelan, author of Naked EconomicsDeservedly a bestseller -- Independent on 'The Organized Mind'Smart, important, exquisitely written -- Daniel Gilbert on 'The Organized Mind'The Organized Mind is the perfect antidote to the effects of information overload. Loved it. -- Scott Turow, New York Times bestselling author of 'Identical' and 'Innocent' on 'The Organized Mind'Daniel Levitin's field guide is a critical thinking primer for our shrill, data-drenched age. From the way averages befuddle to the logical fallacies that sneak by us, every page is enlightening -- Charles Duhigg, author of The Power of Habit and Smarter, Faster, BetterValuable tools for anyone willing to evaluate claims and get to the truth of the matter * Kirkus Reviews *As a lucid guide to critical thinking about statistics, information and assertion it is profoundly welcome * Observer *

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Book SynopsisBaseball is not the only sport to use "moneyball." American football fans, teams, and gamblers are increasingly using data to gain an edge against the competition. This concise book provides a clear introduction to using statistical models to analyze football data.

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Book SynopsisReveals the simple techniques needed to estimate virtually anything and illustrates them using an eclectic array of problems. This title shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store.Trade Review"This follow-up to the popular Guesstimation offers more on the joy of mathematical estimation, and inspiration for the budding analyst."--Nature "The books do a wonderful job at helping the reader to master the craft."--Cut the Knot Insights "A delightful volume... I hope to be able to use many of the tricks I learned in the future. I also hope to teach some of them to students. This would make a great secondary textbook in many classes, ranging from quantitative literacy to a science methods class for future educators. A careful study of this book would certainly improve a student's ability to take a complicated question, break it down into solvable parts, and assemble the parts to find an answer. Because this is quite close to what I want my students to do when faced with a difficult problem in pure mathematics as well, I consider this to be a very valuable book indeed."--Dominic Klyve, MAA Reviews "Guesstimation 2.0: Solving Today's Problems on the Back of a Napkin succeeds where most popular science literature so often fails. This is because it provides its readers with a scientific tool they can use immediately in their everyday lives... [Makes] an excellent addition for the casual scientist, job interviewee, or anyone hoping to impress their friends at a party."--Gabriel Thoumi, Mongabay.com "Readers who enjoyed Weinstein's first volume will be pleased with this instalment."--Choice "Guesstimation 2.0 is a book that was made to mediate between fun and useful... Whether or not a fan of numbers, it's always cool to appear smart, therefore Guesstimation 2.0 is an excellent element to add to one's arsenal."--Sarthak Shankar, Organiser "Certainly a good read for any teacher who enjoys numbers and the world around us."--Mark Hughes, Mathematics Teaching in the Middle School "Guesstimation's problems are fun and engaging in character, and the solutions are intuitive and well explained. Each problem and solution stands independently, and is about four pages long, making the book ideal for passing a quick ten minutes, and easy to pick up and put down. If, like me, you like ill-posed questions to have concrete answers then Guesstimation is definitely a good place to hone your estimation skills!"--Fionntan Roukema, Mathematical SpectrumTable of ContentsAcknowledgments xi Preface xiii 1 How to Solve Problems 1 2 General Questions 11 *2.1 Who unrolled the toilet paper? 13 *2.2 Money height 17 *2.3 Blotting out the Sun 19 *2.4 Really extra-large popcorn 21 *2.5 Building volume 25 *2.6 Mass of money 29 *2.7 A baseball in a glass of beer 33 *2.8 Life on the phone 37 *2.9 Money under the bridge 41 *2.10 Monkeys and Shakespeare 45 *2.11 The titans of siren 49 *2.12 Airheads at the movies 53 *2.13 Heavy cars and heavier people 55 *2.14 Peeing in the pool 59 3 Recycling: What Really Matters? 63 *3.1 Water bottles 67 *3.2 99 bottles of beer on the wall ... 71 *3.3 Can the aluminum 75 *3.4 Paper or plastic? 79 *3.5 Paper doesn't grow on trees! 83 *3.6 The rain in Spain ... 87 *3.7 Bottom feeders 91 *3.8 You light up my life! 95 4 The Five Senses 101 *4.1 Don't stare at the Sun 103 *4.2 Men of vision 105 *4.3 Light a single candle 109 *4.4 Oh say can you see? 113 *4.5 Bigger eyes 117 *4.6 They're watching us! 121 *4.7 Beam the energy down, Scotty! 125 *4.8 Oh say can you hear? 131 *4.9 Heavy loads 135 5 Energy and Work 139 *5.1 Power up the stairs 143 *5.2 Power workout 145 *5.3 Water over the dam 149 *5.4 A hard nut to crack 153 *5.5 Mousetrap cars 155 *5.6 Push hard 159 *5.7 Pumping car tires 161 *5.8 Pumping bike tires 165 *5.9 Atomic bombs and confetti 169 6 Energy and Transportation 173 *6.1 Gas-powered humans 177 *6.2 Driving across country 181 *6.3 Keep on trucking 185 *6.4 Keep on biking 189 *6.5 Keep on training 193 *6.6 Keep on flying 197 *6.7 To pee or not to pee 201 *6.8 Solar-powered cars 205 *6.9 Put a doughnut in your tank 209 *6.10 Perk up your car 213 *6.11 Don't slow down 217 *6.12 Throwing tomatoes 219 7 Heavenly Bodies 223 *7.1 Orbiting the Sun 227 *7.2 Flying off the Earth 229 *7.3 The rings of Earth 233 *7.4 It is not in the stars to hold our destiny 237 *7.5 Orbiting a neutron star 241 *7.6 How high can we jump? 245 *7.7 Collapsing Sun 249 *7.8 Splitting the Moon 253 *7.9 Splitting a smaller moon 257 *7.10 Spinning faster and slower 263 *7.11 Shrinking Sun 267 *7.12 Spinning Earth 271 *7.13 The dinosaur killer and the day 273 *7.14 The Yellowstone volcano and the day 277 *7.15 The orbiting Moon 281 *7.16 The shortest day 283 8 Materials 289 *8.1 Stronger than spider silk 291 *8.2 Beanstalk to orbit 295 *8.3 Bolt failure 299 *8.4 Making mountains out of molecules 303 *8.5 Chopping down a tree 307 9 Radiation 311 *9.1 Nuclear neutrinos 315 *9.2 Neutrinos and you 319 *9.3 Solar neutrinos 323 *9.4 Supernovas can be dangerous 327 *9.5 Reviving ancient bacteria 331 *9.6 Decaying protons 335 *9.7 Journey to the center of the galaxy 337 Appendix A * Dealing with Large Numbers 341 * A.1 Large Numbers 341 * A.2 Precision, Lots of Digits, and Lying 343 * A.3 Numbers and Units 345 Appendix B * Pegs to Hang Things On 347 Bibliography 351 Index 355

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Book SynopsisTrade Review"A thorough, very clearly written overview on the subject of machine learning for those with the prerequisite mathematical tools of calculus, linear algebra and probability."---Jonathan Shock, Mathemafrica"Valuable."---J. Brzezinski, Choice

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Book SynopsisFrom the stock market to covid-19, census figures to marketing email blasts, we are awash with data. But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models-from linear regression to random walks and far beyond-that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. Now culminating in an examination of how to use the multi-model approach to think about pandemics like covid-19, The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.

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Book SynopsisWinner of the 2024 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today's model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work.The text presents causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.Features Integrates working code into the main text. Illustrates concepts through worked data analysis examples. Emphasizes understanding assumptions and how assumptions are reflected in code. Offers more detailed explanations of the mathematics in optional sections. Presents examples of using the dagitty R package to analyze causal graphs. Provides the rethinking R package on the author's website and on GitHub. Trade Review"The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreath’s engaging writing style and humor, and personally found the infusion of humor quite refreshing."- Adam Loy, Carleton College"(The chapter) ‘Generalized Linear Madness’ represents another great chapter of an even better edition of an already awesome textbook."- Benjamin K. Goodrich, Columbia University"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory."- Josep Fortiana Gregori, University of Barcelona"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process." - Nguyet Nguyen, Youngstown State University "As a textbook it successfully brings the statistician’s toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new."- Nathan Green, Journal of the Royal Statistical Society, 2021, https://doi.org/10.1111/rssa.12755"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques."- Abhirup Mallik in Technometrics, August 2021"The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreath’s engaging writing style and humor, and personally found the infusion of humor quite refreshing."~Adam Loy, Carleton College"(The chapter) ‘Generalized Linear Madness’ represents another great chapter of an even better edition of an already awesome textbook."~Benjamin K. Goodrich, Columbia University"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory."~Josep Fortiana Gregori, University of Barcelona"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process." ~Nguyet Nguyen, Youngstown State University"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques."~Abhirup Mallik in Technometrics, August 2021"As a textbook it successfully brings the statistician’s toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new."~ Nathan Green, Journal of the Royal Statistical Society, 2021Table of Contents1. The Golem of Prague. 2. Small Worlds and Large Worlds. Chapter 3. Sampling the Imaginary. 4. Geocentric Models. 5. The Many Variables & The Spurious Waffles. 6. The Haunted DAG & The Causal Terror. 7. Ulysses’ Compass. 8. Conditional Manatees. 8. Conditional Manatees. 9. Markov Chain Monte Carlo. 10. Big Entropy and the Generalized Linear Model. 11. God Spiked the Integers. 12. Monsters and Mixtures. 13. Models With Memory. 14. Adventures in Covariance. 15. Missing Data and Other Opportunities. 16. Generalized Linear Madness. 17. Horoscopes.

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Book SynopsisStigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences. His emphasis is upon how methods of probability theory were developed for measuring uncertainty, for reducing uncertainty, and as a conceptual framework for quantitative studies in the social sciences.Trade ReviewOne is tempted to say that the history of statistics in the nineteenth century will be associated with the name Stigler. -- Morris Kline * New York Times Book Review *An exceptionally searching, almost loving, study of the relevant inspirations and aberrations of its principal characters James Bernoulli, de Moivre, Bayes, Laplace, Gauss, Quetelet, Lexis, Galton, Edgeworth, and Pearson, not neglecting a grand supporting cast… The definitive record of an intellectual Golden Age, an overoptimistic climb to a height not to be maintained. -- M. Stone * Science *In this tour de force of careful scholarship, Stephen Stigler has laid bare the people, ideas, and events underlying the development of statistics… He has written an important and wonderful book… Sometimes Stigler’s prose is so evocative it is almost poetic. -- Howard Wainer * Contemporary Psychology *The book is a pleasure to read: the prose sparkles; the protagonists are vividly drawn; the illustrations are handsome and illuminating; the insights plentiful and sharp. This will remain the definitive work on the early development of mathematical statistics for some time to come. -- Lorraine J. Daston * Journal of Modern History *Stigler’s book exhibits a rare combination of mastery of technical materials, sensitivity to conceptual milieu, and near exhaustive familiarity with primary sources. An exemplary study. -- Lorraine DastonTable of ContentsIntroduction PART 1: The Development of Mathematical Statistics in Astronomy and Geodesy before 1827 1. Least Squares and the Combination of Observations Legendre in 1805 Cotes's Rule Tobias Mayer and the Libration of the Moon Saturn, Jupiter, and Enter Laplace's Rescue of the Solar System Roger Boscovich and the Figure of the Earth Laplace and the Method of Situation Legendre and the Invention of Least Squares 2. Probabilists and the Measurement of Uncertainty Jacob Bernoulli De Moivre and the Expanded Binomial Bernoulli's Failure De Moivre's Approximation De Moivre's Deficiency Simpson and Bayes Simpson's Crucial Step toward Error A Bayesian Critique 3. Inverse Probability Laplace and Inverse Probability The Choice of Means The Deduction of a Curve of Errors in 1772-1774

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Book SynopsisMeasurement is a fundamental concept that underpins almost every aspect of the modern world. It is central to the sciences, social sciences, medicine, and economics, but it affects everyday life. We measure everything - from the distance of far-off galaxies to the temperature of the air, levels of risk, political majorities, taxes, blood pressure, IQ, and weight. The history of measurement goes back to the ancient world, and its story has been one of gradual standardization. Today there are different types of measurement, levels of accuracy, and systems of units, applied in different contexts. Measurement involves notions of variability, accuracy, reliability, and error, and challenges such as the measurement of extreme values.In this Very Short Introduction, David Hand explains the common mathematical framework underlying all measurement, the main approaches to measurement, and the challenges involved. Following a brief historical account of measurement, he discusses measurement as used in the physical sciences and engineering, the life sciences and medicine, the social and behavioural sciences, economics, business, and public policy.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsREFERENCES; FURTHER READING; INDEX

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Book SynopsisA guide to using statistics properly in social science.

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

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Book SynopsisStatistical ConceptsâA First Course presents the first 10 chapters from An Introduction to Statistical Concepts, Fourth Edition. Designed for first and lower-level statistics courses, this book communicates a conceptual, intuitive understanding of statistics that does not assume extensive or recent training in mathematics and only requires a rudimentary knowledge of algebra.Covering the most basic statistical concepts, this book is designed to help readers really understand statistical concepts, in what situations they can be applied, and how to apply them to data. Specifically, the text covers basic descriptive statistics, including ways of representing data graphically, statistical measures that describe a set of data, the normal distribution and other types of standard scores, and an introduction to probability and sampling. The remainder of the text covers various inferential tests, including those involving tests of means (e.g., t tests), proportions, variances, and correlations.Providing accessible and comprehensive coverage of topics suitable for an undergraduate or graduate course in statistics, this book is an invaluable resource for students undertaking an introductory course in statistics in any number of social science and behavioral science disciplines.Trade Review"This edition delivers on many fronts and sets this book apart from the rest. The clear and conversational style emphasizes the applied and practical without compromising the theoretical and conceptual underpinnings. The parallel use of SPSS and R that walks the reader step-by-step through the procedures coupled with fully annotated interpretation of printouts are very appealing to both novice and more seasoned applied researchers. Rather than treating subjects like power and effect size or verification of assumptions in isolation, the authors do a fantastic job of blending them with the analyses to make the story behind the numbers more compelling and complete. The abundance of visuals and APA style write-ups all contribute to simplify and enhance the learning experience." - Devdass Sunnassee, Assistant Clinical Professor, University of North Carolina, USA. "I have relied on previous versions of this textbook to bring to life statistical concepts in my beginning and intermediate level graduate classes. I also share this valuable resource with students who ask questions when working on quantitative projects. This fourth edition brings enhanced materials, explanations, and examples to aid students in gaining basic proficiency in foundational statistical concepts. The detailed and numerous practical examples demonstrate the inner workings of basic statistical methods in the social and behavioural sciences. I look forward to sharing this enhanced edition with our graduate program" -Brian F. French, Washington State University, USA. "Combining theory and mathematical accessibility with examples in various fields of behavioral sciences, SPSS and R applications, APA style write-ups, after-chapter conceptual and practice problems for students, online pedagogical aids, this is a valuable book for introductory statistical courses in behavioral sciences. It has a broad coverage of topics, and the addition of the new chapter on mediation and moderation adds to its value as a classroom text or as a reference for applied researchers." -Feifei Ye, RAND Corporation, USA."Anyone familiar with previous editions of Statistical Concepts from Lomax and Hahs-Vaughn recognize and appreciate the pedigagogically sound treatment of statistical methods comprising introductory and intermediate topics found in many quantitative methods graduate programs. In addition to enhancements found in the past versions such as APA-style write-ups of statistical results and the numerous screen shots depicting both annotated SPSS input commands and output; the fourth edition begins each chapter with a concrete research scenario to motivate the particular statistical method. Another new feature that will resonate with instructors and graduate students are the insightful Stop and Think boxes that offer moments to reflect and to make connections between statistical ideas, data, and the software. Clearly, Lomax and Hahs-Vaughn are committed to preparing the next generation of researchers and practitioners, and the latest edition of Statistical Concepts is a must-have reference for those seeking this type of comprehensive quantitative methods training." - Jeffrey R. Harring, University of Maryland, College Park, USA. "I have required this textbook for my introductory and intermediate-level students throughout multiple editions, and it has continued to get better and better. This new edition continues to emphasize the development of statistical understanding while also providing readers with valuable information on how to perform a variety of procedures using SPSS and R. The authors have added a terrific new chapter on mediation and moderation that reviews concepts and procedures that are often not a point of emphasis in traditional (textbook) coverage of multiple regression (but that are crucial for more modern data analysis). This is a book that not only is a wonderful learning resource for students, but also one they will want to keep in their personal libraries to reference when carrying out their own future research." - H. Michael Crowson, The University of Oklahoma, USA.Table of Contents PrefaceAcknowledgements1. INTRODUCTION2. DATA REPRESENTATION3. UNIVARIATE POPULATION PARAMETERS AND SAMPLE STATISTICS4. THE NORMAL DISTRIBUTION AND STANDARD SCORES5. INTRODUCTION TO PROBABILITY AND SAMPLE STATISTICS6. INTRODUCTION TO HYPOTHESIS TESTING: INFERENCES ABOUT A SINGLE MEAN7. INFERENCES ABOUT THE DIFFERENCE BETWEEN TWO MEANS8. INFERENCES ABOUT PROPORTIONS9. INFERENCES ABOUT VARIANCES10. BIVARIATE MEASURES OF ASSOCIATION AppendixReferencesName Index Subject Index

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Book SynopsisWithout question, statistics is one of the most challenging courses for students in the social and behavioral sciences. Enrolling in their first statistics course, students are often apprehensive or extremely anxious toward the subject matter. And while IBM SPSS is one of the more easy-to-use statistical software programs available, for anxious students who realize they not only have to learn statistics but also new software, the task can seem insurmountable. Keenly aware of studentsâ anxiety with statistics (and the fact that this anxiety can affect performance), Ronald D. Yockey has written SPSS Demystified: A Simple Guide and Reference, now in its fourth edition. Through a comprehensive, step-by-step approach, this text is consistently and specifically designed to both alleviate anxiety toward the subject matter and build a successful experience analyzing data in SPSS . Topics covered in the text are appropriate for most introductory and intermediate statistics and research methods courses.Key features of the text:â Step-by-step instruction and screenshotsâ Designed to be hands-on with the user performing the analyses alongside the text on their computer as they read through each chapterâ Call-out boxes provided, highlighting important information as appropriateâ SPSS output explained, with written results provided using the popular, widely recognized APA formatâ End-of-chapter exercises included, allowing for additional practiceâ SPSS data sets available on the publisherâs websiteNew to the Fourth Edition:â Fully updated to SPSS 28â Updated screenshots in full color to reflect changes in the SPSS software system (version 28)â Exercises updated with up-to-date examplesâ Exact p-values provided (consistent with APA recommendations)Table of ContentsPart I: Introduction to SPSS, Descriptive Statistics, Graphical Procedures of Data, and Reliability Using Coefficient Alpha 1. Introduction to SPSS, 2. Descriptive Statistics: Frequencies, Measures of Central Tendency, and Measures of Variability, 3. Graphical Procedures, 4. Reliability (As Measured by Coefficient Alpha); Part II: Inferential Statistics 5. The One-Sample t Test, 6. The Independent-Samples t Test, 7. The Dependent-Samples t Test, 8. The One-Way Between Subjects Analysis of Variance (ANOVA), 9. The Two-Way Between Subjects Analysis of Variance (ANOVA), 10. The One-Way Within Subjects Analysis of Variance (ANOVA), 11. The One-Between–One-Within Subjects Analysis of Variance (ANOVA), 12. The Pearson r Correlation Coefficient, 13. Simple Linear Regression, 14. Multiple Linear Regression, 15. The Chi-Square Goodness of Fit Test, 16. The Chi-Square Test of Independence; Appendix A. Data Transformations and Other Procedures Appendix B. Solutions to Chapter Exercises

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Book SynopsisAnalysis of Categorical Data with R, Second Editionpresents a modern account of categorical data analysis using the R software environment. It covers recent techniques of model building and assessment for binary, multicategory, and count response variables and discusses fundamentals, such as odds ratio and probability estimation. The authors give detailed advice and guidelines on which procedures to use and why to use them.The second edition is a substantial update of the first based on the authors' experiences of teaching from the book for nearly a decade. The book is organized as before, but with new content throughout, and there are two new substantive topics in the advanced topics chaptergroup testing and splines. The computing has been completely updated, with the emmeans package now integrated into the book. The examples have also been updated, notably to include new examples based on COVID-19, and there are more than 90 new exercises in the book. The s

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Book SynopsisTable of Contents1. Introduction to Probability Theory 2. Random Variables 3. Conditional Probability and Conditional Expectation 4. Markov Chains 5. The Exponential Distribution and the Poisson Process 6. Continuous-Time Markov Chains 7. Renewal Theory and Its Applications 8. Queueing Theory 9. Reliability Theory 10. Brownian Motion and Stationary Processes 11. Simulation 12. Coupling 13. Martingales

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Book SynopsisData, data, data: It''s all one ever hears about these days. Science is all about big data. Our bosses call out for analytics, whatever those might be. And everyone wants to predict what will happen next. Can we accurately predict if a company''s stock will rise, whether or not a disease will spread, or who will become the next President of the United States? As anyone who has ever opened up a spreadsheet groaning with weeks, months, or years of data knows, numbers aren''t enough: we have to know how to make them talk.Enter Scott Page and The Model Thinker. A leading professor of quantitative social science at the University of Michigan, he has taken his expertise as both a teacher and researcher and distilled it into the one book anyone will need to master data and turn it to professional use. This is no armchair exercise in imagined understanding, like The Signal and the Noise or The Black Swan or a legion of books on networks, the purposes of which ar

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Book SynopsisAnalysis of Financial Time Series, Third Edition provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described.Trade Review"Analysis of financial time series, third edition, is an ideal book for introductory courses on time series at the graduate level and a valuable supplement for statistics courses in time series at the upper-undergraduate level." (Mathematical Reviews, 2011) "Nevertheless, all in all the book can be a very useful reference for students as well as for professionals." (Zentralblatt MATH, 2011) "Factor models, an important technique used in quantitative finance, are given a full treatment with macroeconomic factor models and fundamental factor models. The coverage of the book is comprehensive. It starts from basic time series techniques and finishes with advanced concepts such as state space models and MCMC methods. There is a balance between the theoretical background necessary to appreciate the nuances and the practical aspect of implementation. More importantly it gives insights about what time series models can't address. The book has an excellent supporting website which has all the programs and data sets which helps to internalize the concepts. Finally, teaching professionals should find the solutions manual as a valuable tool to explain concepts and to ensure understanding." (BookPleasures.com, January 2011) "This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described." (Insurance News Net, 8 December 2010)Table of ContentsPreface xvii Preface to the Second Edition xix Preface to the First Edition xxi 1 Financial Time Series and Their Characteristics 1 1.1 Asset Returns, 2 1.2 Distributional Properties of Returns, 7 1.3 Processes Considered, 22 2 Linear Time Series Analysis and Its Applications 29 2.1 Stationarity, 30 2.2 Correlation and Autocorrelation Function, 30 2.3 White Noise and Linear Time Series, 36 2.4 Simple AR Models, 37 2.5 Simple MA Models, 57 2.6 Simple ARMA Models, 64 2.7 Unit-Root Nonstationarity, 71 2.8 Seasonal Models, 81 2.9 Regression Models with Time Series Errors, 90 2.10 Consistent Covariance Matrix Estimation, 97 2.11 Long-Memory Models, 101 3 Conditional Heteroscedastic Models 109 3.1 Characteristics of Volatility, 110 3.2 Structure of a Model, 111 3.3 Model Building, 113 3.4 The ARCH Model, 115 3.5 The GARCH Model, 131 3.6 The Integrated GARCH Model, 140 3.7 The GARCH-M Model, 142 3.8 The Exponential GARCH Model, 143 3.9 The Threshold GARCH Model, 149 3.10 The CHARMA Model, 150 3.11 Random Coefficient Autoregressive Models, 152 3.12 Stochastic Volatility Model, 153 3.13 Long-Memory Stochastic Volatility Model, 154 3.14 Application, 155 3.15 Alternative Approaches, 159 3.16 Kurtosis of GARCH Models, 165 4 Nonlinear Models and Their Applications 175 4.1 Nonlinear Models, 177 4.2 Nonlinearity Tests, 205 4.3 Modeling, 214 4.4 Forecasting, 215 4.5 Application, 218 5 High-Frequency Data Analysis and Market Microstructure 231 5.1 Nonsynchronous Trading, 232 5.2 Bid–Ask Spread, 235 5.3 Empirical Characteristics of Transactions Data, 237 5.4 Models for Price Changes, 244 5.5 Duration Models, 253 5.6 Nonlinear Duration Models, 264 5.7 Bivariate Models for Price Change and Duration, 265 5.8 Application, 270 6 Continuous-Time Models and Their Applications 287 6.1 Options, 288 6.2 Some Continuous-Time Stochastic Processes, 288 6.3 Ito's Lemma, 292 6.4 Distributions of Stock Prices and Log Returns, 297 6.5 Derivation of Black–Scholes Differential Equation, 298 6.6 Black–Scholes Pricing Formulas, 300 6.7 Extension of Ito's Lemma, 309 6.8 Stochastic Integral, 310 6.9 Jump Diffusion Models, 311 6.10 Estimation of Continuous-Time Models, 318 7 Extreme Values, Quantiles, and Value at Risk 325 7.1 Value at Risk, 326 7.2 RiskMetrics, 328 7.3 Econometric Approach to VaR Calculation, 333 7.4 Quantile Estimation, 338 7.5 Extreme Value Theory, 342 7.6 Extreme Value Approach to VaR, 353 7.7 New Approach Based on the Extreme Value Theory, 359 7.8 The Extremal Index, 377 8 Multivariate Time Series Analysis and Its Applications 389 8.1 Weak Stationarity and Cross-Correlation Matrices, 390 8.2 Vector Autoregressive Models, 399 8.3 Vector Moving-Average Models, 417 8.4 Vector ARMA Models, 422 8.5 Unit-Root Nonstationarity and Cointegration, 428 8.6 Cointegrated VAR Models, 432 8.7 Threshold Cointegration and Arbitrage, 442 8.8 Pairs Trading, 446 9 Principal Component Analysis and Factor Models 467 9.1 A Factor Model, 468 9.2 Macroeconometric Factor Models, 470 9.3 Fundamental Factor Models, 476 9.4 Principal Component Analysis, 483 9.5 Statistical Factor Analysis, 489 9.6 Asymptotic Principal Component Analysis, 498 10 Multivariate Volatility Models and Their Applications 505 10.1 Exponentially Weighted Estimate, 506 10.2 Some Multivariate GARCH Models, 510 10.3 Reparameterization, 516 10.4 GARCH Models for Bivariate Returns, 521 10.5 Higher Dimensional Volatility Models, 537 10.6 Factor–Volatility Models, 543 10.7 Application, 546 10.8 Multivariate t Distribution, 548 11 State-Space Models and Kalman Filter 557 11.1 Local Trend Model, 558 11.2 Linear State-Space Models, 576 11.3 Model Transformation, 577 11.4 Kalman Filter and Smoothing, 591 11.5 Missing Values, 600 11.6 Forecasting, 601 11.7 Application, 602 12 Markov Chain Monte Carlo Methods with Applications 613 12.1 Markov Chain Simulation, 614 12.2 Gibbs Sampling, 615 12.3 Bayesian Inference, 617 12.4 Alternative Algorithms, 622 12.5 Linear Regression with Time Series Errors, 624 12.6 Missing Values and Outliers, 628 12.7 Stochastic Volatility Models, 636 12.8 New Approach to SV Estimation, 649 12.9 Markov Switching Models, 660 12.10 Forecasting, 666 12.11 Other Applications, 669 Exercises, 670 References, 671 Index 673

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Book SynopsisWhile the literature on reinsurance is vast, there is currently no comprehensive treatment of the major actuarial and financial aspects of the subject. Many publications deal with specific aspects of the theory without putting them into a proper perspective. Reinsurance: Actuarial and Statistical Aspects treats the topic differently.Table of ContentsPreface ix 1 Introduction 1 1.1 What is Reinsurance? 1 1.2 Why Reinsurance? 2 1.3 Reinsurance Data 4 1.3.1 Case Study I: Motor Liability Data 5 1.3.2 Case Study II: Dutch Fire Insurance Data 10 1.3.3 Case Study III: Austrian Storm Claim Data 10 1.3.4 Case Study IV: European Flood Risk Data 11 1.3.5 Case Study V: Groningen Earthquakes 12 1.3.6 Case Study VI: Danish Fire Insurance Data 12 1.4 Notes and Bibliography 16 2 Reinsurance Forms and their Properties 19 2.1 Quota-share Reinsurance 19 2.1.1 Some Practical Considerations 20 2.2 Surplus Reinsurance 21 2.3 Excess-of-loss Reinsurance 24 2.3.1 Moment Calculations 25 2.3.2 Reinstatements 27 2.3.3 Further Practical Considerations 29 2.4 Stop-loss Reinsurance 30 2.5 Large Claim Reinsurance 31 2.6 Combinations of Reinsurance Forms and Global Protections 32 2.7 Facultative Contracts 33 2.8 Notes and Bibliography 33 3 Models for Claim Sizes 35 3.1 Tails of Distributions 35 3.2 Large Claims 36 3.3 Common Claim Size Distributions 40 3.3.1 Light-tailed Models 41 3.3.2 Heavy-tailed Models 44 3.4 Mean Excess Analysis 49 3.5 Full Models: Splicing 50 3.6 Multivariate Modelling of Large Claims 52 4 Statistics for Claim Sizes 59 4.1 Heavy or Light Tails: QQ- and Derivative Plots 60 4.2 Large Claims Modelling through Extreme Value Analysis EVA for Pareto-type Tails 63 4.2.1 EVA for Pareto-type Tails 63 4.2.2 General Tail Modelling using EVA 82 4.2.3 EVA under Upper-truncation 91 4.3 Global Fits: Splicing, Upper-truncation and Interval Censoring 97 4.3.1 Tail-mixed Erlang Splicing 97 4.3.2 Tail-mixed Erlang Splicing under Censoring and Upper-truncation 99 4.4 Incorporating Covariate Information 114 4.4.1 Pareto-type Modelling 114 4.4.2 Generalized Pareto Modelling 116 4.4.3 Regression Extremes with Censored Data 119 4.5 Multivariate Analysis of Claim Distributions 123 4.5.1 The Multivariate POT Approach 124 4.5.2 Multivariate Mixtures of Erlangs 125 4.6 Estimation of Other Tail Characteristics 128 4.7 Further Case Studies 132 4.8 Notes and Bibliography 137 5 Models for Claim Counts 139 5.1 General Treatment 139 5.1.1 Main Properties of the Claim Number Process 140 5.2 The Poisson Process and its Extensions 141 5.2.1 The Homogeneous Poisson Process 141 5.2.2 Inhomogeneous Poisson Processes 143 5.2.3 Mixed Poisson Processes 144 5.2.4 Doubly Stochastic Poisson Processes 149 5.3 Other Claim Number Processes 157 5.3.1 The Nearly Mixed Poisson Model 157 5.3.2 Infinitely Divisible Processes 158 5.3.3 The Renewal Model 160 5.3.4 Markov Models 161 5.4 Discrete Claim Counts 161 5.5 Statistics of Claim Counts 164 5.5.1 Modelling Yearly Claim Counts 164 5.5.2 Modelling the Claim Arrival Process 172 5.6 Claim Numbers under Reinsurance 183 5.6.1 Number of Claims under Excess-loss Reinsurance 183 5.7Notes and Bibliography 187 6 Total Claim Amount 189 6.1 General Formulas for Aggregating Independent Risks 189 6.2 Classical Approximations for the Total Claim Size 191 6.2.1 Approximations based on the First Few Moments 191 6.2.2 Asymptotic Approximations for Light-tailed Claims 193 6.2.3 Asymptotic Approximations for Heavy-tailed Claims 198 6.3 Panjer Recursion 199 6.4 Fast Fourier Transform 200 6.5 Total Claim Amount under Reinsurance 201 6.5.1 Proportional Reinsurance 201 6.5.2 Excess-loss Reinsurance 202 6.5.3 Stop-loss Reinsurance 204 6.6 Numerical Illustrations 206 6.7 Aggregation for Dependent Risks 208 6.8 Notes and Bibliography 212 7 Reinsurance Pricing 217 7.1 Classical Principles of Premium Calculation 219 7.2 Solvency Considerations 219 7.2.1 The Ruin Probability 223 7.2.2 One-year Time Horizon and Cost of Capital 226 7.3 Pricing Proportional Reinsurance 228 7.4 Pricing Non-proportional Reinsurance 229 7.4.1 Exposure Rating 229 7.4.2 Experience Rating 232 7.4.3 Aggregate Pure Premium 234 7.5 The Aggregate Risk Margin 235 7.6 Leading and Following Reinsurers 237 7.7 Notes and Bibliography 238 8 Choice of Reinsurance 241 8.1 Decision Criteria 243 8.2 Classical Optimality Results 245 8.2.1 Pareto-optimal Risk Sharing 245 8.2.2 Stochastic Ordering 247 8.2.3 Minimizing Retained Variance 248 8.2.4 Maximizing Expected Utility 251 8.2.5 Minimizing the Ruin Probability 253 8.2.6 Combining Reinsurance Treaties over Subportfolios 8.3 Solvency Constraints and Cost of Capital 259 8.4 Minimizing Other Risk Measures 261 8.5 Combining Reinsurance Treaties 262 8.6 Reinsurance Chains 263 8.7 Dynamic Reinsurance 264 8.8 Beyond Piecewise Linear Contracts 266 8.9 Notes and Bibliography 268 9 Simulation 273 9.1 The Monte Carlo Method 273 9.2 Variance Reduction Techniques 276 9.2.1 Conditional Monte Carlo 277 9.2.2 Importance Sampling 277 9.3 Quasi-Monte Carlo Techniques 283 9.4 Notes and Bibliography 288 10 Further Topics 291 10.1 More on Large Claim Reinsurance 291 10.1.1 The Ordered Claims 291 10.1.2 Large Claim Reinsurance 296 10.1.3 ECOMOR 298 10.2 Alternative Risk Transfer 300 10.2.1 Notes and Bibliography 304 10.3 Reinsurance and Finance 305 10.4 Catastrophic Risk 306 References 309 Index 347

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Book SynopsisIn their bestselling title MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.With the addition of contributor Brendan Ames, MATHEMATICAL STATISTICS WITH APPLICATIONS now includes an enhanced eTextbook. Simulation activities using interactive applets and R embedded within the MindTap Reader help students visualize statistical concepts, and an appendix introducing students to statistical data analysis using R can be found at the end of the eTextbook.Table of Contents1. What Is Statistics? Introduction. Characterizing a Set of Measurements: Graphical Methods. Characterizing a Set of Measurements: Numerical Methods. How Inferences Are Made. Theory and Reality. Summary. 2. Probability. Introduction. Probability and Inference. A Review of Set Notation. A Probabilistic Model for an Experiment: The Discrete Case. Calculating the Probability of an Event: The Sample-Point Method. Tools for Counting Sample Points. Conditional Probability and the Independence of Events. Two Laws of Probability. Calculating the Probability of an Event: The Event-Composition Methods. The Law of Total Probability and Bayes''''s Rule. Numerical Events and Random Variables. Random Sampling. Summary. 3. Discrete Random Variables and Their Probability Distributions. Basic Definition. The Probability Distribution for Discrete Random Variable. The Expected Value of Random Variable or a Function of Random Variable. The Binomial Probability Distribution. The Geometric Probability Distribution. The Negative Binomial Probability Distribution (Optional). The Hypergeometric Probability Distribution. Moments and Moment-Generating Functions. Probability-Generating Functions (Optional). Tchebysheff''''s Theorem. Summary. 4. Continuous Random Variables and Their Probability Distributions. Introduction. The Probability Distribution for Continuous Random Variable. The Expected Value for Continuous Random Variable. The Uniform Probability Distribution. The Normal Probability Distribution. The Gamma Probability Distribution. The Beta Probability Distribution. Some General Comments. Other Expected Values. Tchebysheff''''s Theorem. Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional). Summary. 5. Multivariate Probability Distributions. Introduction. Bivariate and Multivariate Probability Distributions. Independent Random Variables. The Expected Value of a Function of Random Variables. Special Theorems. The Covariance of Two Random Variables. The Expected Value and Variance of Linear Functions of Random Variables. The Multinomial Probability Distribution. The Bivariate Normal Distribution (Optional). Conditional Expectations. Summary. 6. Functions of Random Variables. Introductions. Finding the Probability Distribution of a Function of Random Variables. The Method of Distribution Functions. The Methods of Transformations. Multivariable Transformations Using Jacobians. Order Statistics. Summary. 7. Sampling Distributions and the Central Limit Theorem. Introduction. Sampling Distributions Related to the Normal Distribution. The Central Limit Theorem. A Proof of the Central Limit Theorem (Optional). The Normal Approximation to the Binomial Distributions. Summary. 8. Estimation. Introduction. The Bias and Mean Square Error of Point Estimators. Some Common Unbiased Point Estimators. Evaluating the Goodness of Point Estimator. Confidence Intervals. Large-Sample Confidence Intervals Selecting the Sample Size. Small-Sample Confidence Intervals for u and u1-u2. Confidence Intervals for o2. Summary. 9. Properties of Point Estimators and Methods of Estimation. Introduction. Relative Efficiency. Consistency. Sufficiency. The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation. The Method of Moments. The Method of Maximum Likelihood. Some Large-Sample Properties of MLEs (Optional). Summary. 10. Hypothesis Testing. Introduction. Elements of a Statistical Test. Common Large-Sample Tests. Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test. Relationships Between Hypothesis Testing Procedures and Confidence Intervals. Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values. Some Comments on the Theory of Hypothesis Testing. Small-Sample Hypothesis Testing for u and u1-u2. Testing Hypotheses Concerning Variances. Power of Test and the Neyman-Pearson Lemma. Likelihood Ration Test. Summary. 11. Linear Models and Estimation by Least Squares. Introduction. Linear Statistical Models. The Method of Least Squares. Properties of the Least Squares Estimators for the Simple Linear Regression Model. Inference Concerning the Parameters BI. Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression. Predicting a Particular Value of Y Using Simple Linear Regression. Correlation. Some Practical Examples. Fitting the Linear Model by Using Matrices. Properties of the Least Squares Estimators for the Multiple Linear Regression Model. Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression. Prediction a Particular Value of Y Using Multiple Regression. A Test for H0: Bg+1 + Bg+2 = . = Bk = 0. Summary and Concluding Remarks. 12. Considerations in Designing Experiments. The Elements Affecting the Information in a Sample. Designing Experiment to Increase Accuracy. The Matched Pairs Experiment. Some Elementary Experimental Designs. Summary. 13. The Analysis of Variance. Introduction. The Analysis of Variance Procedure. Comparison of More than Two Means: Analysis of Variance for a One-way Layout. An Analysis of Variance Table for a One-Way Layout. A Statistical Model of the One-Way Layout. Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout (Optional). Estimation in the One-Way Layout. A Statistical Model for the Randomized Block Design. The Analysis of Variance for a Randomized Block Design. Estimation in the Randomized Block Design. Selecting the Sample Size. Simultaneous Confidence Intervals for More than One Parameter. Analysis of Variance Using Linear Models. Summary. 14. Analysis of Categorical Data. A Description of the Experiment. The Chi-Square Test. A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test. Contingency Tables. r x c Tables with Fixed Row or Column Totals. Other Applications. Summary and Concluding Remarks. 15. Nonparametric Statistics. Introduction. A General Two-Sampling Shift Model. A Sign Test for a Matched Pairs Experiment. The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment. The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples. The Mann-Whitney U Test: Independent Random Samples. The Kruskal-Wallis Test for One-Way Layout. The Friedman Test for Randomized Block Designs. The Runs Test: A Test for Randomness. Rank Correlation Coefficient. Some General Comments on Nonparametric Statistical Test. 16. Introduction to Bayesian Methods for Inference. Introduction. Bayesian Priors, Posteriors and Estimators. Bayesian Credible Intervals. Bayesian Tests of Hypotheses. Summary and Additional Comments. Appendix 1. Matrices and Other Useful Mathematical Results. Matrices and Matrix Algebra. Addition of Matrices. Multiplication of a Matrix by a Real Number. Matrix Multiplication. Identity Elements. The Inverse of a Matrix. The Transpose of a Matrix. A Matrix Expression for a System of Simultaneous Linear Equations. Inverting a Matrix. Solving a System of Simultaneous Linear Equations. Other Useful Mathematical Results. Appendix 2. Common Probability Distributions, Means, Variances, and Moment-Generating Functions. Discrete Distributions. Continuous Distributions. Appendix 3. Tables. Binomial Probabilities. Table of e-x. Poisson Probabilities. Normal Curve Areas. Percentage Points of the t Distributions. Percentage Points of the F Distributions. Distribution of Function U. Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test. Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a). Critical Values of Pearman''s Rank Correlation Coefficient. Random Numbers. Answer to Exercises. Index. R Appendix. Students are introduced to statistical data analysis and shown how to use R to conduct all of the major statistical procedures from the textbook.

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Book SynopsisPrepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in MATHEMATICAL STATISTICS WITH APPLICATIONS, 7th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.

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

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Book SynopsisThis practical introduction for final-year undergraduate and graduate students is ideally suited to computer scientists without a background in calculus and linear algebra. Numerous examples and exercises are provided. Additional resources available online and in the comprehensive software package include computer code, demos and teaching materials for instructors.Trade Review'This book is an exciting addition to the literature on machine learning and graphical models. What makes it unique and interesting is that it provides a unified treatment of machine learning and related fields through graphical models, a framework of growing importance and popularity. Another feature of this book lies in its smooth transition from traditional artificial intelligence to modern machine learning. The book is well-written and truly pleasant to read. I believe that it will appeal to students and researchers with or without a solid mathematical background.' Zheng-Hua Tan, Aalborg University, Denmark'With approachable text, examples, exercises, guidelines for teachers, a MATLAB toolbox and an accompanying website, Bayesian Reasoning and Machine Learning by David Barber provides everything needed for your machine learning course. Only students not included.' Jaakko Hollmén, Aalto University'The chapters on graphical models form one of the clearest and most concise presentations I have seen … The exposition throughout uses numerous diagrams and examples, and the book comes with an extensive software toolbox - these will be immensely helpful for students and educators. It's also a great resource for self-study.' Arindam Banerjee, University of Minnesota'I repeatedly get unsolicited comments from my students that the contents of this book have been very valuable in developing their understanding of machine learning … My students praise this book because it is both coherent and practical, and because it makes fewer assumptions regarding the reader's statistical knowledge and confidence than many books in the field.' Amos Storkey, University of EdinburghTable of ContentsPreface; Part I. Inference in Probabilistic Models: 1. Probabilistic reasoning; 2. Basic graph concepts; 3. Belief networks; 4. Graphical models; 5. Efficient inference in trees; 6. The junction tree algorithm; 7. Making decisions; Part II. Learning in Probabilistic Models: 8. Statistics for machine learning; 9. Learning as inference; 10. Naive Bayes; 11. Learning with hidden variables; 12. Bayesian model selection; Part III. Machine Learning: 13. Machine learning concepts; 14. Nearest neighbour classification; 15. Unsupervised linear dimension reduction; 16. Supervised linear dimension reduction; 17. Linear models; 18. Bayesian linear models; 19. Gaussian processes; 20. Mixture models; 21. Latent linear models; 22. Latent ability models; Part IV. Dynamical Models: 23. Discrete-state Markov models; 24. Continuous-state Markov models; 25. Switching linear dynamical systems; 26. Distributed computation; Part V. Approximate Inference: 27. Sampling; 28. Deterministic approximate inference; Appendix. Background mathematics; Bibliography; Index.

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Book SynopsisThis book promises to be the definitive guide to the field. It provides a highly sophisticated yet exceptionally clear explanation of game theory, with a host of applications to legal issues.Trade ReviewGame Theory and the Law promises to be the definitive guide to the field. It provides a highly sophisticated yet exceptionally clear explanation of game theory, with a host of applications to legal issues. The authors have not only synthesized the existing scholarship, but also created the foundation for the next generation of research in law and economics. -- Daniel A. Farber, University of Minnesota Law SchoolThe most comprehensive and encompassing treatment of this approach… [This] is the first nontechnical, modern introduction to how (noncooperative) game theory can be applied specifically to legal analysis… Game Theory and the Law is a user-friendly analysis of concrete, numerical examples, rather than a theoretical presentation of abstract concepts. The authors introduce and explain, with actual legal cases or hypotheticals, the salient issues of modern game theory. This breadth of coverage is remarkable. This is not just a textbook; it is also something of a research monograph, introducing many new models attributable to the authors alone. -- Peter H. Huang * Jurimetrics Journal *Game Theory and the Law is an important book. It is important in the sense that it will serve as a catalyst for an expanded use of game-theoretic models in the study of law. It will be a book that people will one day recognize as having had a considerable influence on its field. And it will receive the praise that accompanies such influence. Happily, such influence will be beneficial to the field of law and such praise will be richly deserved, because Game Theory and the Law is an extremely intelligent and thoughtful text… One of the features of the book that is most striking (and, for my part, most welcome) is the thoughtful and sensible manner in which they approach the use of game theory. Unlike many proponents of game-theoretic analysis, they do not present it as the only legitimate approach to social-scientific analysis. The authors present game theory as a powerful tool that can be used along with other approaches to enhance our understanding of the role of law in social life… The persuasiveness of their general argument for the utility of game theory derives from a combination of the power of their insights along with the sensibility of their analysis. The book is written in a clear, concise and interesting manner. Its bibliographic references render it a source book for additional research in both game theory and law. This is a book that should be read by scholars of law in particular and scholars of political behavior in particular. -- Jack Knight * Law and Politics Book Review *Table of ContentsPreface Introduction: Understanding Strategic Behavior Bibliographic Notes Simultaneous Decisionmaking and the Normal Form Game The Normal Form Game Using Different Games to Compare Legal Regimes The Nash Equilibrium Civil Liability, Accident Law, and Strategic Behavior Legal Rules and the Idea of Strict Dominance Collective Action Problems and the Two-by-Two Game The Problem of Multiple Nash Equilibria Summary Bibliographic Notes Dynamic Interaction and the Extensive Form Game The Extensive Form Game and Backwards Induction A Dynamic Model of Preemption and Strategic Commitment Subgame Perfection Summary Bibliographic Notes Information Revelation, Disclosure Laws, and Renegotiation Incorporating Beliefs into the Solution Concept The Perfect Bayesian Equilibrium Solution Concept Verifiable Information, Voluntary Disclosure, and the Unraveling Result Disclosure Laws and the Limits of Unraveling Observable Information, Norms, and the Problem of Renegotiation Optimal Incentives and the Need for Renegotiation Limiting the Ability of Parties to Renegotiate Summary Bibliographic Notes Signaling, Screening, and Nonverifiable Information Signaling and Screening Modeling Nonverifiable Information Signals and the Effects of Legal Rules Information Revelation and Contract Default Rules Screening and the Role of Legal Rules Summary Bibliographic Notes Reputation and Repeated Games Backwards Induction and Its Limits Infinitely Repeated Games, Tacit Collusion, and Folk Theorems Reputation, Predation, and Cooperation Summary Bibliographic Notes Collective Action, Embedded Games, and the Limits of Simple Models Collective Action and the Role of Law Embedded Games Understanding the Structure of Large Games Collective Action and Private Information Collective Action Problems in Sequential Decisionmaking Herd Behavior Summary Bibliographic Notes Noncooperative Bargaining Modeling the Division of Gains from Trade Legal Rules as Exit Options Bargaining and Corporate Reorganizations Collective Bargaining and Exit Options Summary Bibliographic Notes Bargaining and Information Basic Models of the Litigation Process Modeling Separate Trials for Liability and Damages Information and Selection Bias Discovery Rules and Verifiable Information Summary Bibliographic Notes Conclusion: Information and the Limits of Law Notes References Glossary Index

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Book SynopsisAnalytical chemists must use a range of statistical tools in their treatment of experimental data to obtain reliable results. Practical Statistics for the Analytical Scientist is a manual designed to help them negotiate the daunting specialist terminology and symbols. Prepared in conjunction with the Department of Trade and Industry''s Valid Analytical Measurement (VAM) programme, this volume covers the basic statistics needed in the laboratory. It describes the statistical procedures that are most likely to be required including summary and descriptive statistics, calibration, outlier testing, analysis of variance and basic quality control procedures. To improve understanding, many examples provide the user with material for consolidation and practice. The fully worked answers are given both to check the correct application of the procedures and to provide a template for future problems. Practical Statistics for the Analytical Scientist will be welcomed by practising analytical chemisTable of ContentsIntroduction: Choosing the Correct Statistics; Descriptive Statistics; Distribution Descriptives; Probability Distributions; Confidence Limits; Accuracy and Precision; Significance Testing; Outlier Tests; The ANalysis Of VAriance; Linear Regression; Polynomial Regression; Repeatability Standard Deviation; Reproducibility Standard Deviation; Analytical Quality Control; Statistical Sampling; Appendices; Subject Index

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