Mathematical Statistics

Basic Ideas and Selected Topics, Volume I, Second Edition

Author: Peter J. Bickel,Kjell A. Doksum

Publisher: CRC Press

ISBN: 1498723810

Category: Business & Economics

Page: 576

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Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition presents fundamental, classical statistical concepts at the doctorate level. It covers estimation, prediction, testing, confidence sets, Bayesian analysis, and the general approach of decision theory. This edition gives careful proofs of major results and explains how the theory sheds light on the properties of practical methods. The book first discusses non- and semiparametric models before covering parameters and parametric models. It then offers a detailed treatment of maximum likelihood estimates (MLEs) and examines the theory of testing and confidence regions, including optimality theory for estimation and elementary robustness considerations. It next presents basic asymptotic approximations with one-dimensional parameter models as examples. The book also describes inference in multivariate (multiparameter) models, exploring asymptotic normality and optimality of MLEs, Wald and Rao statistics, generalized linear models, and more. Mathematical Statistics: Basic Ideas and Selected Topics, Volume II will be published in 2015. It will present important statistical concepts, methods, and tools not covered in Volume I.

Mathematical Statistics

Basic Ideas and Selected Topics

Author: Peter J. Bickel,Kjell A. Doksum

Publisher: CRC Press

ISBN: 1498722709

Category: Business & Economics

Page: 465

View: 5399

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Mathematical Statistics: Basic Ideas and Selected Topics, Volume II presents important statistical concepts, methods, and tools not covered in the authors’ previous volume. This second volume focuses on inference in non- and semiparametric models. It not only reexamines the procedures introduced in the first volume from a more sophisticated point of view but also addresses new problems originating from the analysis of estimation of functions and other complex decision procedures and large-scale data analysis. The book covers asymptotic efficiency in semiparametric models from the Le Cam and Fisherian points of view as well as some finite sample size optimality criteria based on Lehmann–Scheffé theory. It develops the theory of semiparametric maximum likelihood estimation with applications to areas such as survival analysis. It also discusses methods of inference based on sieve models and asymptotic testing theory. The remainder of the book is devoted to model and variable selection, Monte Carlo methods, nonparametric curve estimation, and prediction, classification, and machine learning topics. The necessary background material is included in an appendix. Using the tools and methods developed in this textbook, students will be ready for advanced research in modern statistics. Numerous examples illustrate statistical modeling and inference concepts while end-of-chapter problems reinforce elementary concepts and introduce important new topics. As in Volume I, measure theory is not required for understanding. Check out Volume I for fundamental, classical statistical concepts leading to the material in this volume.

Theoretical Statistics

Author: D.R. Cox,D.V. Hinkley

Publisher: CRC Press

ISBN: 9780412161605

Category: Mathematics

Page: 528

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A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics, emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistical procedures. Chapters 4 and 5 cover hypothesis testing with simple and null hypotheses, respectively. Subsequent chapters discuss non-parametrics, interval estimation, point estimation, asymptotics, Bayesian procedure, and deviation theory. Student familiarity with standard statistical techniques is assumed.

Linear Algebra and Matrix Analysis for Statistics

Author: Sudipto Banerjee,Anindya Roy

Publisher: CRC Press

ISBN: 1420095382

Category: Mathematics

Page: 580

View: 8053

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Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Introduction to Probability with R

Author: Kenneth Baclawski

Publisher: CRC Press

ISBN: 9781420065220

Category: Mathematics

Page: 384

View: 4793

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Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R. This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. The book has an accompanying website with more information.

Bayesian Ideas and Data Analysis

An Introduction for Scientists and Statisticians

Author: Ronald Christensen,Wesley Johnson,Adam Branscum,Timothy E Hanson

Publisher: CRC Press

ISBN: 1439803552

Category: Mathematics

Page: 516

View: 511

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Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data. The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions. The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data. Data sets and codes are provided on a supplemental website.

Linear Models with R, Second Edition

Author: Julian J. Faraway

Publisher: CRC Press

ISBN: 1439887349

Category: Mathematics

Page: 286

View: 2110

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A Hands-On Way to Learning Data Analysis Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates Extensive use of the ggplot2 graphics package in addition to base graphics Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

Statistical Inference

An Integrated Approach, Second Edition

Author: Helio S. Migon,Dani Gamerman,Francisco Louzada

Publisher: CRC Press

ISBN: 1439878803

Category: Mathematics

Page: 385

View: 7115

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A Balanced Treatment of Bayesian and Frequentist Inference Statistical Inference: An Integrated Approach, Second Edition presents an account of the Bayesian and frequentist approaches to statistical inference. Now with an additional author, this second edition places a more balanced emphasis on both perspectives than the first edition. New to the Second Edition New material on empirical Bayes and penalized likelihoods and their impact on regression models Expanded material on hypothesis testing, method of moments, bias correction, and hierarchical models More examples and exercises More comparison between the approaches, including their similarities and differences Designed for advanced undergraduate and graduate courses, the text thoroughly covers statistical inference without delving too deep into technical details. It compares the Bayesian and frequentist schools of thought and explores procedures that lie on the border between the two. Many examples illustrate the methods and models, and exercises are included at the end of each chapter.

Statistical Theory

A Concise Introduction

Author: Felix Abramovich,Ya'acov Ritov

Publisher: CRC Press

ISBN: 148221184X

Category: Mathematics

Page: 240

View: 1879

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Designed for a one-semester advanced undergraduate or graduate course, Statistical Theory: A Concise Introduction clearly explains the underlying ideas and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs. Based on the authors’ lecture notes, this student-oriented, self-contained book maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a "sketched" version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments. Chapters and sections marked by asterisks contain more advanced topics and may be omitted. A special chapter on linear models shows how the main theoretical concepts can be applied to the well-known and frequently used statistical tool of linear regression. Requiring no heavy calculus, simple questions throughout the text help students check their understanding of the material. Each chapter also includes a set of exercises that range in level of difficulty.

Design and Analysis of Experiments with SAS

Author: John Lawson

Publisher: CRC Press

ISBN: 1420060600

Category: Mathematics

Page: 596

View: 2932

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A culmination of the author’s many years of consulting and teaching, Design and Analysis of Experiments with SAS provides practical guidance on the computer analysis of experimental data. It connects the objectives of research to the type of experimental design required, describes the actual process of creating the design and collecting the data, shows how to perform the proper analysis of the data, and illustrates the interpretation of results. Drawing on a variety of application areas, from pharmaceuticals to machinery, the book presents numerous examples of experiments and exercises that enable students to perform their own experiments. Harnessing the capabilities of SAS 9.2, it includes examples of SAS data step programming and IML, along with procedures from SAS Stat, SAS QC, and SAS OR. The text also shows how to display experimental results graphically using SAS ODS graphics. The author emphasizes how the sample size, the assignment of experimental units to combinations of treatment factor levels (error control), and the selection of treatment factor combinations (treatment design) affect the resulting variance and bias of estimates as well as the validity of conclusions. This textbook covers both classical ideas in experimental design and the latest research topics. It clearly discusses the objectives of a research project that lead to an appropriate design choice, the practical aspects of creating a design and performing experiments, and the interpretation of the results of computer data analysis. SAS code and ancillaries are available at http://lawson.mooo.com

Generalized Additive Models

An Introduction with R, Second Edition

Author: Simon N. Wood

Publisher: CRC Press

ISBN: 1498728375

Category: Mathematics

Page: 496

View: 3700

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The first edition of this book has established itself as one of the leading references on generalized additive models (GAMs), and the only book on the topic to be introductory in nature with a wealth of practical examples and software implementation. It is self-contained, providing the necessary background in linear models, linear mixed models, and generalized linear models (GLMs), before presenting a balanced treatment of the theory and applications of GAMs and related models. The author bases his approach on a framework of penalized regression splines, and while firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of R software helps explain the theory and illustrates the practical application of the methodology. Each chapter contains an extensive set of exercises, with solutions in an appendix or in the book’s R data package gamair, to enable use as a course text or for self-study. Simon N. Wood is a professor of Statistical Science at the University of Bristol, UK, and author of the R package mgcv.

Extending the Linear Model with R

Generalized Linear, Mixed Effects and Nonparametric Regression Models

Author: Julian J. Faraway

Publisher: CRC Press

ISBN: 9780203492284

Category: Mathematics

Page: 312

View: 6120

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Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the data described in the book is available at http://people.bath.ac.uk/jjf23/ELM/ Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught.

Probability and Statistics for Computer Scientists, Second Edition

Author: Michael Baron

Publisher: CRC Press

ISBN: 1498760600

Category: Mathematics

Page: 449

View: 2895

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Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling Tools Incorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make optimal decisions under uncertainty; model and evaluate computer systems and networks; and prepare for advanced probability-based courses. Written in a lively style with simple language, this classroom-tested book can now be used in both one- and two-semester courses. New to the Second Edition Axiomatic introduction of probability Expanded coverage of statistical inference, including standard errors of estimates and their estimation, inference about variances, chi-square tests for independence and goodness of fit, nonparametric statistics, and bootstrap More exercises at the end of each chapter Additional MATLAB® codes, particularly new commands of the Statistics Toolbox In-Depth yet Accessible Treatment of Computer Science-Related Topics Starting with the fundamentals of probability, the text takes students through topics heavily featured in modern computer science, computer engineering, software engineering, and associated fields, such as computer simulations, Monte Carlo methods, stochastic processes, Markov chains, queuing theory, statistical inference, and regression. It also meets the requirements of the Accreditation Board for Engineering and Technology (ABET). Encourages Practical Implementation of Skills Using simple MATLAB commands (easily translatable to other computer languages), the book provides short programs for implementing the methods of probability and statistics as well as for visualizing randomness, the behavior of random variables and stochastic processes, convergence results, and Monte Carlo simulations. Preliminary knowledge of MATLAB is not required. Along with numerous computer science applications and worked examples, the text presents interesting facts and paradoxical statements. Each chapter concludes with a short summary and many exercises.

Introduction to Probability

Author: Joseph K. Blitzstein,Jessica Hwang

Publisher: CRC Press

ISBN: 1498759769

Category: Mathematics

Page: 596

View: 6778

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Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Exercises and Solutions in Biostatistical Theory

Author: Lawrence Kupper,Brian Neelon,Sean M. O'Brien

Publisher: CRC Press

ISBN: 1439895023

Category: Mathematics

Page: 420

View: 3007

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Drawn from nearly four decades of Lawrence L. Kupper’s teaching experiences as a distinguished professor in the Department of Biostatistics at the University of North Carolina, Exercises and Solutions in Biostatistical Theory presents theoretical statistical concepts, numerous exercises, and detailed solutions that span topics from basic probability to statistical inference. The text links theoretical biostatistical principles to real-world situations, including some of the authors’ own biostatistical work that has addressed complicated design and analysis issues in the health sciences. This classroom-tested material is arranged sequentially starting with a chapter on basic probability theory, followed by chapters on univariate distribution theory and multivariate distribution theory. The last two chapters on statistical inference cover estimation theory and hypothesis testing theory. Each chapter begins with an in-depth introduction that summarizes the biostatistical principles needed to help solve the exercises. Exercises range in level of difficulty from fairly basic to more challenging (identified with asterisks). By working through the exercises and detailed solutions in this book, students will develop a deep understanding of the principles of biostatistical theory. The text shows how the biostatistical theory is effectively used to address important biostatistical issues in a variety of real-world settings. Mastering the theoretical biostatistical principles described in the book will prepare students for successful study of higher-level statistical theory and will help them become better biostatisticians.

Bayesian Data Analysis, Third Edition

Author: Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin

Publisher: CRC Press

ISBN: 1439840954

Category: Mathematics

Page: 675

View: 5210

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Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Bayesian Methods for Data Analysis, Third Edition

Author: Bradley P. Carlin,Thomas A. Louis

Publisher: CRC Press

ISBN: 9781584886983

Category: Mathematics

Page: 552

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Broadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo (MCMC) methods and related data analytic techniques. New to the Third Edition New data examples, corresponding R and WinBUGS code, and homework problems Explicit descriptions and illustrations of hierarchical modeling—now commonplace in Bayesian data analysis A new chapter on Bayesian design that emphasizes Bayesian clinical trials A completely revised and expanded section on ranking and histogram estimation A new case study on infectious disease modeling and the 1918 flu epidemic A solutions manual for qualifying instructors that contains solutions, computer code, and associated output for every homework problem—available both electronically and in print Ideal for Anyone Performing Statistical Analyses Focusing on applications from biostatistics, epidemiology, and medicine, this text builds on the popularity of its predecessors by making it suitable for even more practitioners and students.

Computer Age Statistical Inference

Algorithms, Evidence, and Data Science

Author: Bradley Efron,Trevor Hastie

Publisher: Cambridge University Press

ISBN: 1108107958

Category: Mathematics

Page: N.A

View: 3370

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The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.

Computer-Aided Multivariate Analysis, Fourth Edition

Author: Abdelmonem Afifi,Susanne May,Virginia A. Clark

Publisher: CRC Press

ISBN: 9781584883081

Category: Mathematics

Page: 512

View: 9679

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Computer-Aided Multivariate Analysis, Fourth Edition enables researchers and students with limited mathematical backgrounds to understand the concepts underlying multivariate statistical analysis, perform analysis using statistical packages, and understand the output. New topics include Loess and Poisson regression, nominal and ordinal logistic regression, interpretation of interactions in logistic and survival analysis, and imputation for missing values. This book includes new exercises and references, and updated options in the latest versions of the statistical packages. All data sets and codebooks are available for download. The authors explain the assumptions made in performing each analysis and test, how to determine if your data meets those assumptions, and what to do if they do not. What to Watch out for sections in each chapter warn of common difficulties. By reading this text, you will know what method to use with your data set, how to get the results, and how to interpret them and explain them to others. New in the Fourth Edition: Expanded explanation of checking for goodness of fit in logistic regression and survival analysis Kaplan-Meier estimates of survival curves, formal tests for comparing survival between groups, interactions and the use of time-dependent covariates in survival analysis Expanded discussion of how to handle missing values Latest features of the S-PLUS package in addition to SAS, SPSS, STATA, and STATISTICA for multivariate analysis Data sets for the problems are available at the CRC web site: http://www.crcpress.com/product/isbn/9781584883081 Commands and output for examples used in the text for each statistical package are available at the UCLA web site: http://www.ats.ucla.edu/stat/examples/cama4/

Statistics for Lawyers

Author: Michael O. Finkelstein,Bruce Levin

Publisher: Springer

ISBN: 1441959858

Category: Social Science

Page: 657

View: 8758

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This classic text, first published in 1990, is designed to introduce law students, law teachers, practitioners, and judges to the basic ideas of mathematical probability and statistics as they have been applied in the law. The third edition includes over twenty new sections, including the addition of timely topics, like New York City police stops, exonerations in death-sentence cases, projecting airline costs, and new material on various statistical techniques such as the randomized response survey technique, rare-events meta-analysis, competing risks, and negative binomial regression. The book consists of sections of exposition followed by real-world cases and case studies in which statistical data have played a role. The reader is asked to apply the theory to the facts, to calculate results (a hand calculator is sufficient), and to explore legal issues raised by quantitative findings. The authors' calculations and comments are given in the back of the book. As with previous editions, the cases and case studies reflect a broad variety of legal subjects, including antidiscrimination, mass torts, taxation, school finance, identification evidence, preventive detention, handwriting disputes, voting, environmental protection, antitrust, sampling for insurance audits, and the death penalty. A chapter on epidemiology was added in the second edition. In 1991, the first edition was selected by the University of Michigan Law Review as one of the important law books of the year.