Bücher der Reihe Springer Texts in Statistics

Suitable 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

Time Series Analysis and Its Applications, presents a comprehensive treatment of both time and frequency domain methods with accompanying theory. Extensive examples illustrate solutions to climate change, monitoring a nuclear test ban treaty, evaluating the volatility of an asset, and more.

Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability¿keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information¿scientific evidence¿ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.This book would be relevant to students, practitioners, and applied statisticiansinterested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.This book is Open Access.

Elements of Large-Sample Theory provides a unified treatment of first- order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level and is suitable for students at the master's level in statistics and in aplied fields who have a background of two years of calculus.E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: Lehmann/Casella, Theory at Point Estimation, 2nd ed. Springer-Verlag New York, Inc., 1998, ISBN 0- 387-98502-6Lehmann, Testing Statistical Hypotheses, 2nd ed. Springer-Verlag New York, Inc., 1997, ISBN 0-387-94919-4

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.

My goal in writing this book has been to provide teachers and students of multi­ variate statistics with a unified treatment ofboth theoretical and practical aspects of this fascinating area. The text is designed for a broad readership, including advanced undergraduate students and graduate students in statistics, graduate students in bi­ ology, anthropology, life sciences, and other areas, and postgraduate students. The style of this book reflects my beliefthat the common distinction between multivariate statistical theory and multivariate methods is artificial and should be abandoned. I hope that readers who are mostly interested in practical applications will find the theory accessible and interesting. Similarly I hope to show to more mathematically interested students that multivariate statistical modelling is much more than applying formulas to data sets. The text covers mostly parametric models, but gives brief introductions to computer-intensive methods such as the bootstrap and randomization tests as well. The selection of material reflects my own preferences and views. My principle in writing this text has been to restrict the presentation to relatively few topics, but cover these in detail. This should allow the student to study an area deeply enough to feel comfortable with it, and to start reading more advanced books or articles on the same topic.

Most data sets collected by researchers are multivariate, and in the majority of cases the variables need to be examined simultaneously to get the most informative results. This requires the use of one or other of the many methods of multivariate analysis, and the use of a suitable software package such as S-PLUS or R.In this book the core multivariate methodology is covered along with some basic theory for each method described. The necessary R and S-PLUS code is given for each analysis in the book, with any differences between the two highlighted. Graduate students, and advanced undergraduates on applied statistics courses, especially those in the social sciences, will find this book invaluable in their work, and it will also be useful to researchers outside of statistics who need to deal with the complexities of multivariate data in their work. From the reviews:"This text is much more than just an R/S programming guide. Brian Everitt's expertise in multivariate data analysis shines through brilliantly." Journal of the American Statistical Association, June 2006

I have endeavored to provide a comprehensive introduction to a wide - riety of statistical methods for the analysis of repeated measurements. I envision this book primarily as a textbook, because the notes on which it is based have been used in a semester-length graduate course I have taught since1991.Thiscourseisprimarilytakenbygraduatestudentsinbiostat- tics and statistics, although students and faculty from other departments have audited the course. I also anticipate that the book will be a useful r- erence for practicing statisticians. This assessment is based on the positive responses I have received to numerous short courses I have taught on this topic to academic and industry groups. Althoughmyintentistoprovideareasonablycomprehensiveoverviewof methodsfortheanalysisofrepeatedmeasurements,Idonotviewthisbook as a de?nitive "e;state of the art"e; compendium of research in this area. Some general approaches are extremely active areas of current research, and it is not feasible, given the goals of this book, to include a comprehensive summary and list of references. Instead, my focus is primarily on methods that are implemented in standard statistical software packages. As a result, thelevelofdetailonsometopicsislessthaninotherbooks,andsomemore recent methods of analysis are not included. One particular example is the topic of nonlinear mixed models for the analysis of repeated measurements (Davidian and Giltinan, 1995; Vonesh and Chinchilli, 1996). With respect to some of the more recent methods of analysis, I do attempt to mention some of the areas of current research.

Though there are many recent additions to graduate-level introductory books on Bayesian analysis, none has quite our blend of theory, methods, and ap­ plications. We believe a beginning graduate student taking a Bayesian course or just trying to find out what it means to be a Bayesian ought to have some familiarity with all three aspects. More specialization can come later. Each of us has taught a course like this at Indian Statistical Institute or Purdue. In fact, at least partly, the book grew out of those courses. We would also like to refer to the review (Ghosh and Samanta (2002b)) that first made us think of writing a book. The book contains somewhat more material than can be covered in a single semester. We have done this intentionally, so that an instructor has some choice as to what to cover as well as which of the three aspects to emphasize. Such a choice is essential for the instructor. The topics include several results or methods that have not appeared in a graduate text before. In fact, the book can be used also as a second course in Bayesian analysis if the instructor supplies more details. Chapter 1 provides a quick review of classical statistical inference. Some knowledge of this is assumed when we compare different paradigms. Following this, an introduction to Bayesian inference is given in Chapter 2 emphasizing the need for the Bayesian approach to statistics.

Categorical data arise often in many fields, including biometrics, economics, management, manufacturing, marketing, psychology, and sociology. This book provides an introduction to the analysis of such data. The coverage is broad, using the loglinear Poisson regression model and logistic binomial regression models as the primary engines for methodology. Topics covered include count regression models, such as Poisson, negative binomial, zero-inflated, and zero-truncated models; loglinear models for two-dimensional and multidimensional contingency tables, including for square tables and tables with ordered categories; and regression models for two-category (binary) and multiple-category target variables, such as logistic and proportional odds models.All methods are illustrated with analyses of real data examples, many from recent subject area journal articles. These analyses are highlighted in the text, and are more detailed than is typical, providing discussion of the context and background of the problem, model checking, and scientific implications. More than 200 exercises are provided, many also based on recent subject area literature. Data sets and computer code are available at a web site devoted to the text. Adopters of this book may request a solutions manual from: textbooks@springer-ny.com. Jeffrey S. Simonoff is Professor of Statistics at New York University. He is author of Smoothing Methods in Statistics and coauthor of A Casebook for a First Course in Statistics and Data Analysis, as well as numerous articles in scholarly journals. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute.

Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.

Applying Generalized Linear Models describes how generalized linear modelling procedures can be used for statistical modelling in many different fields, without becoming lost in problems of statistical inference. Many students, even in relatively advanced statistics courses, do not have an overview whereby they can see that the three areas - linear normal, categorical, and survival models - have much in common. The author shows the unity of many of the commonly used models and provides the reader with a taste of many different areas, such as survival models, time series, and spatial analysis. This book should appeal to applied statisticians and to scientists with a basic grounding in modern statistics. With the many exercises included at the ends of chapters, it will be an excellent text for teaching the fundamental uses of statistical modelling. The reader is assumed to have knowledge of basic statistical principles, whether from a Bayesian, frequentist, or direct likelihood point of view, and should be familiar at least with the analysis of the simpler normal linear models, regression and ANOVA. The author is professor in the biostatistics department at Limburgs University, Diepenbeek, in the social science department at the University of Liege, and in medical statistics at DeMontfort University, Leicester. He is the author of nine other books.

Our initial motivation for writing this book was the observation from various students that the subject of design and analysis of experiments can seem like "e;a bunch of miscellaneous topics. "e;Webelievethattheidenti?cationoftheobjectivesoftheexperimentandthepractical considerations governing the design form the heart of the subject matter and serve as the link between the various analytical techniques. We also believe that learning about design and analysis of experiments is best achieved by the planning, running, and analyzing of a simple experiment. With these considerations in mind, we have included throughout the book the details of the planning stage of several experiments that were run in the course of teaching our classes. The experiments were run by students in statistics and the applied sciences and are suf?ciently simple that it is possible to discuss the planning of the entire experiment in a few pages, and the procedures can be reproduced by readers of the book. In each of these experiments, we had access to the investigators' actual report, including the dif?culties they came across and how they decided on the treatment factors, the needed number of observations, and the layout of the design. In the later chapters, we have included details of a number of published experiments. The outlines of many other student and published experiments appear as exercises at the ends of the chapters. Complementing the practical aspects of the design are the statistical aspects of the anal ysis. We have developed the theory of estimable functions and analysis of variance with somecare,butatalowmathematicallevel.

Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.

As the new title indicates, this second edition of Log-Linear Models has been modi?ed to place greater emphasis on logistic regression. In addition to new material, the book has been radically rearranged. The fundamental material is contained in Chapters 1-4. Intermediate topics are presented in Chapters 5 through 8. Generalized linear models are presented in Ch- ter 9. The matrix approach to log-linear models and logistic regression is presented in Chapters 10-12, with Chapters 10 and 11 at the applied Ph.D. level and Chapter 12 doing theory at the Ph.D. level. The largest single addition to the book is Chapter 13 on Bayesian bi- mial regression. This chapter includes not only logistic regression but also probit and complementary log-log regression. With the simplicity of the Bayesian approach and the ability to do (almost) exact small sample s- tistical inference, I personally ?nd it hard to justify doing traditional large sample inferences. (Another possibility is to do exact conditional inference, but that is another story.) Naturally,Ihavecleaneduptheminor?awsinthetextthatIhavefound. All examples, theorems, proofs, lemmas, etc. are numbered consecutively within each section with no distinctions between them, thus Example 2.3.1 willcomebeforeProposition2.3.2.Exercisesthatdonotappearinasection at the end have a separate numbering scheme. Within the section in which it appears, an equation is numbered with a single value, e.g., equation (1).

This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance.This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.