This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated. An entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. The book is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses." E.L. Lehmann is Professor 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. George Casella is the Liberty Hyde Bailey Professor of Biological Statistics in The College of Agriculture and Life Sciences at Cornell University. Casella has served as associate editor of The American Statistician, Statistical Science and JASA. He is currently the Theory and Methods Editor of JASA. Casella has authored two other textbooks (Statistical Inference, 1990, with Roger Berger and Variance Components, 1992, with Shayle A. Searle and Charles McCulloch). He is a fellow of the IMS and ASA, and an elected fellow of the ISI. Also available: E.L. Lehmann, Testing Statistical Hypotheses Second Edition, Springer-Verlag New York, Inc., ISBN 0-387-949194.

Statistical design is one of the fundamentals of our subject, being at the core of the growth of statistics during the previous century. In this book the basic theoretical underpinnings are covered. It describes the principles that drive good designs and good statistics.

Design played a key role in agricultural statistics and set down principles of good practice, principles that still apply today. Statistical design is all about understanding where the variance comes from, and making sure that is where the replication is. Indeed, it is probably correct to say that these principles are even more important today.

This book introduces the basic concepts and methods that are useful in the statistical analysis and modeling of the DNA-based marker and phenotypic data that arise in agriculture, forestry, experimental biology, and other fields. It concentrates on the linkage analysis of markers, map construction and quantitative trait locus (QTL) mapping, and assumes a background in regression analysis and maximum likelihood approaches. The strength of this book lies in the construction of general models and algorithms for linkage analysis, as well as in QTL mapping in any kind of crossed pedigrees initiated with inbred lines of crops.

Although statistical design is one of the oldest branches of statistics, its importance is ever increasing, especially in the face of the data flood that often faces statisticians. It is important to recognize the appropriate design, and to understand how to effectively implement it, being aware that the default settings from a computer package can easily provide an incorrect analysis. The goal of this book is to describe the principles that drive good design, paying attention to both the theoretical background and the problems arising from real experimental situations. Designs are motivated through actual experiments, ranging from the timeless agricultural randomized complete block, to microarray experiments, which naturally lead to split plot designs and balanced incomplete blocks.

This book introduces the basic concepts and methods that are useful in the statistical analysis and modeling of the DNA-based marker and phenotypic data that arise in agriculture, forestry, experimental biology, and other fields. It concentrates on the linkage analysis of markers, map construction and quantitative trait locus (QTL) mapping, and assumes a background in regression analysis and maximum likelihood approaches. The strength of this book lies in the construction of general models and algorithms for linkage analysis, as well as in QTL mapping in any kind of crossed pedigrees initiated with inbred lines of crops.

Monte Carlo statistical methods, particularly those based on Markov chains, are now an essential component of the standard set of techniques used by statisticians. This new edition has been revised towards a coherent and flowing coverage of these simulation techniques, with incorporation of the most recent developments in the field. In particular, the introductory coverage of random variable generation has been totally revised, with many concepts being unified through a fundamental theorem of simulation

There are five completely new chapters that cover Monte Carlo control, reversible jump, slice sampling, sequential Monte Carlo, and perfect sampling. There is a more in-depth coverage of Gibbs sampling, which is now contained in three consecutive chapters. The development of Gibbs sampling starts with slice sampling and its connection with the fundamental theorem of simulation, and builds up to two-stage Gibbs sampling and its theoretical properties. A third chapter covers the multi-stage Gibbs sampler and its variety of applications. Lastly, chapters from the previous edition have been revised towards easier access, with the examples getting more detailed coverage.

This textbook is intended for a second year graduate course, but will also be useful to someone who either wants to apply simulation techniques for the resolution of practical problems or wishes to grasp the fundamental principles behind those methods. The authors do not assume familiarity with Monte Carlo techniques (such as random variable generation), with computer programming, or with any Markov chain theory (the necessary concepts are developed in Chapter 6). A solutions manual, which coversapproximately 40% of the problems, is available for instructors who require the book for a course.

Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at UniversitA(c) Paris Dauphine, France. He is also Head of the Statistics Laboratory at the Center for Research in Economics and Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris, and Adjunct Professor at Ecole Polytechnique. He has written three other books, including The Bayesian Choice, Second Edition, Springer 2001. He also edited Discretization and MCMC Convergence Assessment, Springer 1998. He has served as associate editor for the Annals of Statistics and the Journal of the American Statistical Association. He is a fellow of the Institute of Mathematical Statistics, and a winner of the Young Statistician Award of the SocietiA(c) de Statistique de Paris in 1995.

George Casella is Distinguished Professor and Chair, Department of Statistics, University of Florida. He has served as the Theory and Methods Editor of the Journal of the American Statistical Association and Executive Editor of Statistical Science. He has authored three other textbooks: Statistical Inference, Second Edition, 2001, with Roger L. Berger; Theory of Point Estimation, 1998, with Erich Lehmann; and Variance Components, 1992, with Shayle R. Searle and Charles E. McCulloch. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association, and an elected fellow of the International Statistical Institute.

This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated. An entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. The book is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses". E.L. Lehmann is Professor 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. George Casella is the Liberty Hyde Bailey Professor of Biological Statistics in The College of Agriculture and Life Sciences at Cornell University. Casella has served as associate editor of The American Statistician, Statistical Science and JASA. He is currently the Theory and Methods Editor of JASA. Casella has authored two other textbooks (Statistical Inference, 1990, with Roger Berger and Variance Components, 1992, with Shayle A. Searle and Charles McCulloch). He is a fellow of the IMS and ASA, and an elected fellow of the ISI. Also available: E.L. Lehmann, Testing Statistical Hypotheses Second Edition, Springer-Verlag New York, Inc., ISBN 0-387-949194.

We have sold 4300 copies worldwide of the first edition (1999).

This new edition contains five completely new chapters covering new developments.

Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those methods, and there is no better way to develop intuition and skills for simulation than to use simulation to solve statistical problems. Introducing Monte Carlo Methods with R covers the main tools used in statistical simulation from a programmer's point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison. While this book constitutes a comprehensive treatment of simulation methods, the theoretical justification of those methods has been considerably reduced, compared with Robert and Casella (2004). Similarly, the more exploratory and less stable solutions are not covered here.

This book does not require a preliminary exposure to the R programming language or to Monte Carlo methods, nor an advanced mathematical background. While many examples are set within a Bayesian framework, advanced expertise in Bayesian statistics is not required. The book covers basic random generation algorithms, Monte Carlo techniques for integration and optimization, convergence diagnoses, Markov chain Monte Carlo methods, including Metropolis {Hastings and Gibbs algorithms, and adaptive algorithms. All chapters include exercises and all R programs are available as an R package called mcsm. The book appeals to anyone with a practical interest in simulation methods but no previous exposure. It is meant to be useful for students and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The programming parts are introduced progressively to be accessible to any reader.