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We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.

Bayesian statistical decision theory. --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Bayesian statistical decision theory --- Statistique bayésienne --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods

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Winner of the 2004 DeGroot Prize This paperback edition, a reprint of the 2001 edition, is a graduate-level textbook that introduces Bayesian statistics and decision theory. It covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, the Stein effect, Bayesian model choice, hierarchical and empirical Bayes modeling, Monte Carlo integration including Gibbs sampling, and other MCMC techniques. It was awarded the 2004 DeGroot Prize by the International Society for Bayesian Analysis (ISBA) for setting "a new standard for modern textbooks dealing with Bayesian methods, especially those using MCMC techniques, and that it is a worthy successor to DeGroot's and Berger's earlier texts". Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at the Université Paris Dauphine, and 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. In addition to many papers on Bayesian statistics, simulation methods, and decision theory, he has written four other books, including Monte Carlo Statistical Method (Springer 2004) with George Casella and Bayesian Core (Springer 2007) with Jean-Michel Marin. He has served or is serving as associate editor for the Annals of Statistics, Bayesian Analysis, the Journal of the American Statistical Association, Statistical Science, and Sankhya. and is editor of the Journal of the Royal Statistical Society (Series B) from 2006–2009. He is a fellow of the Institute of Mathematical Statistics, and received the 1995 Young Statistician Award of the Société de Statistique de Paris. Review of the second edition: "The text reads fluently and beautifully throughout, with light, good-humoured touches that warm the reader without being intrusive. There are many examples and exercises, some of which draw out the essence of work of other authors. Only a few displays and equations have numbers attached. This is an extremely fine, exceptional text of the highest quality." (ISI Short Book Reviews).

Bayesian statistical decision theory. --- Statistique bayésienne --- Bayesian statistical decision theory --- Méthode statistique --- Statistical methods --- Aide à la décision --- decision support --- Statistics --- Statistique bayésienne --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Statistics. --- Statistical decision. --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistique mathematique --- Methodes numeriques

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Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary progr

Monte Carlo method --- Bayesian statistical decision theory --- Markov processes --- Monte-Carlo, Méthode de --- Statistique bayésienne --- Markov, Processus de --- Monte Carlo method. --- Bayesian statistical decision theory. --- Markov processes. --- Simulatiemodellen. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Numerical analysis --- Numerical calculations --- Markov-processen. --- Monte Carlo-methode.

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This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. While R programs are provided on the book website and R hints are given in the computational sections of the book, The Bayesian Core requires no knowledge of the R language and it can be read and used with any other programming language. The Bayesian Core can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Université Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It serves as a unique textbook for a service course for scientists aiming at analyzing data the Bayesian way as well as an introductory course on Bayesian statistics. The prerequisites for the book are a basic knowledge of probability theory and of statistics. Methodological and data-based exercises are included within the main text and students are expected to solve them as they read the book. Those exercises can obviously serve as assignments, as was done in the above courses. Datasets, R codes and course slides all are available on the book website. Jean-Michel Marin is currently senior researcher at INRIA, the French Computer Science research institute, and located at Université Paris-Sud, Orsay. He has previously been Assistant Professor at Université Paris Dauphine for four years. He has written numerous papers on Bayesian methodology and computing, and is currently a member of the council of the French Statistical Society. Christian Robert is Professor of Statistics at Université Paris Dauphine and Head of the Statistics Research Laboratory at CREST-INSEE, Paris. He has written over a hundred papers on Bayesian Statistics and computational methods and is the author or co-author of seven books on those topics, including The Bayesian Choice (Springer, 2001), winner of the ISBA DeGroot Prize in 2004. He is a Fellow and member of the council of the Institute of Mathematical Statistics, and a Fellow and member of the research committee of the Royal Statistical Society. He is currently co-editor of the Journal of the Royal Statistical Society, Series B, after taking part in the editorial boards of the Journal of the American Statistical Society, the Annals of Statistics, Statistical Science, and Bayesian Analysis. He is also the winner of the Young Statistician prize of the Paris Statistical Society in 1996 and a recipient of an Erskine Fellowship from the University of Canterbury (NZ) in 2006.

Mathematics. --- Mathematical statistics. --- Computer simulation. --- Computer mathematics. --- Probabilities. --- Statistics. --- Computational intelligence. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Probability and Statistics in Computer Science. --- Simulation and Modeling. --- Computational Intelligence. --- Computational Mathematics and Numerical Analysis. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Math --- Science --- Bayesian statistical decision theory --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Distribution (Probability theory. --- Computer science. --- Engineering. --- Computer science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Construction --- Industrial arts --- Technology --- Informatics --- Statistics . --- regressie-analyse --- wiskundige statistiek --- R (Computer program language). --- Statistique bayésienne --- GNU-S (Computer program language) --- Domain-specific programming languages --- Bayesian statistical decision theory - Textbooks --- Statistique mathematique --- Methodes numeriques --- Programmes informatiques

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This book provides a compact self-contained introduction to the theory and application of Bayesian statistical methods. The book is accessible to readers having a basic familiarity with probability, yet allows more advanced readers to quickly grasp the principles underlying Bayesian theory and methods. The examples and computer code allow the reader to understand and implement basic Bayesian data analyses using standard statistical models and to extend the standard models to specialized data analysis situations. The book begins with fundamental notions such as probability, exchangeability and Bayes' rule, and ends with modern topics such as variable selection in regression, generalized linear mixed effects models, and semiparametric copula estimation. Numerous examples from the social, biological and physical sciences show how to implement these methodologies in practice. Monte Carlo summaries of posterior distributions play an important role in Bayesian data analysis. The open-source R statistical computing environment provides sufficient functionality to make Monte Carlo estimation very easy for a large number of statistical models and example R-code is provided throughout the text. Much of the example code can be run ``as is'' in R, and essentially all of it can be run after downloading the relevant datasets from the companion website for this book. Peter Hoff is an Associate Professor of Statistics and Biostatistics at the University of Washington. He has developed a variety of Bayesian methods for multivariate data, including covariance and copula estimation, cluster analysis, mixture modeling and social network analysis. He is on the editorial board of the Annals of Applied Statistics.

informatietechnologie --- methodologieën --- database management --- Information systems --- Social sciences (general) --- Operational research. Game theory --- statistisch onderzoek --- speltheorie --- econometrie --- operationeel onderzoek --- sociale wetenschappen --- Quantitative methods (economics) --- Statistical science --- stochastische analyse --- Distribution (Probability theory. --- Mathematical statistics. --- Social sciences --- Computer science. --- Econometrics. --- Methodology. --- Probability Theory and Stochastic Processes. --- Operations Research, Management Science. --- Statistical Theory and Methods. --- Methodology of the Social Sciences. --- Probability and Statistics in Computer Science. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Economics, Mathematical --- Informatics --- Science --- Statistical methods --- Bayesian statistical decision theory --- Data analysis --- Bayesian statistical decision theory. --- Statistical methods. --- Mathematical statistics --- Programming --- Probabilities. --- Operations research. --- Management science. --- Statistics . --- Social sciences. --- Behavioral sciences --- Human sciences --- Sciences, Social --- Social science --- Social studies --- Civilization --- Statistical analysis --- Statistical data --- Econometrics --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Probability --- Combinations --- Chance --- Least squares --- Risk --- Statistique bayésienne --- Social sciences - Statistical methods