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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.

Machine learning. --- Mathematical statistics. --- Probabilities. --- Stochastic processes. --- Probabilities --- Stochastic processes --- Mathematical statistics --- Machine learning --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Statistics. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Probability --- Statistical inference --- Computer simulation. --- Bioinformatics. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Simulation and Modeling. --- Econometrics --- Combinations --- Chance --- Least squares --- Risk --- Distribution (Probability theory. --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Data processing --- Statistics .

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This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics. It can be used as a graduate text, as a versatile research reference, as a source for independent reading on a wide assembly of topics, and as a window to learning the latest developments in contemporary topics. The book is unique in its detailed coverage of fundamental topics such as central limit theorems in numerous setups, likelihood based methods, goodness of fit, higher order asymptotics, as well as of the most modern topics such as the bootstrap, dependent data, Bayesian asymptotics, nonparametric density estimation, mixture models, and multiple testing and false discovery. It provides extensive bibliographic references on all topics that include very recent publications. Anirban DasGupta is Professor of Statistics at Purdue University. He has also taught at the Wharton School of the University of Pennsylvania, at Cornell University, and at the University of California at San Diego. He has been on the editorial board of the Annals of Statistics since 1998 and has also served on the editorial boards of the Journal of the American Statistical Association, International Statistical Review, and the Journal of Statistical Planning and Inference. He has edited two monographs in the lecture notes monograph series of the Institute of Mathematical Statistics, is a Fellow of the Institute of Mathematical Statistics and has 70 refereed publications on theoretical statistics and probability in major journals.

Mathematical statistics -- Asymptotic theory. --- Mathematical statistics --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Asymptotic theory --- Asymptotic theory. --- Mathematics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Asymptotic expansions --- Distribution (Probability theory. --- Mathematical statistics. --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Risk

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Statistical science --- statistisch onderzoek

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This is a text encompassing all of the standard topics in introductory probability theory, together with a significant amount of optional material of emerging importance. The emphasis is on a lucid and accessible writing style, mixed with a large number of interesting examples of a diverse nature. The text will prepare students extremely well for courses in more advanced probability and in statistical theory and for the actuary exam. The book covers combinatorial probability, all the standard univariate discrete and continuous distributions, joint and conditional distributions in the bivariate and the multivariate case, the bivariate normal distribution, moment generating functions, various probability inequalities, the central limit theorem and the laws of large numbers, and the distribution theory of order statistics. In addition, the book gives a complete and accessible treatment of finite Markov chains, and a treatment of modern urn models and statistical genetics. It includes 303 worked out examples and 810 exercises, including a large compendium of supplementary exercises for exam preparation and additional homework. Each chapter has a detailed chapter summary. The appendix includes the important formulas for the distributions in common use and important formulas from calculus, algebra, trigonometry, and geometry. Anirban DasGupta is Professor of Statistics at Purdue University, USA. He has been the main editor of the Lecture Notes and Monographs series, as well as the Collections series of the Institute of Mathematical Statistics, and is currently the Co-editor of the Selected Works in Statistics and Probability series, published by Springer. He has been an associate editor of the Annals of Statistics, Journal of the American Statistical Association, Journal of Statistical Planning and Inference, International Statistical Review, Sankhya, and Metrika. He is the author of Asymptotic Theory of Statistics and Probability, 2008, and of 70 refereed articles on probability and statistics. He is a Fellow of the Institute of Mathematical Statistics.

Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- kansrekening

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This book contains a little more than 20 of Debabrata Basu's  most significant articles and writings. Debabrata Basu is internationally  known for his highly influential and fundamental contributions  to the foundations of statistics, survey sampling, sufficiency,  and invariance. The major theorem bearing his name has had numerous  applications to statistics and probability. The articles in this volume  are reprints of the original articles, in a chronological order. The  book also contains eleven commentaries written by some of the most  distinguished scholars in the area of foundations and statistical  inference. These commentaries are by George Casella and V. Gopal,  Phil Dawid, Tom DiCiccio and Alastair Young, Malay Ghosh, Jay kadane,  Glen Meeden, Robert Serfling, Jayaram Sethuraman, Terry Speed, and  Alan Welsh.

Mathematical statistics -- Study and teaching (Elementary). --- Probabilities -- Study and teaching (Elementary). --- Statistics -- Study and teaching (Elementary). --- Mathematical statistics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Statistical inference --- Statistics, Mathematical --- Statistical methods --- Statistics. --- Statistical Theory and Methods. --- Mathematical statistics. --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics . --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Basu, D. --- Dev Basu --- Basu, Dev --- Basu, Debabrata, --- Basu, D - (Dev)