Mathematical Theory Of Bayesian Statistics

Author : Sumio Watanabe
Publisher : CRC Press
Page : 331 pages
File Size : 44,8 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781482238082

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Mathematical Theory of Bayesian Statistics by Sumio Watanabe Pdf

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

Author : Sumio Watanabe
Publisher : CRC Press
Page : 229 pages
File Size : 48,6 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781315355696

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Mathematical Theory of Bayesian Statistics by Sumio Watanabe Pdf

Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

Author : José M. Bernardo,Adrian F. M. Smith
Publisher : John Wiley & Sons
Page : 608 pages
File Size : 42,9 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317716

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Bayesian Theory by José M. Bernardo,Adrian F. M. Smith Pdf

This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics

Author : D. V. Lindley
Publisher : SIAM
Page : 100 pages
File Size : 43,8 Mb
Release : 1972-01-31
Category : Mathematics
ISBN : 0898710022

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Bayesian Statistics, A Review by D. V. Lindley Pdf

A study of those statistical ideas that use a probability distribution over parameter space. The first part describes the axiomatic basis in the concept of coherence and the implications of this for sampling theory statistics. The second part discusses the use of Bayesian ideas in many branches of statistics.

Author : Paul Damien,Petros Dellaportas,Nicholas G. Polson,David A. Stephens
Publisher : Oxford University Press
Page : 717 pages
File Size : 43,5 Mb
Release : 2013-01-24
Category : Mathematics
ISBN : 9780199695607

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Bayesian Theory and Applications by Paul Damien,Petros Dellaportas,Nicholas G. Polson,David A. Stephens Pdf

This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field.

Author : Anonim
Publisher : Academic Press
Page : 322 pages
File Size : 40,6 Mb
Release : 2022-10-06
Category : Mathematics
ISBN : 9780323952699

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Advancements in Bayesian Methods and Implementations by Anonim Pdf

Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Advancements in Bayesian Methods and Implementation

Author : James O. Berger
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 44,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475742862

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Statistical Decision Theory and Bayesian Analysis by James O. Berger Pdf

In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.

Author : Will Kurt
Publisher : No Starch Press
Page : 258 pages
File Size : 51,8 Mb
Release : 2019-07-09
Category : Mathematics
ISBN : 9781593279561

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Bayesian Statistics the Fun Way by Will Kurt Pdf

Fun guide to learning Bayesian statistics and probability through unusual and illustrative examples. Probability and statistics are increasingly important in a huge range of professions. But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that. This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples. By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to: - How to measure your own level of uncertainty in a conclusion or belief - Calculate Bayes theorem and understand what it's useful for - Find the posterior, likelihood, and prior to check the accuracy of your conclusions - Calculate distributions to see the range of your data - Compare hypotheses and draw reliable conclusions from them Next time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.

Author : Ben Lambert
Publisher : SAGE
Page : 744 pages
File Size : 47,9 Mb
Release : 2018-04-20
Category : Social Science
ISBN : 9781526418265

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A Student’s Guide to Bayesian Statistics by Ben Lambert Pdf

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes′ rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.

Author : William M. Bolstad,James M. Curran
Publisher : John Wiley & Sons
Page : 805 pages
File Size : 55,6 Mb
Release : 2016-09-02
Category : Mathematics
ISBN : 9781118593226

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Introduction to Bayesian Statistics by William M. Bolstad,James M. Curran Pdf

"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.

Author : Krzysztof Burdzy
Publisher : World Scientific
Page : 270 pages
File Size : 40,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814273718

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The Search for Certainty by Krzysztof Burdzy Pdf

This volume represents a radical departure from the current philosophical duopoly in the area of foundations of probability, that is, the frequency and subjective theories. One of the main new ideas is a set of scientific laws of probability. The new laws are simple, intuitive and, last but not least, they agree well with the contents of current textbooks on probability. Another major new claim is that the OC frequency statisticsOCO has nothing in common with the OC frequency philosophy of probability, OCO contrary to popular belief. Similarly, contrary to the general perception, the OC Bayesian statisticsOCO shares nothing in common with the OC subjective philosophy of probability.OCO The book is non-partisan on the scientific side OCo it is supportive of both frequency statistics and Bayesian statistics. On the other hand, it contains well-documented and thoroughly-explained criticisms of the frequency and subjective philosophies of probability. Short reviews of other philosophical theories of probability and basic mathematical methods of probability and statistics are incorporated. The book includes substantial chapters on decision theory and teaching probability, and it is easily accessible to the general audience

Author : Vladimir Savchuk,Chris P. Tsokos
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 51,9 Mb
Release : 2011-09-01
Category : Mathematics
ISBN : 9789491216145

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Bayesian Theory and Methods with Applications by Vladimir Savchuk,Chris P. Tsokos Pdf

Bayesian methods are growing more and more popular, finding new practical applications in the fields of health sciences, engineering, environmental sciences, business and economics and social sciences, among others. This book explores the use of Bayesian analysis in the statistical estimation of the unknown phenomenon of interest. The contents demonstrate that where such methods are applicable, they offer the best possible estimate of the unknown. Beyond presenting Bayesian theory and methods of analysis, the text is illustrated with a variety of applications to real world problems.

Author : Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 51,5 Mb
Release : 2007-07-03
Category : Mathematics
ISBN : 9780387354330

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An Introduction to Bayesian Analysis by Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta Pdf

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,6 Mb
Release : 2024-06-16
Category : Electronic
ISBN : 9789814467834

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The Search for Certainty by Anonim Pdf

Author : Glenn Shafer
Publisher : Princeton University Press
Page : 128 pages
File Size : 46,7 Mb
Release : 2020-06-30
Category : Mathematics
ISBN : 9780691214696

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A Mathematical Theory of Evidence by Glenn Shafer Pdf

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.