Bayesian Theory

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Bayesian Theory

José M. Bernardo,Adrian F. M. Smith
Bayesian Theory Book PDF

Author : José M. Bernardo,Adrian F. M. Smith
Publisher : John Wiley & Sons
Page : 608 pages
File Size : 40,6 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

Mathematical Theory of Bayesian Statistics

Sumio Watanabe
Mathematical Theory of Bayesian Statistics Book PDF

Author : Sumio Watanabe
Publisher : CRC Press
Page : 331 pages
File Size : 46,5 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.

Statistical Decision Theory and Bayesian Analysis

James O. Berger
Statistical Decision Theory and Bayesian Analysis Book PDF

Author : James O. Berger
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 48,6 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.

The Theory That Would Not Die

Sharon Bertsch McGrayne
The Theory That Would Not Die Book PDF

Author : Sharon Bertsch McGrayne
Publisher : Yale University Press
Page : 336 pages
File Size : 49,5 Mb
Release : 2011-05-17
Category : Mathematics
ISBN : 9780300175097

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The Theory That Would Not Die by Sharon Bertsch McGrayne Pdf

"This account of how a once reviled theory, Baye’s rule, came to underpin modern life is both approachable and engrossing" (Sunday Times). A New York Times Book Review Editors’ Choice Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the generations-long human drama surrounding it. McGrayne traces the rule’s discovery by an 18th century amateur mathematician through its development by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—while practitioners relied on it to solve crises involving great uncertainty and scanty information, such as Alan Turing's work breaking Germany's Enigma code during World War II. McGrayne also explains how the advent of computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

Bayes Theory

J. A. Hartigan
Bayes Theory Book PDF

Author : J. A. Hartigan
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461382423

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Bayes Theory by J. A. Hartigan Pdf

This book is based on lectures given at Yale in 1971-1981 to students prepared with a course in measure-theoretic probability. It contains one technical innovation-probability distributions in which the total probability is infinite. Such improper distributions arise embarras singly frequently in Bayes theory, especially in establishing correspondences between Bayesian and Fisherian techniques. Infinite probabilities create interesting complications in defining conditional probability and limit concepts. The main results are theoretical, probabilistic conclusions derived from probabilistic assumptions. A useful theory requires rules for constructing and interpreting probabilities. Probabilities are computed from similarities, using a formalization of the idea that the future will probably be like the past. Probabilities are objectively derived from similarities, but similarities are sUbjective judgments of individuals. Of course the theorems remain true in any interpretation of probability that satisfies the formal axioms. My colleague David Potlard helped a lot, especially with Chapter 13. Dan Barry read proof. vii Contents CHAPTER 1 Theories of Probability 1. 0. Introduction 1 1. 1. Logical Theories: Laplace 1 1. 2. Logical Theories: Keynes and Jeffreys 2 1. 3. Empirical Theories: Von Mises 3 1. 4. Empirical Theories: Kolmogorov 5 1. 5. Empirical Theories: Falsifiable Models 5 1. 6. Subjective Theories: De Finetti 6 7 1. 7. Subjective Theories: Good 8 1. 8. All the Probabilities 10 1. 9. Infinite Axioms 11 1. 10. Probability and Similarity 1. 11. References 13 CHAPTER 2 Axioms 14 2. 0. Notation 14 2. 1. Probability Axioms 14 2. 2.

Bayesian Theory and Applications

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

Author : Paul Damien,Petros Dellaportas,Nicholas G. Polson,David A. Stephens
Publisher : Oxford University Press
Page : 717 pages
File Size : 42,5 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.

Bayesian Theory and Methods with Applications

Vladimir Savchuk,Chris P. Tsokos
Bayesian Theory and Methods with Applications Book PDF

Author : Vladimir Savchuk,Chris P. Tsokos
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 53,6 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.

Bayesian Data Analysis, Third Edition

Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin
Bayesian Data Analysis Third Edition Book PDF

Author : Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin
Publisher : CRC Press
Page : 677 pages
File Size : 53,9 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9781439840955

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Bayesian Data Analysis, Third Edition by Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin Pdf

Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Variational Bayesian Learning Theory

Shinichi Nakajima,Kazuho Watanabe,Masashi Sugiyama
Variational Bayesian Learning Theory Book PDF

Author : Shinichi Nakajima,Kazuho Watanabe,Masashi Sugiyama
Publisher : Cambridge University Press
Page : 561 pages
File Size : 49,7 Mb
Release : 2019-07-11
Category : Computers
ISBN : 9781107076150

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Variational Bayesian Learning Theory by Shinichi Nakajima,Kazuho Watanabe,Masashi Sugiyama Pdf

This introduction to the theory of variational Bayesian learning summarizes recent developments and suggests practical applications.

Bayesian Statistics the Fun Way

Will Kurt
Bayesian Statistics the Fun Way Book PDF

Author : Will Kurt
Publisher : No Starch Press
Page : 258 pages
File Size : 41,5 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.

An Introduction to Bayesian Analysis

Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta
An Introduction to Bayesian Analysis Book PDF

Author : Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 49,8 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.

Non-Bayesian Decision Theory

Martin Peterson
Non Bayesian Decision Theory Book PDF

Author : Martin Peterson
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 54,9 Mb
Release : 2008-06-06
Category : Science
ISBN : 9781402086991

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Non-Bayesian Decision Theory by Martin Peterson Pdf

For quite some time, philosophers, economists, and statisticians have endorsed a view on rational choice known as Bayesianism. The work on this book has grown out of a feeling that the Bayesian view has come to dominate the academic com- nitytosuchanextentthatalternative,non-Bayesianpositionsareseldomextensively researched. Needless to say, I think this is a pity. Non-Bayesian positions deserve to be examined with much greater care, and the present work is an attempt to defend what I believe to be a coherent and reasonably detailed non-Bayesian account of decision theory. The main thesis I defend can be summarised as follows. Rational agents m- imise subjective expected utility, but contrary to what is claimed by Bayesians, ut- ity and subjective probability should not be de?ned in terms of preferences over uncertain prospects. On the contrary, rational decision makers need only consider preferences over certain outcomes. It will be shown that utility and probability fu- tions derived in a non-Bayesian manner can be used for generating preferences over uncertain prospects, that support the principle of maximising subjective expected utility. To some extent, this non-Bayesian view gives an account of what modern - cision theory could have been like, had decision theorists not entered the Bayesian path discovered by Ramsey, de Finetti, Savage, and others. I will not discuss all previous non-Bayesian positions presented in the literature.

Bayesian Probability Theory

Wolfgang von der Linden,Volker Dose,Udo von Toussaint
Bayesian Probability Theory Book PDF

Author : Wolfgang von der Linden,Volker Dose,Udo von Toussaint
Publisher : Cambridge University Press
Page : 653 pages
File Size : 41,8 Mb
Release : 2014-06-12
Category : Mathematics
ISBN : 9781107035904

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Bayesian Probability Theory by Wolfgang von der Linden,Volker Dose,Udo von Toussaint Pdf

Covering all aspects of probability theory, statistics and data analysis from a Bayesian perspective for graduate students and researchers.

Practice of Bayesian Probability Theory in Geotechnical Engineering

Wan-Huan Zhou,Zhen-Yu Yin,Ka-Veng Yuen
Practice of Bayesian Probability Theory in Geotechnical Engineering Book PDF

Author : Wan-Huan Zhou,Zhen-Yu Yin,Ka-Veng Yuen
Publisher : Springer Nature
Page : 324 pages
File Size : 40,6 Mb
Release : 2020-11-13
Category : Science
ISBN : 9789811591051

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Practice of Bayesian Probability Theory in Geotechnical Engineering by Wan-Huan Zhou,Zhen-Yu Yin,Ka-Veng Yuen Pdf

This book introduces systematically the application of Bayesian probabilistic approach in soil mechanics and geotechnical engineering. Four typical problems are analyzed by using Bayesian probabilistic approach, i.e., to model the effect of initial void ratio on the soil–water characteristic curve (SWCC) of unsaturated soil, to select the optimal model for the prediction of the creep behavior of soft soil under one-dimensional straining, to identify model parameters of soils and to select constitutive model of soils considering critical state concept. This book selects the simple and easy-to-understand Bayesian probabilistic algorithm, so that readers can master the Bayesian method to analyze and solve the problem in a short time. In addition, this book provides MATLAB codes for various algorithms and source codes for constitutive models so that readers can directly analyze and practice. This book is useful as a postgraduate textbook for civil engineering, hydraulic engineering, transportation, railway, engineering geology and other majors in colleges and universities, and as an elective course for senior undergraduates. It is also useful as a reference for relevant professional scientific researchers and engineers.

Bayes Or Bust?

John Earman
Bayes Or Bust Book PDF

Author : John Earman
Publisher : Bradford Books
Page : 272 pages
File Size : 49,7 Mb
Release : 1992
Category : Psychology
ISBN : 0262050463

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Bayes Or Bust? by John Earman Pdf

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh.