Subjective And Objective Bayesian Statistics
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Subjective And Objective Bayesian Statistics
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Author : S. James Press
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Subjective And Objective Bayesian Statistics written by S. James Press and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.
Ein Wiley-Klassiker über Bayes-Statistik, jetzt in durchgesehener und erweiterter Neuauflage! - Werk spiegelt die stürmische Entwicklung dieses Gebietes innerhalb der letzten Jahre wider - vollständige Darstellung der theoretischen Grundlagen - jetzt ergänzt durch unzählige Anwendungsbeispiele - die wichtigsten modernen Methoden (u. a. hierarchische Modellierung, linear-dynamische Modellierung, Metaanalyse, MCMC-Simulationen) - einzigartige Diskussion der Finetti-Transformierten und anderer Themen, über die man ansonsten nur spärliche Informationen findet - Lösungen zu den Übungsaufgaben sind enthalten
Objective Bayesian Inference
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Author : James O Berger
language : en
Publisher: World Scientific
Release Date : 2024-03-06
Objective Bayesian Inference written by James O Berger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-06 with Mathematics categories.
Bayesian analysis is today understood to be an extremely powerful method of statistical analysis, as well an approach to statistics that is particularly transparent and intuitive. It is thus being extensively and increasingly utilized in virtually every area of science and society that involves analysis of data.A widespread misconception is that Bayesian analysis is a more subjective theory of statistical inference than what is now called classical statistics. This is true neither historically nor in practice. Indeed, objective Bayesian analysis dominated the statistical landscape from roughly 1780 to 1930, long before 'classical' statistics or subjective Bayesian analysis were developed. It has been a subject of intense interest to a multitude of statisticians, mathematicians, philosophers, and scientists. The book, while primarily focusing on the latest and most prominent objective Bayesian methodology, does present much of this fascinating history.The book is written for four different audiences. First, it provides an introduction to objective Bayesian inference for non-statisticians; no previous exposure to Bayesian analysis is needed. Second, the book provides an overview of the development and current state of objective Bayesian analysis and its relationship to other statistical approaches, for those with interest in the philosophy of learning from data. Third, the book presents a careful development of the particular objective Bayesian approach that we recommend, the reference prior approach. Finally, the book presents as much practical objective Bayesian methodology as possible for statisticians and scientists primarily interested in practical applications.
An Introduction To Bayesian Analysis
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Author : Jayanta K. Ghosh
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-03
An Introduction To Bayesian Analysis written by Jayanta K. Ghosh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-03 with Mathematics categories.
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.
The Subjectivity Of Scientists And The Bayesian Approach
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Author : S. James Press
language : en
Publisher: Courier Dover Publications
Release Date : 2016-03-16
The Subjectivity Of Scientists And The Bayesian Approach written by S. James Press and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-16 with Mathematics categories.
Originally published: New York: John Wiley & Sons, Inc., 2001.
Bayesian Statistics
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Author : S. James Press
language : en
Publisher:
Release Date : 1989-05-10
Bayesian Statistics written by S. James Press and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-10 with Mathematics categories.
An introduction to Bayesian statistics, with emphasis on interpretation of theory, and application of Bayesian ideas to practical problems. First part covers basic issues and principles, such as subjective probability, Bayesian inference and decision making, the likelihood principle, predictivism, and numerical methods of approximating posterior distributions, and includes a listing of Bayesian computer programs. Second part is devoted to models and applications, including univariate and multivariate regression models, the general linear model, Bayesian classification and discrimination, and a case study of how disputed authorship of some of the Federalist Papers was resolved via Bayesian analysis. Includes biographical material on Thomas Bayes, and a reproduction of Bayes's original essay. Contains exercises.
In Defence Of Objective Bayesianism
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Author : Jon Williamson
language : en
Publisher: Oxford University Press
Release Date : 2010-05-13
In Defence Of Objective Bayesianism written by Jon Williamson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-13 with Computers categories.
Objective Bayesianism is a methodological theory that is currently applied in statistics, philosophy, artificial intelligence, physics and other sciences. This book develops the formal and philosophical foundations of the theory, at a level accessible to a graduate student with some familiarity with mathematical notation.
A Bayesian Model For Resolving Differences Between Subjective Views And Objective Data
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Author :
language : en
Publisher:
Release Date : 1981
A Bayesian Model For Resolving Differences Between Subjective Views And Objective Data written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Bayesian statistical decision theory categories.
Bayesian Thinking Modeling And Computation
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Author :
language : en
Publisher: Elsevier
Release Date : 2005-11-29
Bayesian Thinking Modeling And Computation written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-29 with Mathematics categories.
This volume describes how to develop Bayesian thinking, modelling and computation both from philosophical, methodological and application point of view. It further describes parametric and nonparametric Bayesian methods for modelling and how to use modern computational methods to summarize inferences using simulation. The book covers wide range of topics including objective and subjective Bayesian inferences with a variety of applications in modelling categorical, survival, spatial, spatiotemporal, Epidemiological, software reliability, small area and micro array data. The book concludes with a chapter on how to teach Bayesian thoughts to nonstatisticians. Critical thinking on causal effects Objective Bayesian philosophy Nonparametric Bayesian methodology Simulation based computing techniques Bioinformatics and Biostatistics
Bayesian Philosophy Of Science
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Author : Jan Sprenger
language : en
Publisher: Oxford University Press
Release Date : 2019-08-23
Bayesian Philosophy Of Science written by Jan Sprenger and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Philosophy categories.
How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners.
Objective Bayesian Analysis Of The 2 X 2 Contingency Table And The Negative Binomial Distribution
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Author : John Christian Snyder
language : en
Publisher:
Release Date : 2018
Objective Bayesian Analysis Of The 2 X 2 Contingency Table And The Negative Binomial Distribution written by John Christian Snyder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
In Bayesian analysis, the "objective" Bayesian approach seeks to select a prior distribution not by using (often subjective) scientific belief or by mathematical convenience, but rather by deriving it under a pre-specified criteria. This approach takes the decision of prior selection out of the hands of the researcher. Ideally, for a given data model, we would like to have a prior which represents a \neutral" prior belief in the phenomenon we are studying. In categorical data analysis, the odds ratio is one of several approaches to quantify how strongly the presence or absence of one property is associated with the presence or absence of another property. In this project, we present a Reference prior for the odds ratio of an unrestricted 2 x 2 table. Posterior simulation can be conducted without MCMC and is implemented on a GPU via the CUDA extensions for C. Simulation results indicate that the proposed approach to this problem is far superior to the widely used Frequentist approaches that dominate this area. Real data examples also typically yield much more sensible results, especially for small sample sizes or for tables that contain zeros. An R package is also presented to allow for easy implementation of this methodology. Next, we develop an approximate reference prior for the negative binomial distribution, applying this methodology to a continuous parameterization often used for modeling over-dispersed count data as well as the typical discrete case. Results indicate that the developed prior equals the performance of the MLE in estimating the mean of the distribution but is far superior when estimating the dispersion parameter.