Likelihood And Bayesian Inference
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Likelihood And Bayesian Inference
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Author : Leonhard Held
language : en
Publisher: Springer Nature
Release Date : 2020-03-31
Likelihood And Bayesian Inference written by Leonhard Held and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-31 with Medical categories.
This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.
Applied Statistical Inference
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Author : Leonhard Held
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-12
Applied Statistical Inference written by Leonhard Held 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 2013-11-12 with Mathematics categories.
This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.
Bayesian Inference
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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2023-07-01
Bayesian Inference written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-01 with Computers categories.
What Is Bayesian Inference Bayesian inference is a type of statistical inference that updates the probability of a hypothesis based on new data or information using Bayes' theorem. This way of statistical inference is known as the Bayesian method. In the field of statistics, and particularly in the field of mathematical statistics, the Bayesian inference method is an essential tool. When conducting a dynamic analysis of a data sequence, bayesian updating is an especially useful technique to utilize. Inference based on Bayes' theorem has been successfully implemented in a diverse range of fields, including those of science, engineering, philosophy, medicine, athletics, and the legal system. Bayesian inference is strongly related to subjective probability, which is why it is frequently referred to as "Bayesian probability" in the field of decision theory philosophy. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Bayesian Inference Chapter 2: Likelihood Function Chapter 3: Conjugate Prior Chapter 4: Posterior Probability Chapter 5: Maximum a Posteriori Estimation Chapter 6: Bayes Estimator Chapter 7: Bayesian Linear Regression Chapter 8: Dirichlet Distribution Chapter 9: Variational Bayesian Methods Chapter 10: Bayesian Hierarchical Modeling (II) Answering the public top questions about bayesian inference. (III) Real world examples for the usage of bayesian inference in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of bayesian inference' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of bayesian inference.
Probability And Bayesian Statistics
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Author : R. Viertl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability And Bayesian Statistics written by R. Viertl 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 2012-12-06 with Mathematics categories.
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics and stochastic processes, to real applications in economics, reliability and hydrology. Also the question is raised if it is necessary to develop new techniques to model and analyze fuzzy observations in samples. The articles are arranged in alphabetical order according to the family name of the first author of each paper to avoid a hierarchical ordering of importance of the different topics. Readers interested in special topics can use the index at the end of the book as guide.
Likelihood And Bayesian Inference
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Author : Leonhard Held
language : en
Publisher:
Release Date : 2020
Likelihood And Bayesian Inference written by Leonhard Held and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Bayesian statistical decision theory categories.
This book covers statistical inference based on the likelihood function. Discusses frequentist likelihood-based inference from a Fisherian viewpoint, Bayesian inference techniques including point and interval estimates, model choice and prediction and more.
Likelihood Bayesian And Mcmc Methods In Quantitative Genetics
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Author : Daniel Sorensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-22
Likelihood Bayesian And Mcmc Methods In Quantitative Genetics written by Daniel Sorensen 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 2007-03-22 with Science categories.
This book, suitable for numerate biologists and for applied statisticians, provides the foundations of likelihood, Bayesian and MCMC methods in the context of genetic analysis of quantitative traits. Although a number of excellent texts in these areas have become available in recent years, the basic ideas and tools are typically described in a technically demanding style and contain much more detail than necessary. Here, an effort has been made to relate biological to statistical parameters throughout, and the book includes extensive examples that illustrate the developing argument.
Statistical Inference
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Author : Murray Aitkin
language : en
Publisher: CRC Press
Release Date : 2010-06-02
Statistical Inference written by Murray Aitkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-02 with Mathematics categories.
Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct
Comparative Statistical Inference
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Author : Vic Barnett
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Comparative Statistical Inference written by Vic Barnett 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.
This fully updated and revised third edition, presents a wide ranging, balanced account of the fundamental issues across the full spectrum of inference and decision-making. Much has happened in this field since the second edition was published: for example, Bayesian inferential procedures have not only gained acceptance but are often the preferred methodology. This book will be welcomed by both the student and practising statistician wishing to study at a fairly elementary level, the basic conceptual and interpretative distinctions between the different approaches, how they interrelate, what assumptions they are based on, and the practical implications of such distinctions. As in earlier editions, the material is set in a historical context to more powerfully illustrate the ideas and concepts. Includes fully updated and revised material from the successful second edition Recent changes in emphasis, principle and methodology are carefully explained and evaluated Discusses all recent major developments Particular attention is given to the nature and importance of basic concepts (probability, utility, likelihood etc) Includes extensive references and bibliography Written by a well-known and respected author, the essence of this successful book remains unchanged providing the reader with a thorough explanation of the many approaches to inference and decision making.
Bayesian Inference
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Author : William A Link
language : en
Publisher: Academic Press
Release Date : 2009-08-07
Bayesian Inference written by William A Link and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-07 with Science categories.
This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analytical software and examples Leading authors with world-class reputations in ecology and biostatistics
The Likelihood Principle
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Author : James O. Berger
language : en
Publisher: IMS
Release Date : 1988
The Likelihood Principle written by James O. Berger and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.