Statistics Based On Dirichlet Processes And Related Topics
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Bayesian Nonparametrics
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Author : J.K. Ghosh
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Bayesian Nonparametrics written by J.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 2006-05-11 with Mathematics categories.
This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.
Statistics Based On Dirichlet Processes And Related Topics
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Author : Hajime Yamato
language : en
Publisher: Springer Nature
Release Date : 2020-07-17
Statistics Based On Dirichlet Processes And Related Topics written by Hajime Yamato and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-17 with Mathematics categories.
This book focuses on the properties associated with the Dirichlet process, describing its use a priori for nonparametric inference and the Bayes estimate to obtain limits for the estimable parameter. It presents the limits and the well-known U- and V-statistics as a convex combination of U-statistics, and by investigating this convex combination, it demonstrates these three statistics. Next, the book notes that the Dirichlet process gives the discrete distribution with probability one, even if the parameter of the process is continuous. Therefore, there are duplications among the sample from the distribution, which are discussed. Because sampling from the Dirichlet process is described sequentially, it can be described equivalently by the Chinese restaurant process. Using this process, the Donnelly–Tavaré–Griffiths formulas I and II are obtained, both of which give the Ewens’ sampling formula. The book then shows the convergence and approximation of the distribution for its number of distinct components. Lastly, it explains the interesting properties of the Griffiths–Engen–McCloskey distribution, which is related to the Dirichlet process and the Ewens’ sampling formula.
Combinatorial Stochastic Processes
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Author : Jim Pitman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Combinatorial Stochastic Processes written by Jim Pitman 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 2006-05-11 with Mathematics categories.
The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
Prior Processes And Their Applications
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Author : Eswar G. Phadia
language : en
Publisher: Springer
Release Date : 2016-07-27
Prior Processes And Their Applications written by Eswar G. Phadia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-27 with Mathematics categories.
This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the past four decades for dealing with Bayesian approach to solving selected nonparametric inference problems. This revised edition has been substantially expanded to reflect the current interest in this area. After an overview of different prior processes, it examines the now pre-eminent Dirichlet process and its variants including hierarchical processes, then addresses new processes such as dependent Dirichlet, local Dirichlet, time-varying and spatial processes, all of which exploit the countable mixture representation of the Dirichlet process. It subsequently discusses various neutral to right type processes, including gamma and extended gamma, beta and beta-Stacy processes, and then describes the Chinese Restaurant, Indian Buffet and infinite gamma-Poisson processes, which prove to be very useful in areas such as machine learning, information retrieval and featural modeling. Tailfree and Polya tree and their extensions form a separate chapter, while the last two chapters present the Bayesian solutions to certain estimation problems pertaining to the distribution function and its functional based on complete data as well as right censored data. Because of the conjugacy property of some of these processes, most solutions are presented in closed form. However, the current interest in modeling and treating large-scale and complex data also poses a problem – the posterior distribution, which is essential to Bayesian analysis, is invariably not in a closed form, making it necessary to resort to simulation. Accordingly, the book also introduces several computational procedures, such as the Gibbs sampler, Blocked Gibbs sampler and slice sampling, highlighting essential steps of algorithms while discussing specific models. In addition, it features crucial steps of proofs and derivations, explains the relationships between different processes and provides further clarifications to promote a deeper understanding. Lastly, it includes a comprehensive list of references, equipping readers to explore further on their own.
Current Issues In Statistical Inference
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Author : Dev Basu
language : en
Publisher: IMS
Release Date : 1992
Current Issues In Statistical Inference written by Dev Basu and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Lectures On Probability Theory And Statistics
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-14
Lectures On Probability Theory And Statistics written by Sergio Albeverio 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 2003-07-14 with Mathematics categories.
In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.
Statistical Modeling In Biomedical Research
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Author : Yichuan Zhao
language : en
Publisher: Springer Nature
Release Date : 2020-03-19
Statistical Modeling In Biomedical Research written by Yichuan Zhao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-19 with Medical categories.
This edited collection discusses the emerging topics in statistical modeling for biomedical research. Leading experts in the frontiers of biostatistics and biomedical research discuss the statistical procedures, useful methods, and their novel applications in biostatistics research. Interdisciplinary in scope, the volume as a whole reflects the latest advances in statistical modeling in biomedical research, identifies impactful new directions, and seeks to drive the field forward. It also fosters the interaction of scholars in the arena, offering great opportunities to stimulate further collaborations. This book will appeal to industry data scientists and statisticians, researchers, and graduate students in biostatistics and biomedical science. It covers topics in: Next generation sequence data analysis Deep learning, precision medicine, and their applications Large scale data analysis and its applications Biomedical research and modeling Survival analysis with complex data structure and its applications.
The Oxford Handbook Of Computational And Mathematical Psychology
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Author : Jerome R. Busemeyer
language : en
Publisher: Oxford University Press
Release Date : 2015-03-20
The Oxford Handbook Of Computational And Mathematical Psychology written by Jerome R. Busemeyer 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 2015-03-20 with Psychology categories.
This Oxford Handbook offers a comprehensive and authoritative review of important developments in computational and mathematical psychology. With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience. The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition). The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.
Practical Nonparametric And Semiparametric Bayesian Statistics
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Author : Dipak D. Dey
language : en
Publisher: Springer
Release Date : 1998-08-01
Practical Nonparametric And Semiparametric Bayesian Statistics written by Dipak D. Dey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-01 with Mathematics categories.
A compilation of original articles by Bayesian experts, this volume presents perspectives on recent developments on nonparametric and semiparametric methods in Bayesian statistics. The articles discuss how to conceptualize and develop Bayesian models using rich classes of nonparametric and semiparametric methods, how to use modern computational tools to summarize inferences, and how to apply these methodologies through the analysis of case studies.
Game Theory Optimal Stopping Probability And Statistics
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Author : Thomas Shelburne Ferguson
language : en
Publisher: IMS
Release Date : 2000
Game Theory Optimal Stopping Probability And Statistics written by Thomas Shelburne Ferguson and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.