Bayesian Nonparametrics

Author: J.K. Ghosh
Publisher: Springer Science & Business Media
ISBN: 0387226540
Format: PDF, ePub
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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.

Bayesian Nonparametric Data Analysis

Author: Peter Müller
Publisher: Springer
ISBN: 3319189689
Format: PDF, ePub, Mobi
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This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.

Practical Nonparametric and Semiparametric Bayesian Statistics

Author: Dipak D. Dey
Publisher: Springer Science & Business Media
ISBN: 1461217326
Format: PDF, ePub, Mobi
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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.

Prior Processes and Their Applications

Author: Eswar G. Phadia
Publisher: Springer
ISBN: 3319327895
Format: PDF, Mobi
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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.

Finite Mixture and Markov Switching Models

Author: Sylvia Frühwirth-Schnatter
Publisher: Springer Science & Business Media
ISBN: 0387357688
Format: PDF, ePub
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The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

Nonparametric Bayesian Inference in Biostatistics

Author: Riten Mitra
Publisher: Springer
ISBN: 3319195182
Format: PDF, ePub, Mobi
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As chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters cover: clinical trials, spatial inference, proteomics, genomics, clustering, survival analysis and ROC curve.

Bayesian and Frequentist Regression Methods

Author: Jon Wakefield
Publisher: Springer Science & Business Media
ISBN: 1441909257
Format: PDF, ePub
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Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines.

All of Nonparametric Statistics

Author: Larry Wasserman
Publisher: Springer Science & Business Media
ISBN: 9780387306230
Format: PDF, Kindle
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This text provides the reader with a single book where they can find accounts of a number of up-to-date issues in nonparametric inference. The book is aimed at Masters or PhD level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. It covers a wide range of topics including the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book’s dual approach includes a mixture of methodology and theory.

Semiparametric and Nonparametric Methods in Econometrics

Author: Joel L. Horowitz
Publisher: Springer Science & Business Media
ISBN: 9780387928708
Format: PDF, ePub, Mobi
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Standard methods for estimating empirical models in economics and many other fields rely on strong assumptions about functional forms and the distributions of unobserved random variables. Often, it is assumed that functions of interest are linear or that unobserved random variables are normally distributed. Such assumptions simplify estimation and statistical inference but are rarely justified by economic theory or other a priori considerations. Inference based on convenient but incorrect assumptions about functional forms and distributions can be highly misleading. Nonparametric and semiparametric statistical methods provide a way to reduce the strength of the assumptions required for estimation and inference, thereby reducing the opportunities for obtaining misleading results. These methods are applicable to a wide variety of estimation problems in empirical economics and other fields, and they are being used in applied research with increasing frequency. The literature on nonparametric and semiparametric estimation is large and highly technical. This book presents the main ideas underlying a variety of nonparametric and semiparametric methods. It is accessible to graduate students and applied researchers who are familiar with econometric and statistical theory at the level taught in graduate-level courses in leading universities. The book emphasizes ideas instead of technical details and provides as intuitive an exposition as possible. Empirical examples illustrate the methods that are presented. This book updates and greatly expands the author’s previous book on semiparametric methods in econometrics. Nearly half of the material is new.