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Author : Subhashis Ghosal
Publisher : Cambridge University Press
Page : 671 pages
File Size : 22,57 MB
Release : 2017-06-26
Category : Business & Economics
ISBN : 0521878268
Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.
Author : Subhashis Ghosal
Publisher : Cambridge University Press
Page : 671 pages
File Size : 24,11 MB
Release : 2017-06-26
Category : Mathematics
ISBN : 1108210120
Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.
Author : Riten Mitra
Publisher : Springer
Page : 448 pages
File Size : 11,33 MB
Release : 2015-07-25
Category : Medical
ISBN : 3319195182
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.
Author : J.K. Ghosh
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 43,70 MB
Release : 2006-05-11
Category : Mathematics
ISBN : 0387226540
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.
Author : Peter Müller
Publisher :
Page : 110 pages
File Size : 36,91 MB
Release : 2013
Category : Bayesian statistical decision theory
ISBN : 9780940600829
Author : Peter Müller
Publisher : Springer
Page : 203 pages
File Size : 25,45 MB
Release : 2015-06-17
Category : Mathematics
ISBN : 3319189689
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.
Author : Andrew Gelman
Publisher : CRC Press
Page : 677 pages
File Size : 33,81 MB
Release : 2013-11-01
Category : Mathematics
ISBN : 1439840954
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.
Author : Nils Lid Hjort
Publisher : Cambridge University Press
Page : 309 pages
File Size : 31,59 MB
Release : 2010-04-12
Category : Mathematics
ISBN : 1139484605
Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.
Author : Dipak D. Dey
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 50,46 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461217326
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.
Author : Jean-Pierre Florens
Publisher : Springer
Page : 0 pages
File Size : 19,77 MB
Release : 2024-07-22
Category : Mathematics
ISBN : 9783031613289
This book is a compilation of unpublished papers written by Jean-Marie Rolin (with several co-authors) on nonparametric bayesian estimation. Jean-Marie was professor of statistics at University of Louvain and died on November 5th, 2018. He made important contributions in mathematical statistics with applications to different fields like econometrics or biometrics. These papers cover a variety of topics, including: • Mathematical structure of the Bayesian model and main concepts (sufficiency, analarity, invariance...) • Representation of the Dirichlet processes and of the associated Polya urn model and applications to nonparametric bayesian analysis. • Contributions on duration models and on their non parametric bayesian treatment.