Prior Processes and Their Applications Nonparametric Bayesian Estima
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 be
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Eswar G. Phadia
Prior Processes and Their Applications Nonparametric Bayesian Estimation Second Edition
Springer Series in Statistics
Series editors Peter Bickel, CA, USA Peter Diggle, Lancaster, UK Stephen E. Fienberg, Pittsburgh, PA, USA Ursula Gather, Dortmund, Germany Ingram Olkin, Stanford, CA, USA Scott Zeger, Baltimore, MD, USA
More information about this series at http://www.springer.com/series/692
Eswar G. Phadia
Prior Processes and Their Applications Nonparametric Bayesian Estimation Second Edition
123
Eswar G. Phadia Department of Mathematics William Paterson University of New Jersey WAYNE New Jersey, USA
ISSN 0172-7397 Springer Series in Statistics ISBN 978-3-319-32788-4 DOI 10.1007/978-3-319-32789-1
ISSN 2197-568X (electronic) ISBN 978-3-319-32789-1 (eBook)
Library of Congress Control Number: 2016940383 © Springer International Publishing Switzerland 2013, 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To my Daughter SONIA and Granddaughter ALEXIS
Preface
The foundation of the subject of nonparametric Bayesian inference was laid in two technical reports: a 1969 UCLA report by Thomas S. Ferguson (later published in 1973 as a paper in the Annals of Statistics) entitled “A Bayesian analysis of some nonparametric problems” and a 1970 report by Kjell Doksum (later published in 1974 as a paper in the Annals of Probability) entitled “Tailfree and neutral random probabilities and their posterior distributions.” In view of simplicity with which the posterior distributions were calculated (by updating the parameters), the Dirichlet process became an instant hit and generated quite an enthusiastic response. In contrast, Doksum’s approach which was more general than the Dirichlet process, but restricted to the real line, did not receive the same kind of attention since the posterior distribution
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