Prior Processes
This chapter is devoted to introducing various prior processes, their formulation, properties, inter-relationships, and their relative strengths and weaknesses. The sequencing of presentation of these priors reflects mostly the order in which they were di
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Prior Processes and Their Applications Nonparametric Bayesian Estimation
Prior Processes and Their Applications
Eswar G. Phadia
Prior Processes and Their Applications Nonparametric Bayesian Estimation
Eswar G. Phadia Department of Mathematics William Paterson University of New Jersey Wayne, NJ, USA
ISBN 978-3-642-39279-5 ISBN 978-3-642-39280-1 (eBook) DOI 10.1007/978-3-642-39280-1 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013945285 © Springer-Verlag Berlin Heidelberg 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
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. During the decades of 1970s and 1980s, hundred
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