ECON123A+Excerpts+from+Bayesian+Econometric+Methods

ECON123A+Excerpts+from+Bayesian+Econometric+Methods -...

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Bayesian Econometric Methods Gary Koop University of Strathclyde, Scotland Dale J. Poirier University of California, Irvine, USA Justin L. Tobias Iowa State University, USA
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CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521855716 c ± Gary Koop, Dale J. Poirier, and Justin L. Tobias 2007 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2007 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Koop, Gary. Bayesian econometric methods / Gary Koop, Dale J. Poirier, Justin L. Tobias. p. cm. – (Econometric exercises) Includes bibliographical references and index. ISBN 0-521-85571-3 (hardback) – ISBN 0-521-67173-6 (pbk.) 1. Econometrics. 2. Bayesian statistical decision theory. I. Poirier, Dale J. II. Tobias, Justin L. III. Title. IV. Series. HB139.K6359 2007 330.01 0 519542–dc22 2006031157 ISBN 978-0-521-85571-6 hardback ISBN 978-0-521-67173-6 paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
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1 The subjective interpretation of probability Reverend Thomas Bayes (born circa 1702; died 1761) was the oldest son of Reverend Joshua Bayes, who was one of the first ordained nonconformist ministers in England. Rel- atively little is known about the personal life of Thomas Bayes. Although he was elected a Fellow of the Royal Society in 1742, his only known mathematical works are two articles published posthumously by his friend Richard Price in 1763. The first dealt with the diver- gence of the Stirling series, and the second, “An Essay Toward Solving a Problem in the Doctrine of Chances,” is the basis of the paradigm of statistics named for him. His ideas appear to have been independently developed by James Bernoulli in 1713, also published posthumously, and later popularized independently by Pierre Laplace in 1774. In their com- prehensive treatise, Bernardo and Smith (1994, p. 4) offer the following summarization of Bayesian statistics : Bayesian Statistics offers a rationalist theory of personalistic beliefs in contexts of uncertainty, with the central aim of characterizing how an individual should act in order to avoid certain kinds of undesirable behavioral inconsistencies. The the- ory establishes that expected utility maximization provides the basis for rational decision making and that Bayes’ Theorem provides the key to the ways in which beliefs should fit together in the light of changing evidence. The goal, in effect, is
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