Bayesian Inference Data Evaluation and Decisions
This new edition offers a comprehensive introduction to the analysis of data using Bayes rule. It generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. This is particularly useful when the observed
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Bayesian Inference Data Evaluation and Decisions Second Edition
Bayesian Inference
Hanns Ludwig Harney
Bayesian Inference Data Evaluation and Decisions Second Edition
123
Hanns Ludwig Harney Max Planck Institute for Nuclear Physics Heidelberg Germany
ISBN 978-3-319-41642-7 DOI 10.1007/978-3-319-41644-1
ISBN 978-3-319-41644-1
(eBook)
Library of Congress Control Number: 2016945790 © Springer International Publishing Switzerland 2003, 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
Preface
The present book, although theoretical, deals with experience. It questions how to draw conclusions from random events. Combining ideas from Bayes and Laplace with concepts of modern physics, we answer some aspects of this question. The book combines features of a textbook and a monograph. Arguments are presented as explicitely as possible with the aid of of appendices containing lengthy derivations. There are numerous examples and illustrations, often taken from physics research. Problems are posed and their solutions provided. The theory presented in the book is conservative in that the most widely-known Gaussian methods of error estimation remain untouched. At the same time, some material is unconventional. The non-informative prior is considered the basis of statistical inference and a unique definition is given and defended. Not only does the prior allow one to find the posterior distribution, it also provides the measure one needs to construct error intervals and make decisions. The example of binomial distribution — sketched on the book-cover — represents 300 years of statistics research. It was the first clearly formulated statistical model and the first example of statistical inference. We hope to convince the reader this subject is not yet closed. Heidelberg, Germany
Hanns Ludwig Harney
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Acknowledgement
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