Introduction to Bayesian Statistics

From the reviews of the second edition: "This is a well-written introduction to Bayesian Analysis that contains many applications to Geodesy and Engineering at the cutting edge of these topics. ... There is a good treatment of Bayesian Analysis of Linear Models ... . The references are very interesting ... by a group of scientists of whose work many of us in the Statistical profession may not be aware. The strength of the book lies in its coverage, careful mathematics and many contemporary applications." (Jayanta K. Ghosh, International Statistical Review, Vol. 76 (1), 2008) To Bayesian Statistics Second, updated and enlarged Edition With 17 Figures Professor Dr.-Ing., Dr.-Ing. E. h. mult. Karl-Rudolf Koch (em.) University of Bonn Institute of Theoretical Geodesy Nussallee 17 53115 Bonn E-mail: koch@geod. uni-bonn. de Library of Congress Control Number: 2007929992 ISBN 978-3-540-72723-1 Springer Berlin Heidelberg New York ISBN (1. Aufl) 978-3-540-66670-7 Einführung in Bayes-Statistik This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer. com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, 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. Cover design: deblik, Berlin Production: Almas Schimmel Typesetting: Camera-ready by Author Printed on acid-free paper 30/3180/as 5 4 3 2 1 0 PrefacetotheSecondEdition This is the secondandtranslatededitionof the Germanbook "Einfuhr · ung in die Bayes-Statistik, Springer-Verlag, Berlin Heidelberg New York, 2000." "The Introduction to Bayesian Statistics (2nd edition) presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters, in a manner that is simple, intuitive and easy to comprehend. The methods are applied to linear models, in models for a robust estimation, for prediction and filtering and in models for estimating variance components and covariance components. Regularization of inverse problems and pattern recognition are also covered while Bayesian networks serve for reaching decisions in systems with uncertainties. If analytical solutions cannot be derived, numerical algorithms are presented, such as the Monte Carlo integration and Markov Chain Monte Carlo methods."--Jacket This book presents Bayes'theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed. Front Matter....Pages I-XII Introduction....Pages 1-1 Probability....Pages 3-62 Parameter Estimation, Confidence Regions and Hypothesis Testing....Pages 63-83 Linear Model....Pages 85-127 Special Models and Applications....Pages 129-192 Numerical Methods....Pages 193-234 Back Matter....Pages 235-249