Synopses & Reviews
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.
Review
Aus den Rezensionen zur 2. Auflage: "... Es ist schön zu sehen, dass K.-R. Koch die Zeit gefunden hat, sein exzellentes Lehrbuch zur Bayes-Statistik in verschiedenen Teilen an den Stand der Forschung anzupassen und - mit dem Übergang auf die englische Sprache - zu internationalisieren. ... Die jetzt in zweiter Auflage vorliegende Einführung ... ist ohne Zweifel ein äußerst nützliches und sehr zu empfehlendes Grundlagenwerk für die in Forschung und Lehre tätigen Kollegen aller Fachgebiete innerhalb der Geodäsie und Geoinformatik, für die Studierenden, insbesondere in den Master-Studiengängen ..." (Hansjörg Kutterer, in: zfv - Zeitschrift für Geodäsie, Geoinformation und Landmanagement, 2009, Vol. 134, Issue 3, S. 185 f.)
Review
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)
Synopsis
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.
Table of Contents
1 Introduction.- 2 Probability.- 3 Parameter Estimation, Confidence Regions and Hypothesis Testing.- 4 Linear Model.- 5 Special Models and Applications.- 6 Numerical Methods.- References.- Index.