Bayesian Inference with Geodetic Applications
This introduction to Bayesian inference places special emphasis on applications. All basic concepts are presented: Bayes' theorem, prior density functions, point estimation, confidence region, hypothesis testing and predictive analysis. In addition, Monte
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31 Karl-Rudolf Koch
Bayesian Inference with Geodetic Applications
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona
Author Professor Karl-Rudolf Koch Institute of Theoretical Geodesy, Unwerslty of Bonn Nussallee 17, D-5300 Bonn, FRG
ISBN 3-540-53080-0 Spnnger-Verlag Berlin Heidelberg N e w York ISBN 0-387-53080-0 Sprmger-Verlag NewYork Berlin Hewdelberg
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Preface There are problems, when applying statistical inference to the analysis of data, which are not readily solved by the inferential methods of the standard statistical techniques. One example is the computation of confidence intervals for variance components or for functions of variance components. Another example is the statistical inference on the random parameters of the mixed model of the standard statistical techniques or the inference on parameters of nonlinear models. Bayesian analysis gives answers to these problems. The advantage of the Bayesian approach is its conceptual simplicity. It is based on Bayes' theorem only. In general, the posterior distribution for the unknown parameters following from Bayes' theorem can be readily written down. The statistical inference is then solved by this distribution. Often the posterior distribution cannot be integrated analytically. However, this is not a serious drawback, since efficient methods exist for the numerical integration. The results of the standard statistical techniques concerning the linear models can also be derived by the Bayesian inference. These techniques may therefore be considered as special cases of the Bayesian analysis. Thus, the Bayesian inference is more general. Linear models and models closely related to linear models will be assumed for the analysis of the observations which contain the information on the unknown parameters of the models. The models, which are presented, are well suited for a variety of tasks connected with the evaluation of data. When applications are considered, data will be analyzed which have been taken to solve problems of surveying engineering. This does not mean, of course, that the applications are restricted to geodesy. Bayesian statistics may be applied wherever data need to be evaluated, for instance in geophysics. After an introduction the basic concepts of Bayesian inference are presented in Chapter 2. Bayes' theorem is
