## Bayesian inference with geodetic applicationsThis 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 Carlo methods are discussed since the applications mostly rely on the numerical integration of the posterior distribution. Furthermore, Bayesian inference in the linear model, nonlinear model, mixed model and in the model with unknown variance and covariance components is considered. Solutions are supplied for the classification, for the posterior analysis based on distributions of robust maximum likelihood type estimates, and for the reconstruction of digital images. |

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### Contents

Introduction | 1 |

Recursive Application | 8 |

Maximum Entropy Priors | 15 |

Copyright | |

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accept H applied assume Bayes estimate Bayes rule Bayesian analysis Bayesian inference confidence interval confidence region conjugate prior covariance components covariance matrix data points defined denotes density values derived determined epoch Example expected value follows gamma distribution given gives gray levels Hence identical ie{l informative priors integration with respect introduce iteration least squares likelihood function line elements linear model M-estimate marginal density marginal distribution marginal posterior density marginal posterior distribution mixed model Monte Carlo integration multivariate t-distribution noninformative prior nonlinear model normal-gamma distribution null hypothesis numerical observation vector obtain outliers parame parameter space parameter vector pixel posterior density function posterior distribution predicted observation prior density function prior distribution prior information rameters random numbers random variable random vector robust estimation solved standard statistical techniques statistical inference subspace theorem tion transformation unknown parameters uxl vector variance and covariance variance components variance factor o2 vector ft yy ss