Ebook: 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 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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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 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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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 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.
Content:
Front Matter....Pages -
Introduction....Pages 1-2
Basic concepts....Pages 3-3
Bayes’ Theorem....Pages 4-8
Prior density functions....Pages 9-32
Point estimation....Pages 33-36
Confidence regions....Pages 37-39
Hypothesis testing....Pages 40-48
Predictive analysis....Pages 49-51
Numerical techniques....Pages 52-60
Models and special applications....Pages 61-61
Linear models....Pages 62-98
Nonlinear models....Pages 99-108
Mixed models....Pages 109-121
Linear models with unknown variance and covariance components....Pages 122-134
Classification....Pages 135-143
Posterior analysis based on distributions for robust maximum likelihood type estimates....Pages 144-155
Reconstruction of digital images....Pages 156-167
Back Matter....Pages -

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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 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.
Content:
Front Matter....Pages -
Introduction....Pages 1-2
Basic concepts....Pages 3-3
Bayes’ Theorem....Pages 4-8
Prior density functions....Pages 9-32
Point estimation....Pages 33-36
Confidence regions....Pages 37-39
Hypothesis testing....Pages 40-48
Predictive analysis....Pages 49-51
Numerical techniques....Pages 52-60
Models and special applications....Pages 61-61
Linear models....Pages 62-98
Nonlinear models....Pages 99-108
Mixed models....Pages 109-121
Linear models with unknown variance and covariance components....Pages 122-134
Classification....Pages 135-143
Posterior analysis based on distributions for robust maximum likelihood type estimates....Pages 144-155
Reconstruction of digital images....Pages 156-167
Back Matter....Pages -
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