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. Basic concepts.- Bayes' Theorem.- Prior density functions.- Point estimation.- Confidence regions.- Hypothesis testing.- Predictive analysis.- Numerical techniques.- Models and special applications.- Linear models.- Nonlinear models.- Mixed models.- Linear models with unknown variance and covariance components.- Classification.- Posterior analysis based on distributions for robust maximum likelihood type estimates.- Reconstruction of digital images.
