الصفحة 1
الصفحة 1
Introduction to Bayesian Statistics
This is the second and translated edition of the German book “Einf ̈uhrung in die Bayes-Statistik, Springer-Verlag, Berlin Heidelberg New York, 2000”. It has been completely revised and numerous new developments are pointed out together with the relevant literature. The Chapter 5.2.4 is extended by the stochastic trace estimation for variance components. The new Chapter 5.2.6 presents the estimation of the regularization parameter of type Tykhonov regularization for inverse problems as the ratio of two variance components.The reconstruction and the smoothing of digital three-dimensional images is demonstrated in the new Chapter 5.3. The Chapter 6.2.1 on importance sampling for the Monte Carlo integration is rewritten to solve a more general integral. This chapter contains also the derivation of the SIR (sampling-importance-resampling) algorithm as an alternative to the rejection method for generating random samples. Markov Chain Monte Carlo methods are now frequently applied in Bayesian statistics.
Linear and Generalized Linear Mixed Models and Their Applications
This book covers two major classes of mixed effects models—linear mixed models and generalized linear mixed models—and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. It offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it discusses the latest developments and methods in the field, incorporating relevant updates since publication of the first edition. These include advances in high-dimensional linear mixed models in genome-wide association studies (GWAS), advances in inference about generalized linear mixed models with crossed random effects, new methods in mixed model prediction, mixed model selection, and mixed model diagnostics.
