The student has knowledge of basic concepts of Bayesian inference.

Bayesian methods, statistical modeling

This course is the successor to the course Introduction to Bayesian Inference. Both courses are based on the book Bayesian Biostatistics of Lesaffre and Lawson (2012, John Wiley & Sons). In the course Concepts of Bayesian Inference some basic Bayesian principles have been introduced and it was taught how to use BUGS software. These skills will be assumed in the present course. New Bayesian topics will be introduced but also the topics introduced in the previous course will be further developed. An example of the latter is that we will explore the role of the prior distribution in more detail, but also that the MCMC techniques will be explained in more technical detail. In this course, Bayesian methods for model selection and model criticism will be treated. In addition, more complex statistical analyses will be tackled. 

Contents

Exploring the prior distribution:
The conjugate prior distribution: derivation, further examples and semi-conjugacy
Expressing ignorance: the noninformative prior, the vague prior, Jeffreys prior, improper priors
Informative priors: data-based priors, elicitation of prior knowledge, archetypal priors, prior distributions of regression models, modeling priors

Alternatives to Markov Chain Monte Carlo techniques:
Laplace approximations
           
Hierarchical models:
Poisson-gamma hierarchical model
Gaussian hierarchical model
Comparison full Bayesian approach with empirical Bayesian approach
Bayesian mixed models: linear, generalized linear and non-linear models
Miscellaneous topics: choice of level 2 variance prior, propriety of posterior, comparison with frequentist approaches

Model building and assessment:
Bayes factor and variants, e.g. pseudo-Bayes factor
Model selection based on predictive loss functions
Residual analysis
Sensitivity analysis
Posterior predictive checks
Model expansion techniques