Bayesian Robustness: Theory and Applications

Abstract

This talk considers Bayesian robustness where there is a conflict between the data and the prior. Robust inference can be achieved by using heavy-tailed distributions. We present two classes of scale mixtures distributions, namely the scale mixtures of normal (SMN) distributions and scale mixtures of uniform (SMU) distributions for statistical modelling. Both SMN and SMU distributions have special members which are well known distributions such as normal, Student-t, Laplace, exponential power, generalized-t distributions, etc. and most of them are heavy-tailed than the normal distribution. Another advantage of using SMN and SMU distributions is that they simplify the Gibbs sampler in Bayesian simulation-based inference. We demonstrate the applications of SMN and SMU distributions in robust modelling, Hierarchical modelling, GLMM, insurance and financial time series modelling.