Robustifying Bayesian Procedures

Abstract In this paper we discuss two approaches to robustifying standard Bayesian procedures. The first involves regarding common statistical problems as decision problems where the ‘relevant unknown’ is modelled nonparametrically. Problems considered include model selection, empirical Bayes inference and interval estimation. In particular we generalise a model selection criterion of San Martini and Spezzaferri (1984). The second approach is based on suitable generalisations of well-known densities. For example, we generalise the standard normal density to include both skewness and kurtosis.