Block unimodality for multivariate Bayesian robustness

Summary The development of Bayesian robustness has been growing in the last decade. The theory has extensively dealt with the univariate parameter case. Among the vast amount of proposals in the literature, only a few of them have a straightforward extension to the multivariate case. In this paper we consider the multidimensional version of the class of ε-contaminated prior distributions, with unimodal contaminations. In the multivariate case there is not a unique definition of unimodality and one's choice must be based on statistical ground. Here we propose the use of the block unimodal distributions, which proved to be very suitable for modelling situations where the coordinates of the parameter ϑ are deemed, a priori, weakly correlated.