Numerical treatment of Bayesian robustness problems

The problem of analyzing the robustness of Bayesian procedures with respect to the prior has been considered to some extent in the last years. In spite of this, robustness analysis has not yet entered into routine Bayesian analysis, mainly because of the inadequate development of numerical algorithms and related software. When the prior belongs to a class defined in terms of the so called generalized moment conditions, it has been shown that the problem can be reduced to one of linear semi-infinite programming (LSIP). A new way of performing such a reduction is presented here aimed at providing proper scaling of the functions defining the problem and keeping into account their possible unboundedness. An algorithm for solving LSIP problems under rather mild assumptions, as required by the typical presence of indicator functions in the generalized moment conditions, has been previously developed by the author and its applicability to Bayesian robustness is discussed here. The algorithm, called accelerated central cutting plane (ACCP) algorithm, is also numerically illustrated by an example.