Bayesian robustness in bidimensional models: Prior independence

When θ is a multidimensional parameter, the issue of prior dependence or independence of coordinates is a serious concern. This is especially true in robust Bayesian analysis; Lavine et al. (J. Amer. Statist. Assoc. 86, 964-971 (1991)) show that allowing a wide range of prior dependencies among coordinates can result in near vacuous conclusions. It is sometimes possible, however, to make confidently the judgement that the coordinates of θ are independent a priori and, when this can be done, robust Bayesian conclusions improve dramatically. In this paper, it is shown how to incorporate the independence assumption into robust Bayesian analysis involving ε{lunate}-contamination and density band classes of priors. Attention is restricted to the case θ = (θ1, θ2) for clarity, although the ideas generalize. © 1994.

Duke Scholars

Author James O. Berger Statistical Science