Variational Approximations of Possibilistic Inferential Models

Inferential models (IMs) offer reliable, data-driven, possibilistic statistical inference. But despite IMs’ theoretical/foundational advantages, efficient computation in applications is a major challenge. This paper presents a simple and apparently powerful Monte Carlo-driven strategy for approximating the IM’s possibility contour, or at least its \(\alpha \) -level set for a specified \(\alpha \) . Our proposal utilizes a parametric family that, in a certain sense, approximately covers the credal set associated with the IM’s possibility measure, which is reminiscent of variational approximations now widely used in Bayesian statistics.