Computationally efficient variational-like approximations of possibilistic inferential models

Abstract: Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite IMs' theoretical and foundational advantages, efficient computation is often a challenge. This paper presents a simple and powerful numerical strategy for approximating the IM's possibility contour, or at least its $\alpha$-cut for a specified $\alpha \in (0,1)$. Our proposal starts with the specification a parametric family that, in a certain sense, approximately covers the credal set associated with the IM's possibility measure. Then the parameters of that parametric family are tuned in such a way that the family's $100(1-\alpha)\%$ credible set roughly matches the IM contour's $\alpha$-cut. This is reminiscent of the variational approximations now widely used in Bayesian statistics, hence the name variational-like IM approximation.