Computationally efficient variational-like approximations of possibilistic inferential models

TL;DR

This paper introduces a computationally efficient variational-like method for approximating possibilistic inferential models' contours, enabling faster and scalable statistical inference.

Contribution

It proposes a parametric approximation strategy that matches IM contours with credible sets, significantly reducing computational costs.

Findings

Achieves accurate approximation of IM contours with less computation

Provides a scalable method for possibilistic inference

Demonstrates effectiveness through numerical experiments

Abstract

Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple yet 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 of a parametric family that, in a certain sense, approximately covers the credal set associated with the IM's possibility measure. Akin to variational inference, we then propose to tune the parameters of that parametric family so that its $100(1-\alpha)\%$ credible set roughly matches the IM contour's $\alpha$-cut. This parametric $\alpha$-cut matching strategy implies a full approximation to the IM's possibility contour at a fraction of the computational cost associated with previous strategies.