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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 -level set for a specified. 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.
Cella et al. (Mon,) studied this question.