  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.
