On an inferential model construction using generalized associations

TL;DR

This paper introduces a flexible generalized inferential model (IM) approach based on generalized associations, which relaxes the need for complete data-generating process specification and maintains validity under mild conditions.

Contribution

It proposes a novel generalized IM construction that is more adaptable than traditional IMs, with methods for computation, marginalization, and practical applications.

Findings

The generalized IM is provably valid under mild conditions.

The approach allows for flexible modeling without full data-generating process specification.

Two applications demonstrate the effectiveness of the generalized IM method.

Abstract

The inferential model (IM) approach, like fiducial and its generalizations, depends on a representation of the data-generating process. Here, a particular variation on the IM construction is considered, one based on generalized associations. The resulting generalized IM is more flexible than the basic IM in that it does not require a complete specification of the data-generating process and is provably valid under mild conditions. Computation and marginalization strategies are discussed, and two applications of this generalized IM approach are presented.