Fusing independent inferential models in a black-box manner

TL;DR

This paper presents a flexible framework for combining independent inferential models in a black-box way, ensuring valid and calibrated possibilistic statistical inference without needing details of the original models.

Contribution

It introduces a novel, general method for fusing independent IMs that does not require knowledge of their internal construction, enhancing the applicability of IMs.

Findings

Framework guarantees validity of fused IMs

Method is applicable without detailed knowledge of original models

Ensures calibrated and normalized possibility contours

Abstract

Inferential models (IMs) represent a novel possibilistic approach for achieving provably valid statistical inference. This paper introduces a general framework for fusing independent IMs in a "black-box" manner, requiring no knowledge of the original IMs construction details. The underlying logic of this framework mirrors that of the IMs approach. First, a fusing function for the initial IMs' possibility contours is selected. Given the possible lack of guarantee regarding the calibration of this function for valid inferences, a "validification" step is performed. Subsequently, a straightforward normalization step is executed to ensure that the final output conforms to a possibility contour.