Valid and Efficient Possibilistic Inferential Models for Categorical Data

Thomas M. Menino Convention & Exhibition Center 

In this exposé of the inferential model (IM), we investigate how finite-sample calibrated inference can be done when you have categorical data. IMs produce plausibility and necessity measures that are provably reliable for all sample sizes while simultaneously providing a Bayesian-like interpretable output. For multinomial and categorical regression inference, we show how plausibility contours derived from validified relative likelihoods yield regions with guaranteed frequentist coverage.

A key challenge in the applications of IMs to categorical data problems is computation. Discrete models produce "jumps" in plausibility that invalidate existing methods aimed at doing gradient descent on the contour to find a probabilistic approximation to the IM. We propose using an importance sampling procedure to amortize plausibility evaluations. We provide guidance on using the importance sampler in the multinomial and categorical regression problems using questions about odds ratio and the Iris dataset as motivating examples.

categorical data

Bayesian

possibility theory

importance sampling

multinomial

categorical regression 

Section on Bayesian Statistical Science