Checking the Model and the Prior for the Constrained Multinomial

TL;DR

This paper addresses the challenges of model checking and prior-data conflict detection in constrained multinomial models, providing theoretical results and applications in quantum state estimation and ordered probability models.

Contribution

It introduces a theorem proving the consistency of prior checks in constrained multinomial models and demonstrates applications in quantum and ordered probability contexts.

Findings

The prior check is consistent under certain conditions.

Applications include quantum state estimation models.

Bayesian analysis of ordered probability models is demonstrated.

Abstract

The multinomial model is one of the simplest statistical models. When constraints are placed on the possible values for the probabilities, however, it becomes much more difficult to deal with. Model checking and checking for prior-data conflict is considered here for such models. A theorem is proved that establishes the consistency of the check on the prior. Applications are presented to models that arise in quantum state estimation as well as the Bayesian analysis of models for ordered probabilities.