Objective Bayesian Comparison of Order-Constrained Models in Contingency Tables

TL;DR

This paper introduces objective Bayesian methods for testing and comparing order-constrained models in contingency tables, effectively handling monotone order restrictions using intrinsic and encompassing priors.

Contribution

It develops a unified Bayesian framework combining intrinsic and encompassing priors for order-constrained model testing in contingency tables.

Findings

Method performs well in simulations

Accurately distinguishes ordered from unordered models

Effective on real datasets

Abstract

In social and biomedical sciences testing in contingency tables often involves order restrictions on cell-probabilities parameters. We develop objective Bayes methods for order-constrained testing and model comparison when observations arise under product binomial or multinomial sampling. Specifically, we consider tests for monotone order of the parameters against equality of all parameters. Our strategy combines in a unified way both the intrinsic prior methodology and the encompassing prior approach in order to compute Bayes factors and posterior model probabilities. Performance of our method is evaluated on several simulation studies and real datasets.