Joint p-Values for Higher-Powered Bayesian Model Checking with Frequentist Guarantees

2023/09/22 by Collin Cademartori, Cademartori, Collin · 1 citation
Mathematics · Computer Science · #Statistical Methods in Clinical Trials #Bayesian Modeling and Causal Inference #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2309.13001

Abstract

We introduce a joint posterior p-value, an extension of the posterior predictive p-value for multiple test statistics, designed to address limitations of existing Bayesian p-values in the setting of continuous model expansion. In particular, we show that the posterior predictive p-value, as well as its sampled variant, become more conservative as the parameter dimension grows, and we demonstrate the ability of the joint p-value to overcome this problem in cases where we can select test statistics that are negatively associated under the posterior. We validate these conclusions with a pair of simulation examples in which the joint p-value achieves substantial gains to power with only a modest increase in computational cost.

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