Hypothesis testing for Markov chain Monte Carlo

TL;DR

This paper develops hypothesis testing methods tailored for Markov chain Monte Carlo samples, providing non-asymptotic error bounds and sample size estimates, with applications in Bayesian inference for biochemical models.

Contribution

It introduces hypothesis tests for MCMC samples with theoretical error bounds and sample size analysis, a novel approach for decision-making in dependent sampling contexts.

Findings

Non-asymptotic error bounds established

Sample size bounds for different test types derived

Application demonstrated in Bayesian biochemical pathway inference

Abstract

Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are useful when one is interested in deciding whether the expected value of a certain quantity is above or below a given threshold. We show non-asymptotic error bounds and bounds on the expected number of samples for three types of tests, a fixed sample size test, a sequential test with indifference region, and a sequential test without indifference region. Our tests can lead to significant savings in sample size. We illustrate our results on an example of Bayesian parameter inference involving an ODE model of a biochemical pathway.