Unit Testing for MCMC and other Monte Carlo Methods

Abstract: We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for example, check if individual steps in a Gibbs sampler or a reversible jump MCMC have the desired invariant distribution. Two exact tests for assessing whether a given Markov chain has a specified invariant distribution are discussed. These and other tests of Monte Carlo methods can be embedded into a sequential method that allows low expected effort if the simulation shows the desired behavior and high power if it does not. Moreover, the false rejection probability can be kept arbitrarily low. For general Monte Carlo methods, this allows testing, for example, if a sampler has a specified distribution or if a sampler produces samples with the desired mean. The methods have been implemented in the R-package MCUnit.