general.md

General Usage

Introduction

The tests provided by MCMCTesting are frequentist hypothesis tests for testing the correctness of MCMC kernels. In particular, it compute the p-value for the null hypothesis that the MCMC kernel has the correct stationary distribution against the alternative hypothesis that it doesn't.

Currently, MCMCTesting provide three different tests originally proposed by Gandy and Scott¹:

1. [Simple Two-Sample Test](@ref twosample)
2. [Two-Sample Test with an Additional Gibbs Step](@ref twosamplegibbs)
3. [Exact Rank Test](@ref exactrank)

The two-sample tests are generally applicable. On the other hand, the exact rank test assumes that the MCMC kernel is reversible. Therefore, it can specifically be used to test reversibility.

Interface

The user needs to implement the following function specializations for the model and kernel subject to the test.

sample_joint
markovchain_transition

Some tests might be require additional interfaces to be implemented. For an overview of how to implement these interfaces, refer to the [tutorial](@ref tutorial).

The model and kernel are then passed to MCMCTesting through the following struct:

TestSubject

Simulating a P-Value with mcmctest

Each of the test internally run simulations and compute a single p-value through the following routine:

mcmctest

Increasing Power with seqmcmctest

seqmcmctest (Algorithm 3¹) sequentially calls mcmctest to increase the power and ensure a low false rejection rate. Furthermore, the p-values from each component of the statistics are combined through multiple hypothesis adjustment.

seqmcmctest

References

Footnotes

1. Gandy, A., & Scott, J. (2020). Unit testing for MCMC and other Monte Carlo methods. arXiv preprint arXiv:2001.06465. ↩ ↩²