Unbiased MCMC with Couplings

coupled mcmc chains

A Research Implementation and Interactive Environment

Colin Carroll

Introduction

This repo is both a pip-installable library, and it generates this essay of the same name, which is meant as a reading companion to, and implementation of, the papers.

Link to github repository.

Install and experiment with

pip install git+git://github.com/colcarroll/couplings.git

Table of Contents

  1. Maximal Couplings: What is a coupling? What are some properties of couplings?
  2. (Biased) MCMC: What is statistical bias? How does that manifest in MCMC?
  3. Unbiased Metropolis-Hastings with Couplings (TODO)
  4. Unbiased Estimator (TODO)
  5. Unbiased Hamiltonian Monte Carlo with Couplings (IN PROGRESS)

References, Thanks

Many thanks of course to the authors below for interesting papers, and to the authors of the open source libraries used here for the useful code. Some ideas in the implementation are due to conversations and code from both the PyMC developers, and the TensorFlow Probability team. Thanks especially to Pierre Jacob for helpful conversations and encouragement

Primary References

Secondary References

Code References