# Post-Processing of MCMC

arXiv: https://arxiv.org/abs/2103.16048 · HTML: https://mlsanity.com/paper/2103.16048/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2021.

## Built on by (most cited first, 5 of 5)

- [Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularization](https://mlsanity.com/paper/2301.13528/) (2023)
- [Bayesian neural networks via MCMC: a Python-based tutorial](https://mlsanity.com/paper/2304.02595/) (2023)
- [Meta-learning Control Variates: Variance Reduction with Limited Data](https://mlsanity.com/paper/2303.04756/) (2023)
- [Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis](https://mlsanity.com/paper/2105.12778/) (2021)
- [A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces](https://mlsanity.com/paper/2206.04552/) (2022)

## Abstract (arXiv)

Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is post-processed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not account for (common) situations where a limited computational budget engenders a bias-variance trade-off. The aim of this article is to review state-of-the-art techniques for post-processing Markov chain output. Our review covers methods based on discrepancy minimisation, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest.