# Markov Chain Monte Carlo methods

August 28, 2017 — June 8, 2022

Bayes
estimator distribution
generative
Markov processes
Monte Carlo
probabilistic algorithms
probability

Despite studying within this area, I have nothing to say about MCMC broadly, but I do have some things I wish to keep notes on.

Deep. See

See SGD MCMC.

## 5 Tempering

e.g. Ge, Lee, and Risteski (2020);Syed et al. (2020). Saif Syed can explain this quite well. Or, as Lee and Risteski put it:

The main idea is to create a meta-Markov chain (the simulated tempering chain) which has two types of moves: change the current “temperature” of the sample, or move “within” a temperature. The main intuition behind this is that at higher temperatures, the distribution is flatter, so the chain explores the landscape faster.

## 7 Debiasing via coupling

Pierre E. Jacob, John O’Leary, Yves Atchadé, crediting Glynn and Rhee (2014), made MCMC estimators without finite-time-bias, which is nice for parallelisation .

## 8 Affine invariant

J. Goodman and Weare (2010)

We propose a family of Markov chain Monte Carlo methods whose performance is unaffected by affine transformations of space. These algorithms are easy to construct and require little or no additional computational overhead. They should be particularly useful for sampling badly scaled distributions. Computational tests show that the affine invariant methods can be significantly faster than standard MCMC methods on highly skewed distributions.

Implemented in, e.g. emcee .

## 9 Efficiency of

Want to adaptively tune the MCMC? See tuning MCMC.

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