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.

## Hamiltonian Monte Carlo

A method inspired by conservation laws in physics. See, e.g. Hamiltonian Monte Carlo.

## Connection to variational inference

Deep. See (Salimans, Kingma, and Welling 2015)

## Adaptive MCMC

See Adaptive MCMC.

## Langevin Monte carlo

See log concave distributions for now. Connection to SGD somehow?

## 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 βtemperatureβ of the sample, or move βwithinβ a temperature. The main intuition behind this is that at higher temperatures, the distribution is flatter, so the chain explores the landscape faster.

## Mixing rates

## Debiasing via coupling

Pierre E. Jacob, John OβLeary, Yves AtchadΓ©, crediting Glynn and Rhee (2014), made MCMC estimators without finite-time-bias, which is nice for parallelisation (Jacob, OβLeary, and AtchadΓ© 2017).

## Efficiency of

Want to adaptively tune the MCMC? See tuning MCMC.

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