# Particle Markov Chain Monte Carlo

Particle systems as MCMC proposals

July 25, 2014 — April 8, 2022

algebra

approximation

Bayes

distributed

dynamical systems

generative

graphical models

machine learning

Monte Carlo

networks

optimization

probabilistic algorithms

probability

signal processing

state space models

statistics

stochastic processes

swarm

time series

Particle filters inside general MCMC samplers. Darren Wilkinson wrote a series of blog posts introducing this idea:

- MCMC, Monte Carlo likelihood estimation, and the bootstrap particle filter
- The particle marginal Metropolis-Hastings (PMMH) particle MCMC algorithm
- Introduction to the particle Gibbs Sampler

Turns out to be especially natural for, e.g. change point problems.

## 1 References

Andrieu, Doucet, and Holenstein. 2010. “Particle Markov Chain Monte Carlo Methods.”

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*.
Ashton, Bernstein, Buchner, et al. 2022. “Nested Sampling for Physical Scientists.”

*Nature Reviews Methods Primers*.
Chopin, and Singh. 2015. “On Particle Gibbs Sampling.”

*Bernoulli*.
Devlin, Horridge, Green, et al. 2021. “The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler with a Near-Optimal L-Kernel.”

Godsill, Doucet, and West. 2004. “Monte Carlo Smoothing for Nonlinear Time Series.”

*Journal of the American Statistical Association*.
Lindsten, Jordan, and Schön. 2014. “Particle Gibbs with Ancestor Sampling.”

*arXiv:1401.0604 [Stat]*.
Lindsten, and Schön. 2012. “On the Use of Backward Simulation in the Particle Gibbs Sampler.” In

*2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*.
Salomone, South, Drovandi, et al. 2018. “Unbiased and Consistent Nested Sampling via Sequential Monte Carlo.”

Whiteley, Andrieu, and Doucet. 2010. “Efficient Bayesian Inference for Switching State-Space Models Using Discrete Particle Markov Chain Monte Carlo Methods.”

*arXiv:1011.2437 [Stat]*.