Particle Markov Chain Monte Carlo

Particle systems as MCMC proposals

July 25, 2014 — April 8, 2022

dynamical systems
graphical models
machine learning
Monte Carlo
probabilistic algorithms
signal processing
state space models
stochastic processes
time series
Figure 1

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

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).
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].