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.
References
Andrieu, Christophe, Arnaud Doucet, and Roman Holenstein. 2010. “Particle Markov Chain Monte Carlo Methods.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (3): 269–342.
Chopin, Nicolas, and Sumeetpal S. Singh. 2015. “On Particle Gibbs Sampling.” Bernoulli 21 (3).
Devlin, Lee, Paul Horridge, Peter L Green, and Simon Maskell. 2021. “The No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler with a Near-Optimal L-Kernel,” 5.
Godsill, Simon J, Arnaud Doucet, and Mike West. 2004. “Monte Carlo Smoothing for Nonlinear Time Series.” Journal of the American Statistical Association 99 (465): 156–68.
Lindsten, Fredrik, Michael I. Jordan, and Thomas B. Schön. 2014. “Particle Gibbs with Ancestor Sampling.” arXiv:1401.0604 [Stat], January.
Lindsten, Fredrik, and Thomas B. 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), 3845–48.
Salomone, Robert, Leah F. South, Christopher C. Drovandi, and Dirk P. Kroese. 2018. “Unbiased and Consistent Nested Sampling via Sequential Monte Carlo,” May.
Whiteley, Nick, Christophe Andrieu, and Arnaud Doucet. 2010. “Efficient Bayesian Inference for Switching State-Space Models Using Discrete Particle Markov Chain Monte Carlo Methods.” arXiv:1011.2437 [Stat], November.
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