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. βParticle Markov Chain Monte Carlo Methods.β Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (3): 269β342.
Chopin, Nicolas, and Sumeetpal S. Singh. 2015. βOn Particle Gibbs Sampling.β Bernoulli 21 (3).
Devlin, Lee, Paul Horridge, Peter L Green, and Simon Maskell. 2021. βThe No-U-Turn Sampler as a Proposal Distribution in a Sequential Monte Carlo Sampler with a Near-Optimal L-Kernel,β 5.
Godsill, Simon J, Arnaud Doucet, and Mike West. 2004. βMonte Carlo Smoothing for Nonlinear Time Series.β Journal of the American Statistical Association 99 (465): 156β68.
Lindsten, Fredrik, Michael I. Jordan, and Thomas B. SchΓΆn. 2014. βParticle Gibbs with Ancestor Sampling.β arXiv:1401.0604 [Stat], January.
Lindsten, Fredrik, and Thomas B. SchΓΆn. 2012. βOn the Use of Backward Simulation in the Particle Gibbs Sampler.β In 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 3845β48.
Salomone, Robert, Leah F. South, Christopher C. Drovandi, and Dirk P. Kroese. 2018. βUnbiased and Consistent Nested Sampling via Sequential Monte Carlo,β May.
Whiteley, Nick, Christophe Andrieu, and Arnaud Doucet. 2010. βEfficient Bayesian Inference for Switching State-Space Models Using Discrete Particle Markov Chain Monte Carlo Methods.β arXiv:1011.2437 [Stat], November.
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