**Particle Markov Chain Monte Carlo**

*By Roman Holenstein*

Abstract:

Markov chain Monte Carlo (MCMC) algorithms are used routinely in statistics and physics to sample from high-dimensional non-standard probability distributions. Although asymptotic convergence of such iterative procedures is ensured under weak assumptions, the performance for a realistic finite number of iterations can be disastrous if the proposal distributions used to explore the space are poorly chosen. We show how one can construct efficient high-dimensional proposal distributions using Sequential Monte Carlo (SMC). This allows us to design effective MCMC algorithms in complex scenarios where standard methods fail. We demonstrate these algorithms on non-linear non-Gaussian state-space models and on finite mixture of Gaussians.