Stirring the soup with Piecewise deterministic Markov processes

In the first part of the talk, I will introduce Monte Carlo methods based on piecewise deterministic Markov processes (PDMP samplers). PDMP samplers are non-reversible processes with momentum satisfying a skew-detail balance condition which is metaphorically seen as a way to stir the soup in order to mix the ingredients faster and has been shown to improve, in some cases, the performance of sampling methods, both in terms of convergence to stationarity and asymptotic variance.

In the second part of the talk, I will discuss some of my recent work on PDMPs with boundary conditions used to target efficiently a rich class of measures arising in Bayesian inference. I will motivate and illustrate the framework with three challenging statistical applications: Bayesian variable selection, for sampling the latent space of infection times with unknown infected population size in the SIR model with notifications and for sampling efficiently the invariant measure in hard-sphere models. The class of processes presented here extends the Sticky PDMP samplersLink opens in a new window which is joint work with J. Bierkens, F. van der Meulen and M. Schauer.