Traditional Bayesian computational methods, such as MCMC, are based on discrete-time Markov chains. In recent years there has been interest in using continuous-time Markov processes within an MCMC-like procedure. This involves constructing and simulating a so-called piecewise deterministic Markov process that has the posterior distribution as its stationary distribution. Exact simulation is possible as these processes are finite-dimensional (to simulate their trajectories over any finite time interval requires simulating and storing only a finite-number of events). This talk will introduce these methods and their underlying theory and explain why they hold promise for scalable Bayesian inference: a piecewise deterministic Markov process with the correct stationary distribution can be simulated whilst only requiring access to a small sub-sample of data points at each iteration.
This is joint work with Joris Bierkens and Gareth Roberts, see https://arxiv.org/abs/1607.03188 and https://arxiv.org/abs/1611.07873.