Continuously Tempered PDMP samplers
Matthew Sutton · Robert Salomone · Augustin Chevallier · Paul Fearnhead
Tue Nov 29 02:00 PM -- 04:00 PM (PST) @ Hall J #811
New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or heavy-tailed distributions. We show how tempering ideas can improve the mixing of PDMPs in such cases. We introduce an extended distribution defined over the state of the posterior distribution and an inverse temperature, which interpolates between a tractable distribution when the inverse temperature is 0 and the posterior when the inverse temperature is 1. The marginal distribution of the inverse temperature is a mixture of a continuous distribution on $[0,1)$ and a point mass at 1: which means that we obtain samples when the inverse temperature is 1, and these are draws from the posterior, but sampling algorithms will also explore distributions at lower temperatures which will improve mixing. We show how PDMPs, and particularly the Zig-Zag sampler, can be implemented to sample from such an extended distribution. The resulting algorithm is easy to implement and we show empirically that it can outperform existing PDMP-based samplers on challenging multimodal posteriors.
Matthew Sutton (Queensland University of Technology)
Robert Salomone (Queensland University of Technology)
Augustin Chevallier (Lancaster University)
Paul Fearnhead (Lancaster University)
Paul Fearnhead is Professor of Statistics at Lancaster University. He received his DPhil in Statistics from the University of Oxford in 1998; was a postdoctoral researcher at the University of Oxford until 2001; and then moved to the University of Lancaster, initially as a Lecturer in Statistics. He has worked on Monte Carlo methods within Bayesian statistics, including applications in population genetics, changepoint detection and inference for diffusions. He was awarded the Royal Statistical Society's Guy medal in Bronze in 2007, and Cambridge University's Adams Prize in 2006.
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