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Monte Carlo without rejection

Presented by: 
Alexandre Bouchard University of British Columbia
Monday 3rd July 2017 - 14:15 to 15:00
INI Seminar Room 1
Co-authors: Arnaud Doucet (Oxford), Sebastian Vollmer (Warwick), George Deligiannidis (King's College London), Paul Vanetti (Oxford)

Markov chain Monte Carlo methods have become standard tools to sample from complex high-dimensional probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels built up over the Metropolis-Hastings algorithm. In our recent work, we investigate an alternative approach, the Bouncy Particle Sampler (BPS) where the target distribution of interest is explored using a continuous-time, non reversible Markov process. In this alternative approach, a particle moves along straight lines continuously around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. The resulting non-reversible Markov process provides a rejection-free Markov chain Monte Carlo sampling scheme. This method, inspired from recent work in the molecular simulation literature, is shown to be a valid, efficient sampling scheme applicable to a wide range of Bayesian problems. We present several additional original methodological extensions and establish various theoretical properties of these procedures. We demonstrate experimentally the efficiency of these algorithms on a variety of Bayesian inference problems.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons