A0758
Title: Sampling using time-changed Markov processes
Authors: Andrea Bertazzi - Ecole Polytechnique (France)
Giorgos Vasdekis - Newcastle University (United Kingdom) [presenting]
Abstract: A framework of time-changed Markov processes is introduced to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms in the context of multimodal distributions and rare event simulation. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent function. This framework is applied to several Markov processes from the MCMC literature, such as Langevin diffusions and piecewise deterministic Markov processes, obtaining novel modifications of classical algorithms and also rediscovering known MCMC algorithms. Theoretical properties of the time-changed process are proven under suitable conditions on the base process, focusing on connecting the stationary distributions and qualitative convergence properties such as geometric and uniform ergodicity, as well as a functional central limit theorem. Time permitting, the approach will be compared with the framework of space transformations, clarifying the similarities between the approaches.
