Markov Chain Monte Carlo for Continuous-Time Discrete-State Systems

• Activity Number: 235
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Vinayak Rao* and Yee Whye Teh
• Companies: Purdue University and University of Oxford
• Keywords: Markov chain Monte Carlo ; continuous time ; Markov jump process ; uniformization ; doubly intractable ; forward-backward algorithm

Abstract

A variety of phenomena are best described using dynamical models which operate on a discrete state space and in continuous time. Examples include Markov jump processes, continuous time Bayesian networks, renewal processes and other point processes, with applications ranging from systems biology, genetics, computing networks and human-computer interactions. Posterior computations typically involve approximations like time discretization and can be computationally intensive. In this talk I will describe recent work on a class of Markov chain Monte Carlo methods that allow efficient computations while still being exact. The core idea is an auxiliary variable Gibbs sampler that alternately resamples a random discretization of time given the state-trajectory of the system, and then samples a new trajectory given this discretization. For the Markov jump process, our construction is related to the idea of 'uniformization', which we generalize to develop samplers for systems with infinite state spaces, unbounded rates, as well as systems taking continuous values, or indexed by more general continuous spaces than time.