Speaker: Dr. Ben Calderhead, Imperial College London
Title: “Quasi Markov Chain Monte Carlo Methods”
Abstract: Generalised Metropolis-Hastings is a Markov chain Monte Carlo (MCMC) method that was introduced to allow for parallelisation by proposing multiple samples in each iteration, such that the stationary distribution is still the correct target density. In this more recent work, we prove that the consistency property still holds true when the driving sequence of pseudo-random numbers is replaced by completely uniformly distributed (c.u.d.) numbers. In essence this allows us to combine ideas from Quasi Monte Carlo with Markov chain Monte Carlo. In this talk I’ll present ideas used to construct this new Monte Carlo method, along with the results of initial numerical simulations that confirm our theoretical result, and suggest a scaling of order n^-1 as we increase parallelisation instead of the usual n^-1/2 convergence rate of standard MCMC methods.