The Metropolis-Hastings algorithm is extended so that it can generate non-reversible Markov chains, using the notion of vorticity. The theory is applied to MCMC sampling on the $n$-cycle, resulting in significant improvements in spectral gap and mixing time. We discuss the observation by Sun et al., 2010, that adding vorticity will improve asymptotic variance and apply it so to non-reversible Metropolis-Hastings will have guaranteed improved performance over classical Metropolis-Hastings.
Extension to general spaces is provided and discussed within the setting of the Bayesian approach to inverse problems.
Practical spatial statistics
This talk will be a fruit salad of topics in and around spatial statistics. The main focus will be on spatial statistics as a cousin to Bayesian inverse problems. I will discuss what we want to compute, what we can compute, how well we can compute it and how all of this talk of computing impacts on modelling. I will also talk a lot about the importance of priors in spatial modelling.
Design of Experiments for Computational Models
In essence, statistical design of experiments is the choice of combinations of values of controllable variables at which a physical process or computer code will be observed. Our focus will be on design for estimation or calibration of computational models derived from underpinning scientific theory and implemented in computer code. We will address challenges arising from (i) the need to accelerate the numerical search for optimal designs through the development and application of statistical emulators, or surrogates, of the computational model; and (ii) explicitly acknowledging the discrepancy between reality and the postulated model(s).
Joint work: Dave Woods*, Antony Overstall**, Tim Waite*; *University of Southampton **University of St Andrews