Daniel Rudolf, Institute for Mathematical Stochastics, Georg-August-Universität Göttingen

Title: Quantitative spectral gap estimate and Wasserstein contraction of simple slice sampling

Abstract: By proving Wasserstein contraction of simple slice sampling for approximate sampling of distributions determined by log-concave rotational invariant unnormalized densities we derive an explicit quantitative lower bound of the spectral gap. In particular, the lower bound of the spectral gap carries over to more general distributions depending only on the volume of the (super-)level sets of the unnormalized density.

Speaker: Dr. Ben Calderhead, Department of Mathematics, Imperial College London
Title: Quasi Markov Chain Monte Carlo Methods

Abstract: Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior densities within the Bayesian framework, in particular for inverse problems. We introduce a general parallel Markov chain Monte Carlo(MCMC) framework, for which we prove a law of large numbers and a central limit theorem. In that context, non-reversible transitions are investigated. We then extend this approach to the use of adaptive kernels and state conditions, under which ergodicity holds. As a further extension, an importance sampling estimator is derived, for which asymptotic unbiasedness is proven. We consider the use of completely uniformly distributed (CUD) numbers within the above mentioned algorithms, which leads to a general parallel quasi-MCMC (QMCMC) methodology. We prove consistency of the resulting estimators and demonstrate numerically that this approach scales close to n^{-2} as we increase parallelisation, instead of the usual n^{-1} that is typical of standard MCMC algorithms. In practical statistical models we observe multiple orders of magnitude improvement compared with pseudo-random methods.

Prof. Renauld Lambiote, University of Oxford, UK (15:00-16:00)

Dr. Yoav Zemel, University of Göttingen, Germany (15:00-16:00)

Prof. Karla Hemming, University of Birmingham, UK (15:00-16:00)

Speaker: Clair Barnes, University College London, UK

Death & the Spider: postprocessing multi-ensemble weather forecasts with uncertainty quantification

Ensemble weather forecasts often under-represent uncertainty, leading to overconfidence in their predictions. Multi-model forecasts combining several individual ensembles have been shown to display greater skill than single-ensemble forecasts in predicting temperatures, but tend to retain some bias in their joint predictions. Established postprocessing techniques are able to correct bias and calibration issues in univariate forecasts, but are generally not designed to handle multivariate forecasts (of several variables or at several locations, say) without separate specification of the structure of the inter-variable dependence.

We propose a flexible multivariate Bayesian postprocessing framework, developed around a directed acyclic graph representing the relationships between the ensembles and the observed weather. The posterior forecast is inferred from the ensemble forecasts and an estimate of their shared discrepancy, which is obtained from a collection of past forecast-observation pairs. The approach is illustrated with an application to forecasts of UK surface temperatures during the winter period from 2007-2013.

Prof. Malgorzata Bogdan, University of Wroclaw, Poland (15:00-16:00)