Parallel Adaptive Importance Sampling: Parallelism PAIS Seminar

MCMC algorithms are a powerful family of tools which allow us to sample from any probability distribution, and are often used in the context of Bayesian inverse problems. Standard MCMC algorithms can be easily parallelised, simply by executing many independent chains across a cluster. However, since a priori we do not have much information about the target distribution, each chain does not start in equilibrium, and as such must be "burned-in". Since it takes each chain the same amount of time to burn-in, this process takes the same amount of time no matter how many processors are used. This motivates a method which allows communication across the chains, allowing for better mixing properties. In this talk, we will introduce the Parallel Adaptive Importance Sampling (PAIS) algorithm, which incorporates function space MALA proposals, and optimal transport resampling methods from particle filtering in order to construct a proposal regime which incorporates information from the previous state of chain from all processors, leading to better mixing properties.