Dr Nicholas Tawn - Sampling from multimodal distributions

Modern Monte Carlo methods have enabled the widespread application of Bayesian statistics where posterior distributions are typically only known up to a constant of proportionality. The task of sampling from a posterior distribution is challenging particularly in high dimensions. One of the most widespread approaches in high dimensions is to use MCMC, which designs a Markov chain whose invariant distribution is the posterior distribution. One major problem with the gold standard approaches in MCMC is that the chain can get stuck in local modes of the posterior distribution and so in the finite realisation of the chain the sample exhibits severe bias.