Gideon Simpson,  Drexel University

Relative Entropy Preconditioning for Markov Chain Monte Carlo

One of the challenges in using Markov Chain Monte Carlo methods to sample from a target distribution, such as the distribution of trajectories in a molecular dynamics problem or the parameter distribution in a statistical inverse problem, is finding a good proposal distribution. An ideal prior distribution would both be easy to sample from and have a high acceptance rate in the Metropolis step of the algorithm. This latter property ensures that the Markov chain will rapidly explore the configuration space under the target distribu- tion. In this talk, we present work on functionalized Gaussian priors which are preconditioned to minimize the distance, with respect to relative entropy, to the target measure.