CEE Seminar - A Tour of Transport Methods for Bayesian Computation

Bayesian inference provides a natural framework for quantifying uncertainty in parameter estimates and model predictions, and for combining heterogeneous sources of information. Characterizing the results of Bayesian inference-by simulating from the posterior distribution-often proceeds via Markov chain Monte Carlo or sequential Monte Carlo sampling, but remains computationally challenging for complex posteriors and large-scale models.

This talk will describe a broad framework for using measure transport in Bayesian computation. This framework seeks a deterministic coupling of the posterior measure with a tractable "reference" measure (e.g., a standard Gaussian). Such couplings are induced by transport maps, and enable direct simulation from the desired measure simply by evaluating the transport map at samples from the reference. Approximate transports can also be used to "precondition" and accelerate standard Monte Carlo schemes. Within this framework, one can describe many useful notions of low-dimensional structure associated with inference: for instance, sparse or decomposable transports underpin modeling and computation with non-Gaussian Markov random fields, and low-rank transports arise frequently in inverse problems.......