Title: Exact MCMC Using Approximations and Bernoulli Factories
Speaker: Radu Herbei (Associate Professor of Statistics, The Ohio State University)
Hosted by Jenný Brynjarsdóttir
Abstract: With the ever increasing complexity of models used in modern science, there is a need for new computing strategies. Classical MCMC algorithms (Metropolis-Hastings, Gibbs) have difficulty handling very high-dimensional state spaces and models where likelihood evaluation is impossible. In this work we study a collection of models for which the likelihood cannot be evaluated exactly; however, it can be estimated unbiasedly in an efficient way via distributed computing. Such models include, but are not limited to cases where the data are discrete noisy observations from a class of diffusion processes or partial measurements of a solution to a partial differential equation. In each case, an exact MCMC algorithm targeting the correct posterior distribution can be obtained either via the “auxiliary variable trick” or by using a Bernoulli factory to advance the current state. We explore the advantages and disadvantages of such an MCMC algorithm and show how it can be used in an oceanographic application.