Exact MCMC Using Approximations

• Activity Number: 223
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Radu Herbei*+
• Companies: The Ohio State University
• Keywords: MCMC ; exact sampling ; Bernoulli factory

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 MCMC algorithms and show how they can be used in applications from oceanography and phylogenetics.