|Posterior Exploration for Computationally Intensive Forward Models
Shane Reese, Brigham Young University
Monday, August 20, 2012
4:00 p.m., room 223, Weber Bldg
In this talk we apply a standard single site updating scheme that dates back to Metropolis (1953) to sample from the posterior of a computationally intensive inverse problem. While this approach has proven effective in a variety of applications, it has the drawback of requiring hundreds of thousands of calls to the simulation model. We also consider two broad classes of MCMC schemes that use highly multivariate updates to sample from f(xjy): the multivariate random walk Metropolis algorithm (Gelman 1996) and the distributed evolution-MCMC (DE-MC) sampler of terBraak (2005). Such multivariate updating schemes are alluring for computationally demanding inverse problems since they have the potential to update many (or all) components of x at once, while requiring only a single evaluation of the simulator. Additionally, we consider augmenting the basic posterior formulation with additional formulations based on faster, approximate simulators. The faster, approximate simulators are created by altering the multigrid solver used to compute f(x). These approximate simulators can be used in a delayed acceptance scheme (Fox 1997, Christen 2005), as well as in an augmented formulation (Higdon 2002). Both of these recipes can be utilized with any of the above MCMC schemes, often leading to substantial improvements in efficiency.