Bayesian Computation, Guaranteed Efficient (or Intractable)

Cornell University, Ithaca NY

Investigators

Abstract

This research and education program will characterize and reduce the error associated with Markov chain and other computational methods in Bayesian statistics. The introduction of simulation-based computational methods has allowed the field of Bayesian statistics to dramatically expand; despite this, the biggest challenge for its wider adoption is still its computational difficulty. Understanding of the error associated with Bayesian computational methods has lagged far behind their use, and in some cases all available methods are too inefficient. The goals of this project are (1) distinguish classes of computationally tractable Bayesian models from those of computationally intractable models, (2) develop methods for guaranteed efficient computation for tractable models, and (3) introduce alternatives to intractable models that allow efficient computation. Tractability means that there exists a computational method that scales efficiently with the number of parameters, observations, or other statistical quantities. For motivation and application of the techniques, statistical problems arising in management of commercial and nonprofit operations will be used; case studies include Emergency Medical Services operations and (distributed computing) data-center operations. Statistical challenges in these contexts include estimation on road networks and fine-scale spatio-temporal demand estimation. When statistics are used to guide business, engineering, or public policy decisions, for instance, there may be large amounts of information and data from different sources that have to be drawn together to inform those decisions. These large and various sources of information must be analyzed in a way that does not require a large amount of computing time. This program advances understanding regarding what analyses we can expect to be able to do quickly; it develops more efficient computational methods for those analyses; and in the case of analyses that are simply too time-consuming it develops easier alternatives. Case studies and scientific approaches from this project will be incorporated into the classroom, and Master's and Ph.D. students will be an integral part of the research process.