DMS Applied and Computational Mathematics Seminar

PLEASE NOTE TIME IS 11:00am

Speaker: Habib Najm, Sandia National Laboratory

Title: Approximate Bayesian Computation for Model Calibration Given Summary Statistics

Abstract: It is often the case in Bayesian parameter estimation that one has to contend with summary statistics on functions of the data on model observables, rather than having access to the data itself. For example, one may have access only to marginal moments on some quantity estimated from the data, but not the original data. In this setting, the challenge is to estimate a posterior density on model parameters given constraints on derived quantities. We have used maximum entropy and approximate Bayesian computation methods in this context to sample the joint space of data and parameters, accepting data sets consistent with available statistics, and employing opinion pooling methods to arrive at a pooled posterior on quantities of interest. We have applied this approach in multiple contexts, invoking approximations where necessary to tackle problem complexity. This talk will explore this landscape, and will highlight effective use of this construction in a recent study where we used summary information, in the form of nominal values and error bars, from multiple legacy experimental data sets, to arrive at a posterior on model parameters.