Emulator-Based Bayesian Models for Spatial Inverse Problems

• Activity Number: 179
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Anirban Mondal*
• Companies: Case Western Reserve University
• Keywords: Inverse Problem ; Spatial Statistics ; Bayesian Hierarchical Model ; Markov Chain Monte Carlo

Abstract

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity (input) is a random spatial field. The Bayesian approach contains a natural mechanism for regularization in the form of prior information and casts the inverse solution as a posterior probability distribution. Data from different sources and scales are also integrated using a Bayesian hierarchical model. The likelihood term in the posterior distribution contains forward simulator, which is complex and non-linear, therefore computationally expensive. We develop an emulator based approach where the Bayesian multivariate adaptive splines (BMARS) has been used to model unknown functions of the model input. The emulators run almost instantaneously hence they are much computationally efficient as compared to the forward simulators. The estimation is carried out using trans-dimensional Markov chain Monte Carlo method. Numerical results are presented by analyzing simulated as well as real data from reservoir characterization.