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Activity Number: 368
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #319473
Title: Bayesian Inversion of a Large Spatial Field Using Predictive Process
Author(s): Anirban Mondal*
Companies: Case Western Reserve University
Keywords: Spatial Statistics ; Bayesian Inference ; Inverse Problem ; Markov Chain Monte Carlo ; Uncertainty Quantification
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. Predictive Process have been used for a low rank approximation of the spatial process where the original process is projected onto a subspace that is generated by realizations of the original process at a specified set of locations called knot points. The estimation is carried out using Markov chain Monte Carlo method. Numerical results are presented by analyzing simulated as well as real data.


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