Paper Info
Title
Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems.
Abstract
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data on quantities of interest. The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a posterior probability measure that when propagated through the deterministic model produces a push-forward measure that exactly matches the observed probability measure on the data. Our approach for finding such posterior measures, which we call consistent Bayesian inference or push-forward based inference, is simple and only requires the computation of the push-forward probability measure induced by the combination of a prior probability measure and the deterministic model. We establish existence and uniqueness of observation-consistent posteriors and present both stability and error analyses. We also discuss the relationships between consistent Bayesian inference, classical/statistical Bayesian inference, and a recently developed measure-theoretic approach for inference. Finally, analytical and numerical results are presented to highlight certain properties of the consistent Bayesian approach and the differences between this approach and the two aforementioned alternatives for inference.
Year
DOI
Venue
2018
10.1137/16M1087229
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
stochastic inverse problems,Bayesian inference,uncertainty quantification,density estimation
Applied mathematics,Mathematical optimization,Bayesian inference,Inference,Measure (mathematics),Probability measure,Posterior probability,Prior probability,Mathematics,Bayes' theorem,Bayesian probability
Journal
Volume
Issue
ISSN
40
2
1064-8275
Citations 
PageRank 
References 
1
0.40
0
Authors
3
Name
Order
Citations
PageRank
T Butler1274.27
John D. Jakeman2527.65
Tim Wildey3599.61