Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification
Year: 2018
Type: article
Abstract: We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on parameters is propagated through the approximate model to produce a probability density, often called a push-forward probability density, on a set of quantities of interest (QoI). The inverse problem considered in this paper seeks to update an initial probability density assumed on model input parameters such that the subsequent push-forward of this updated density through the parameter-to-QoI map matches a given probability density on the QoI. We prove that the densities obtained from solving the forward and inverse problems, using approximate models, converge to the true densities as the approximate models converge to the true models. Numerical results are presented to demonstrate convergence rates of densities for sparse grid approximations of parameter-to-QoI maps and standard spatial and temporal discretizations of PDEs and ODEs.
DOI: 10.1137/18m1181675
Authors: T. Butler, J. Jakeman, T. Wildey
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2810998233