Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification: Extensions to L^p

2020/01/13 by Troy Butler, Butler, Troy, Timothy Wildey +4
Computer Science · Decision Sciences · Mathematics · #Applied mathematics #Combinatorics #Convergence (economics) #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Geometry #Inverse #Inverse problem #Mathematical analysis #Mathematics #Numerical Methods and Algorithms #Polynomial #Probabilistic and Robust Engineering Design #Probability (math.PR) #Sequence (biology) #math.PR

paper · pdf · doi:10.48550/arxiv.2001.04369

published in arXiv (Cornell University) (Cornell University)

arxiv created 2020/01/13 · openalex publication_date 2020/01/13 · arxiv updated 2020/01/14 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28

Abstract

A previous study analyzed the convergence of probability densities for forward and inverse problems when a sequence of approximate maps between model inputs and outputs converges in L^∞. This work generalizes the analysis to cases where the approximate maps converge in L^p for any 1≤ p < ∞. Specifically, under the assumption that the approximate maps converge in L^p, the convergence of probability density functions solving either forward or inverse problems is proven in L^q where the value of 1≤ q

Citations

• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• The Homogeneous Chaos

Related

• Spectral convergence of probability densities for forward problems in uncertainty quantification
• Density Estimation in Uncertainty Propagation Problems Using a Surrogate Model
• Sampling Methods for Bayesian Inference Involving Convergent Noisy Approximations of Forward Maps
• Inverse problems and uncertainty quantification
• Inverse Problems in a Bayesian Setting