Uncertainty Quantification for Inverse Problems with Poisson measurement error

Authors

• John Bardsley, University of Montana, Missoula

Document Type

Presentation Abstract

Presentation Date

2-2-2026

Abstract

Inverse problems arise when physics-based models are fit to observational data. The unknown parameters in such models are often spatially distributed and become large-scale after discretization. These parameter estimation problems are typically ill-posed, meaning that solutions are unstable with respect to errors in the data. Regularization is the standard approach to mitigate this instability.

In this talk, I will focus on inverse problems where the data follows a Poisson distribution, a common scenario in imaging applications. I will demonstrate how to implement regularization in the Poisson noise case. Then, building on the connection between inverse problems and Bayesian statistics, I will reformulate the problem within a Bayesian inference framework. This allows for uncertainty quantification through the posterior distribution. I will then present a Markov chain Monte Carlo (MCMC) method for sampling from the posterior, enabling robust parameter estimation and uncertainty analysis.

Additional Details

February 2, 2026 at 3:00 p.m. Math 103

Recommended Citation

Bardsley, John, "Uncertainty Quantification for Inverse Problems with Poisson measurement error" (2026). Colloquia of the Department of Mathematical Sciences. 699.
https://scholarworks.umt.edu/mathcolloquia/699