Chapter 16: A primer on solving PDE-based Bayesian inverse problems
Abstract
The next step in our study of Bayesian inverse problems is to consider computational methods. Before delving into details of such methods, it is instructive to consider some numerical illustrations. This is the goal of this chapter, which is similar in structure to the primer in Chapter 2. We again consider the problem of estimating the initial state in a one-dimensional heat equation. Focusing on the Bayesian formulation of this inverse problem, we provide some insight into the common steps in solving infinite-dimensional Bayesian inverse problems.
Fields of Study & Subjects
Numerical methods in inverse problems
Markov Chains and Monte Carlo Methods
Gaussian Processes and Bayesian Inference
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Pages
- 233–243
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Book chapter