Bayesian Inverse Problems
This course covers the use of Bayesian methods for the solution of inverse problems. Students will learn the theory and practice of Bayesian methods for parameter identification in differential equations.
Instructor: Prof. Mark Asch
Term: Autumn
Location: INRIA, Pau
Course Overview
This course provides a comprehensive introduction to Bayesian approaches for solving direct and inverse problems. Students will:
- Learn the theoretical basis of Bayesian inference.
- Gain practical experience with Monte-Carlo Markov-Chain (MCMC) methods.
- Develop skills in uncertainty quantification.
- Apply Bayesian methods to solve direct and inverse problems.
Prerequisites
- Basic programming knowledge (preferably in Python)
- Introductory statistics
- Comfort with basic probability and statistics
Textbooks
- “Bayesian Data Analysis” by Murray Gelman, et al.
- “A Toolbox for Digital Twins” by Mark Asch
Grading
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1 | Introduction to inverse problems and data assimilation Overview of the key concepts. | ||
| 2 | Bayesian inverse problems Formulation and solution of stochastic inverse problems. | ||
| 3 | Posterior estimation methods Techniques for performing estimation of the Bayesian posterior. |