LMS short course: Introduction to the Bayesian approach to inverse problems


11 May, 2017


University of Edinburgh
7 George Square
Room F.21


A picture of Edinburgh.


Uncertainty Quantification (UQ) is an interesting, fast growing research area aimed at developing methods to address the impact of parameter, data and model uncertainty in complex systems. In this course we will focus on the identification of parameters through observations of the response of the system - the inverse problem. The uncertainty in the solution of the inverse problem will be described via the Bayesian approach. We will derive Bayes' theorem in the setting of finite dimensional parameter spaces, and discuss properties such as well-posedness, statistical estimates and connections to classical regularization methods. We will briefly examine the extension of the Bayesian approach to the infinite dimensional setting. The remainder of this course will be devoted to algorithms for the efficient approximation of the solution of the Bayes inverse problem. We will give a detailed discussion on Monte Carlo methods in this context, and review alternative approaches such as multilevel Monte Carlo and Markov-chain Monte Carlo.

Expected Audience

PhD and MSc students, and other researchers with a maths-based degree (e.g. mathematics, statistics with maths component, computer science, physics, engineering etc), as the focus of the course is on theory and algorithms.



9:15 - 10:30 Mathematical Foundations of Bayesian Inverse ProblemsDr Claudia Schillings
11:00 - 12:00 Well-posedness and Statistical Estimates in Bayesian Inverse ProblemsDr Claudia Schillings
12:00 - 13:00 Lunch Break
13:00 - 14:15 Convergence Properties of Ratio Estimators for Posterior ExpectationsDr Aretha Teckentrup
14:45 - 15:45 Convergence Properties of Markov-chain Monte Carlo Estimators for Posterior ExpectationsDr Aretha Teckentrup
16:00 - 16:45 Discussion on Current Research DirectionsLed by Dr Claudia Schillings and Dr Aretha Teckentrup

Lecture Slides

Here are some of the lecture slides from the course: Part 1; Part 2: Algorithms, Lecture 3; Part 2: Algorithms, Lecture 4.


Registration is free - please register here. The deadline for registration is 4 May, 2017.