MATJ5125 IP2: Introduction to Uncertainty Quantification for Inverse Problems (JSS34) (2 op)

In this course, we will explore how to formulate inverse problems within a Bayesian framework. This involves representing both noise and unknowns using probability distributions. We will then define the solution to the inverse problem as the conditional probability distribution of the unknown given the measurements, commonly known as the posterior distribution. Finally, we will examine how to interpret the posterior to quantify the uncertainty in our predictions and reconstructions.

Formulate an inverse problem with additive noise using a Bayesian framework.
• Identify appropriate prior distributions based on the problem context.
• Perform point estimation using maximum a posteriori (MAP) and conditional mean estimates.
• Implement the Metropolis-Hastings algorithm to explore the posterior distribution.
• Conduct uncertainty quantification to assess prediction reliability.

Basics of numerical and computational skills, coding in Python is mandatory; Basic knowledge of probability theory and statistics.