Theme: Bayesian Inference & Data Assimilation
Course Title: Computational Algorithms for Bayesian Statistics

Lecturer: Dr Chris Drovandi

Course Content
Statistical inferences in a Bayesian framework are obtained through the posterior distribution, which quantifies the uncertainty in model parameters based on information from observed data and prior knowledge. To make these inferences it is often necessary to generate samples from the posterior distribution, but this can generally not be done perfectly. During the Winter School you will have already been introduced to one of the foundational methods, Markov chain Monte Carlo (MCMC), for approximate sampling from the posterior. This part of the Winter School will describe some more advanced MCMC methods that are more efficient when the posterior distribution has a complex landscape to traverse. An alternative and complementary method to MCMC called sequential Monte Carlo (SMC) will also be covered. SMC methods are easier to adapt than MCMC, are more suitable to implementation on parallel computing devices and can straightforwardly estimate quantities required to compare models in a Bayesian framework. The methods will be illustrated with MATLAB code.

Course delivery

3 x 1.5 hr Lectures

1 x 1 hr Computer Lab

Background Reading

An undergraduate course in statistical inference (the concept of a likelihood function and parameter estimation). An introductory knowledge of Bayesian statistics would also be desirable.

Read sections 4, 7, 8, 9, 10.   Read section 1, if interested.

Course Title: Data Assimilation: A Mathematical Introduction

Lecturer: Dr Kody Law

Course Content
These lectures will provide a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically we will develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms. Explicit calculations, numerical examples, and exercises and matlab code will be provided in order to illustrate the theory. The lectures will also include an introduction to some state-of-the-art algorithms.

Background Reading