Topics in computational Bayesian statistics

Overview

Bayesian statistics provide a framework for a statistical inference for quantifying the uncertainty of unknowns based on information pre and post data collection.

This information is captured in the posterior distribution, which is a probability distribution over the space of unknowns given the observed data.

The ability to make inferences based on the posterior essentially amounts to efficiently simulating from the posterior distribution, which can generally not be done perfectly in practice.

This task of sampling may be challenging for various reasons:

• The posterior distribution is irregular (e.g. multi-modal, non-normal and/or complex dependency structures between components).
• The likelihood function (the probability function of the data given unknowns) of the statistical model of interest may be expensive to compute.
• The likelihood function is intractable but can be estimated unbiasedly.
• The likelihood function is completely intractable but simulation from the model is feasible.
• The model involves a hierarchy of several levels and has a large number of parameters.
• There are several competing models of interest.

Research activities

Your project will develop new computational statistics algorithms to address one or more of these challenges.

A related problem is in optimal Bayesian experimental design, where the optimal value of controllable variables of an experiment needs to be determined in order to maximise the information contained in the posterior distribution.

This problem is at least an order of magnitude more computationally expensive than the Bayesian inference problem.

A project in this direction will develop new statistical algorithms to expand the class of problems for which it is computationally feasible to apply optimal Bayesian design.

There may be opportunities to collaborate with external institutions.

Outcomes

By the completion of this research topic you will:

• develop new statistical algorithms that are computationally efficient and implement them in relevant computer software
• discover new insights into challenging applications
• present results as journal articles.

Skills and experience

We expect our students to have the following necessary skills:

• stochastic modelling
• programming
• an understanding of statistical inference is highly desirable.

Keywords

• Bayesian statistics
• computational statistics
• data science
• statistical inference
• stochastic modelling
• parameter estimation

Contact

Contact the supervisor for more information.