Bayesian inference provides a way of drawing conclusions about a system, such as climate or financial markets, by combining new evidence with prior knowledge. This project aims to develop a method for optimising algorithms that utilise Bayesian inference and related ‘Markov chain Monte Carlo’ methods.
Explaining the science
Bayesian inference is often the preferred methodological approach for researchers in modelling genomics, infectious diseases, climate, financial markets, and many others. It provides a way of combining new evidence with prior beliefs – after observing some evidence, the resulting output or ‘posterior distribution’ of a model can then be treated as an input or ‘prior distribution’, and a new posterior distribution can be computed from new evidence, and so on.
These posterior distributions are often explored using Markov chain Monte Carlo (MCMC) algorithms. Monte Carlo methods are a broad class of computational algorithms that rely on repeated, random sampling to obtain numerical results. Markov chains are algorithms used for working with a series of events (for example a system being in particular states) to predict the possibility of a certain event based on what other events have happened. Used in conjunction, MCMC methods approximate the posterior distribution of a parameter of interest through random sampling.
MCMC methods include the Metropolis-Hastings, the Metropolis Adjusted Langevin algorithm, the Gibbs sampler, Hybrid Monte Carlo, or the slice sampler. However, in modern high-dimensional applications, off the shelf versions of these algorithms often need extensive tuning for optimised performance, that are time consuming and require expert knowledge.
The project involves the development of adaptive MCMC. This is a way of designing self-tuning MCMC algorithms that learn about the target distribution as the sampling of data progresses and optimise parameters of the sampling algorithm accordingly.
The approach developed will allow for automated and reliable Bayesian inference in important applications such as genomics, infectious diseases, climate, and financial and industrial models.