Description

Many problems in science and technology, involving understanding, forecasting and control of physical systems, are addressed by constructing complex mathematical models of the physical system in question, for example climate models are used to analyse climate and cosmological hydrodynamic models are used to analyse galaxy formation.

However often these mathematical models, referred to as simulators, are extremely complex, have to be evaluated on a computer, and can take significant time to complete a single evaluation, taking from minutes to days to even weeks in some cases. To fully explore the behaviour of such a slow model, and to understand its response to changes in the input parameters of the model, is an extremely challenging task, but one that confronts many major research groups across a range of scientific disciplines (e.g. climate, cosmology, systems biology, geology, energy systems, environmental modelling and disease modelling).

A strategy to solve the above problem involves the construction of a Bayesian Emulator: a Bayesian statistical construct that mimics the expensive simulator, but which is often several orders of magnitude faster to evaluate. The emulator is used to explore the model’s behaviour and in any other downstream calculations, such as determining the input parameters that provide acceptable fits to observed data.

Often there are known physical attributes of the model such as various monotonicities, derivative information, and boundary information in addition to informative results from lower resolution models.

In the project, the students will learn the very powerful technique of Bayesian emulation, apply this to various models starting with models of gene networks in systems biology, and then explore efficient ways of including the extra physical attributes described above to greatly increase the power of the emulation methodology.

Prerequisites

Resources

For an introduction to Bayesian emulation as applied to a complex model of Galaxy Formation see our paper entitled "Galaxy Formation: Bayesian History Matching for the Observable Universe" which can be found at Statistical Science Volume 29, No 1.

An excellent web-site which describes (in sometimes overwhelming detail!) the types of analyses which this project gives an introduction to is:

The MUCM Web-site

This is the web-site for the Managing Uncertainty in Complex Models (MUCM) project, a consortium in which we were involved, (with the Universities of Sheffield, Aston, LSE and Southampton). There are an enormous number of links to follow at this site. One in particular, which gives an introduction to emulation, is:

O'Hagan, A. (2006). Bayesian analysis of computer code outputs: a tutorial. Reliability Engineering and System Safety 91, 1290–1300.

See also the MUCM toolkit for a detailed list of emulation and History Matching related techniques and tools.