Uncertainty Quantification and Decision Support for Complex Model Chains - Mathematics - EPSRC DTP funded PhD Studentship

Project Description

Complex and computationally expensive numerical models are used to help address some of the most important challenges faced by society, business and policy makers today. Uncertainty quantification (UQ) is an area of research within statistics that aims to develop methods for understanding what these models can tell us about the real world in order to assist decision making under uncertainty. In particular, many of the input parameters for these models are uncertain, leading to uncertain model output that can be combined using statistical models with observations and further structural understanding to say something about reality for decision makers.

For complex problems, often models must be combined in chains. For example, a global climate model under a future CO2 profile gives output that can be used as the input to a regional climate model. The outputs of this model can be used to drive rain runoff models and water management models that are needed to help decision makers in water planning. When standard UQ methods are applied naively to model chains, the uncertainty cascades and blooms so that, at the end of the chain, where the decision lies, the uncertainty is too great to be useful to decision makers. This project will develop new methods to restrict this uncertainty bloom. The approach will involve first reducing the number of inputs across the chain to those considered to be “decision critical” and the first phase of the PhD will develop methods for identifying decision critical elements of the chain. The next phase will look to constrain the uncertainty of these chain elements specifically using observations and Bayesian calibration methods. The final phase, having quantified uncertainty will look to develop decision support tools for model chains.

The methods will be developed using a model chain provided by Dstl for responding to chemical and biological hazards linking: a hazard plume model, a meteorological model, models for building ventiliation and exposure risk models in order to help decide how to respond to the releasing of such a hazard (e.g. evacuate and in which direction, or remain in place).

The successful applicant will join a world-leading group in uncertainty quantification comprising 10 researchers, including academics, postdoctoral researchers and PhD students.

Entry Requirements

You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in mathematics (or equivalent) with a substantial statistical component. Experience in programming with R and with Gaussian processes is desirable.

If English is not your first language you will need to meet the English language requirements and provide proof of proficiency.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes. If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.