Description
Many major scientific disciplines now employ detailed mathematical models to describe complex physical systems of interest, for example, galaxy formation models are used to understand structure formation in our Universe, climate models are used to study and predict global warming, UK energy distribution models are used to plan to ensure the provision of sufficient UK power supply and epidemiology models are used to predict and control the development of epidemics such as Covid-19.
Often we wish to find input parameter settings that optimise features of these models, to guide real world decision making processes. For example, we use Covid models to find optimal intervention strategies to slow the pandemic, and we use climate models to optimise (in this case minimise) the damage caused by global warming. However, many of these scientific models are complex, take significant time to evaluate and have several input parameters to explore. The large evaluation time in particular makes optimisation far more challenging. A solution to this problem is to use a Bayesian emulator: a powerful Bayesian statistical construct, that mimics the slow scientific model but which is often several orders of magnitude faster to evaluate. Emulators can then be used to perform the optimisation, a process now known as "Bayesian Optimisation", a topic which has been generating great excitement in the fields of both statistics and machine learning. However, this raises several interesting challenges, such as how to design runs of the model so as to best optimise using a small number of model evaluations, and how we can be sure we have not missed alternative optima. The realisation that the model is only an approximation of the real world system, and that it may be used by decision makers with undisclosed utilities raises deeper questions still, undermining the meaning of the optima and suggesting more sophisticated strategies. In this project the student will learn how to construct emulators: powerful Bayesian tools for mimicking expensive models, and then learn to employ these to perform Bayesian Optimisation in various settings. They will investigate improved strategies of various types and then apply these to scientific models of interest.
Prerequisites
Statistical Inference II or Statistical Modelling II
Corequisites
Optional, but very helpful: Uncertainty Quantification IV
Resources
For an introduction to 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.
For more of a tutorial in building emulators see (the first half of the paper) entitled "Bayesian uncertainty analysis for complex systems biology models : emulation, global parameter searches and evaluation of gene functions", which can be found here.
A tutorial in some of the concepts around using emulators for optimisation can be found in the first half of "A Tutorial on Bayesian Optimisation" although don't worry about some of the more technical aspects: we will do things in a more efficient (and simpler!) way.