DescriptionMany 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. However, to use such models for understanding, prediction and subsequent decision making, a full (Bayesian) uncertainty analysis should be performed, a process now referred to as ``Uncertainty Quantification". However, many of these scientific models are complex, take significant time to evaluate and have several unknown input parameters. The large evaluation time in particular precludes the use of standard Bayesian approaches for parameter inference and prediction. 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 (now very popular across statistics and machine learning). Emulators can then be used to perform all the required Bayesian calculations, for example History Matching: a process of searching for all input parameter choices which give acceptable matches to observed data, an award winning method that has been successfully applied across a wide variety of scientific areas. In this project the student will learn how to construct emulators and perform History Matching and investigate advances to the standard versions of these two techniques. There will be some freedom in terms of which advances they examine, but possibilities are the construction of emulators that can handle discontinuities, boundary conditions and derivative information, and improvements to designing sets of runs for history matching or for Bayesian optimisation (a very important area where emulators are used to optimise some output of interest of the scientific model). This project will link to continuing work in the Statistics group in the Dept. of Mathematical Sciences, which is actively engaged with several UK wide modelling efforts in the areas of galaxy formation, geological modelling, epidemiology and systems biology.
PrerequisitesStatistical Inference II
ResourcesFor an introduction to History Matching 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. An excellent web-site which describes (in sometimes overwhelming detail!) the types of analyses which this project gives an introduction to is: 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.
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email: Ian Vernon