DescriptionThe ongoing Covid-19 crisis has had a deep impact on the whole world. In an attempt to understand, predict and ultimately control the Covid-19 outbreak, many mathematical models have been created that describe the major epidemiological processes thought to underpin Covid-19 transmission. These models can be deterministic or stochastic and can have varying levels of complexity. However, these models all contain several uncertain parameters that need to be explored in order to match the model output to observed data (e.g. on Covid-19 case rates or death rates), which itself involves several large uncertainties. The Bayesian paradigm can be used to address this problem, and hence aid our understanding and control of this serious disease. However, many Covid-19 models are complex and take significant time to evaluate. This precludes the use of standard Bayesian approaches for parameter inference. A solution to this problem is to use Bayesian emulators: a Bayesian statistical construct that mimics the slow Covid-19 model but which is often several orders of magnitude faster to evaluate. These are then combined to perform History Matching: a process of searching for all input parameter choices which give acceptable matches to observed data, a method that has been successfully applied across a wide variety of scientific areas including the analysis of climate models, galaxy formation simulations, oil reservoirs, models of systems biology and now epidemiology models of Covid-19. In this project the student will learn how to construct and simulate from simple models of Covid-19 of both deterministic and stochastic form. They will explore the behaviour of such models, develop model improvements, and then investigate the application of Bayesian emulation and History Matching techniques. Many extensions are possible including analysis of various interventions (e.g. lockdown), decision support and designing future data collection strategies. 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 designed to aid the UK's response to Covid-19.
PrerequisitesStatistical Concepts II and Statistical Methods III
ResourcesA good site that makes you aware of the standard traps modellers fall into is Epidemic Modelling 101: Or why your CoVID-19 exponential fits are wrong but do be aware that we will go much further than the models discussed here. For 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