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Details of Grant 

EPSRC Reference: EP/K005723/1
Title: Information geometry for Bayesian hierarchical models
Principal Investigator: Byrne, Dr SPJ
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Open University University of Cambridge
Department: Statistical Science
Organisation: UCL
Scheme: EPSRC Fellowship
Starts: 31 March 2013 Ends: 30 November 2015 Value (£): 237,546
EPSRC Research Topic Classifications:
Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
01 Aug 2012 EPSRC Mathematics Fellowships - August 2012 Announced
04 Jul 2012 Mathematics Prioritisation Panel Meeting July 2012 Announced
Summary on Grant Application Form
Modern society is deluged by data. We systematically digitally record and store everything from the seemingly mundane, such as search engine queries, to the valuable and important, such as health care records. The volume of recorded data is only set to increase as technologies such as personalised genome sequencing, which records the six billion base pairs that make up each individual's genome, become commonplace. The challenge for statisticians is to convert this torrent of data into useful and useable information.

Statistics is usually taught as a collection of disparate prescriptive techniques-t-tests, analysis of variance, time series, etc.-which can give the impression that each statistical problem falls nicely into one of these categories. Of course this is false: every practical problem has its own particular features, and failing to take these into account can lead to biased or misleading conclusions.

In recent years, a more powerful analytical approach has been developed, known as Bayesian hierarchical modelling. These models are constructed in a modular fashion, each component chosen to accurately represent pertinent features of the statistical problem, which are then built into a larger model, forming a hierarchy. As a result, the model is specifically tailored to the problem at hand, leading to more accurate inferences and predictions. Hierarchical models have been applied with great success in a wide variety of areas, including identifying the complicated factors that affect voter behaviour in political science, instrument calibration in engineering, ecological modelling of species populations, and the monitoring and predicting of outcomes in healthcare policy.

However, as these models get larger and more detailed, the calculations required to implement them become increasingly complicated and computationally intensive. The aim of this fellowship is to develop theory and methods to make hierarchical modelling feasible for larger and more complex situations.

I will apply the mathematical tools and techniques of curvature, known as differential geometry, by interpreting the model as a smooth curved surface called a manifold-think of a rubber sheet that has been twisted, poked and pulled in different places. These computational difficulties then correspond to regions of this surface that are highly curved. I can then adapt various techniques that have been developed for related geometric problems, such as numerical Hamiltonian integrators, in order to construct efficient algorithms that twist, poke and pull this surface into a shape that is more amenable to computation.

This research will provide both theoretical developments on which other statisticians can build, as well as practical tools and techniques which applied researchers will be able to use. Such advances will help change our current "data age" into a true "information age".

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