Dr Patrick E McSharry

Mathematical Institute
University of Oxford
24-29 St Giles'
Oxford
OX1 3LB
UK

Tel: +44 1865 596778

Research

My research takes a multidisciplinary approach to modelling complex dynamical systems. Typical characteristics include non-normal distributions, nonlinear interactions and spatio-temporal dynamics. This research has practical predictive applications in quantifying risk and uncertainty for effective decision-making. The general aim is to construct parsimonious data-driven models from empirical observations. Information about the underlying dynamics, such as existing first-principle models or conservation laws, may be imposed to constrain the model class. This approach uses a diverse range of techniques from areas including time series analysis, signal processing, forecasting, operations research, data-mining and machine learning.

Methodology

Observations are invariably contaminated by measurement errors, leading to uncertainty in the data and structural errors in all models derived from this data. I am developing an approach that propagates this uncertainty through all the different levels of the modelling process in order to provide the end-user with the maximum amount of information available for decision-making. In particular, I have developed techniques for the construction and evaluation of probabilistic forecasts. Probabilistic forecasts are required for understanding the inherent uncertainty in the modelling process and have the additional value of providing estimates of the implied uncertainty. Furthermore, such forecasts are essential for risk management and the maximisation of utility functions.

Models and Techniques

The model structures employed are linear stochastic models such as ARIMA models and nonlinear models such as local polynomials, radial basis functions, neural networks, threshold auto-regressive (TAR) models and Markov switching models. Techniques used for classification, clustering and visualisation include k-means, self-organising maps, support vector machines and genetic algorithms.

Applications

Applications of this research include forecasting, classification, signal processing, fault detection and the analysis of biomedical, economic, energy and financial time series. Examples include:
(i) risk management in healthcare and energy sectors;
(ii) diagnosing, classifying and monitoring states of health/illness using non-invasive biomedical signals;
(iii) biomedical engineering (prediction and classification of epilepsy and heart disease),
(iv) telemedicine (influence of weather on asthma and self-management of diabetes);
(v) decision science (financial trading strategies, weather forecasting, risk management, forecasting hospital bed availability);
(vi) energy sector (forecasting demand, price dynamics);
(vii) systems biology (gene networks, biochemical reaction networks);
(viii) speech modelling (vocal fold dynamics, speech processing, patent pending);
(ix) fault detection and condition-monitoring (aircraft failure, reactor disruptions, nucleate boiling, medical disorders) and
(x) social science (policy optimisation for the World Bank and the analysis of human development indicators).