Bayes Linear Methods
Bayes linear methods offer a systematic way of analysing uncertainty, based on the combination of statistical data and a linear analysis of limited aspects of expert judgements. Similar in spirit to other Bayesian approaches, it is often more straightforward to apply to complex problems. The approach addresses fundamental practical and philosophical issues about learning based on partial knowledge. To implement the rich mathematical theory underlying this methodology, we have developed a general purpose programming language, which handles large practical applications by using graphical models to analyse and display information flow. You can find out more about the development of Bayes linear methods at Durham by accessing the Bayes linear methods home page.Bayes linear methods home page
[B/D] - The Bayes linear computer programming language
We are particularly interested in substantial research problems, arising from our contacts with other academic departments and with industry. Current projects include: computer experiments for history matching and forecasting for hydrocarbon reservoirs; applications of Bayes linear methods to problems in oil and gas pipeline technology; sales forecasting in large competitive markets; industrial experimentation for quality control; collaborations with engineers developing hip replacements; with archaeologists using spectrometry to determine object composition; with medical physicists on measurement problems in dermatology; with geologists on exploring the environmental impact of pesticides; new approaches to software testing using Bayesian graphical models, collaborating with computer scientists and industrial collaborators; medical applications with Accident and Emergency departments in North-Eastern hospitals.Bayesian Methods for Large Physical Systems Project Homepage
Software Testing Project Homepage
Robust Analysis of Designed Experiments
Anomalous behaviour in data from designed experiments is common and can seriously affect their classical analysis. In particular, outliers or, more generally, one or a few extreme interaction effects in an interaction sub-table can distort the corresponding interaction line and other lines of the analysis of variance table appropriate to an experiment, possibly resulting in totally misleading conclusions. Such an interaction effect could be an important discovery, but least squares analysis may result in its distinctive nature being undetected and/or distorting other parts of the analysis. Robust methods are tailored to detect, highlight and accommodate such unusual behaviour.
Complex Stochastic Systems and Statistical Physics
Interaction between components of large systems often results in complex behaviour and new phenomena, e.g. phase transitions. Many of the phenomena can be successfully analysed with a probabilistic approach. We are interested in applications including percolation, random walks in random environment, various lattice models of statistical mechanics such as dependent percolation and interacting particle systems.
Applied Probability and Operations Research
The probability group here is actively involved in research in many areas of probability and its applications. We have an active interest in Markov processes including: random walks on complexes and random walks in random environment with particular interest in explicit conditions for stability and transience; branching processes and branching random walks.
We also work on applications of this theory to operations research topics including: control of queueing systems; admission and routing problems in communications networks; search and other Markov decision problems.
Research interest is in a wide range of topics within reliability modelling and demonstration, and related statistical inference, including imprecise probabilistic methods.
Nonparametric Predictive Inference
Nonparametric predictive inference provides a newly developed statistical method for inference using only few structural assumptions. Novel solutions to both statistical and Operational Research problems have been developed recently, resulting in publications on, e.g., multiple comparisons, Bayes' problem, survival analysis with right-censored data, queuing, and a variety of replacement problems. Work in progress includes comparison of proportions data, multinomial data, and opportunity-based replacement.
Some transient Markov chains seem to settle down to an equilibrium long before the inherent unstable or evanescent behaviour becomes manifest. This phenomenon is called quasi-stationary behaviour of a Markov chain and has applications in biology, chemistry and telecommunication systems.
Adaptive replacement and maintenance strategies based on nonparametric predictive inference
Nonparametric predictive inference (NPI) is a recently developed statistical approach using few structural assumptions in addition to data. Application of such inferential methods for lifetimes of units enables fully adaptive strategies for replacement and maintenance. In particular, we are concentrating on the developing and analysing of NPI-based strategies for (opportunity-based) age-replacement.
Smoothing of complex data structures
Research interest is in the development of smoothing methods for complex (i.e. branched, high-dimensional, clustered) data structures as found e.g. in astrophysics, traffic engineering (simple example: speed-flow diagrams) and the environmental sciences. The methods employed include local smoothing and partitioning techniques, principal curves, and approaches to multi-valued nonparametric smoothing.
Other areas of methodology
These include: modelling and inference for spatial phenomena; time series analysis and forecasting; statistics in the earth sciences; foundations of statistical inference and decision making; survival analysis; expert judgements and uncertainty; statistical selection.