Research

My primary research interest is in the field of applied statistics. I am especially interested in real-world applications and working with clients to leverage statistical methods to solve genuine problems. This interest began with work during my PhD on the analysis of orthopaedic outcome data and investigating effective methods to communicate the results to clinicians, and has developed through subse- quent projects working on Bayesian belief network software for the charity Scope. More recently, I have been working with petroleum engineers on uncertainty analysis methods for petroleum reservoir flow simulations during the MUCM projects, and my present research on statistical methods for well-test analysis.

Deconvolution

My current research focus is the application of statistical methods to the problem of well-test analysis in petroleum engineering. The standard approach to well-test analysis is a simple numerical deconvolution procedure, which is limited by requiring prior parameter specifications, a lack of robust uncertainty statements on its results, and an inability to extend the theory to more advanced problems. My work in this area has been to re-interpret the problem as a statistical one, to develop methods for estimation of the required parameters, to develop an uncertainty quantification methodology, and to expand the underlying mathematical theory to permit the investigation of more complex well tests involving multiple wells and interference between wells.

Managing Uncertainty in Complex Models

My second research interest is in uncertainty analysis for complex systems whose behaviour is described by a computer simulation. Using the computer simulation as an inexpensive surrogate for the complex system and a careful specification of the relationships between the simulator, the system and reality, inferences can be made about the behaviour of the real-world system and its parameters. My particular areas of interest in this work was the development of methodology for linking computer simulations of different quality. Much of the work in this area was performed at Durham University collaboratively with Prof Michael Goldstein as part of the Managing Uncertainty in Complex Models (MUCM) project, and its successor project MUCM2. A key aspect of the MUCM projects was that the computer models that were multi-disciplinary and studied in partnership with other disciplines within academia, the public sector, and industry.

Other Interests

Several topics naturally intersect these these themes and are also of interest to me. First, statistical computation and programming are essential for any analysis of any problem of realistic size and complexity. Consequently, I have a keen interest in statistical programming. Second, creating effective visualisations for data and results are crucial to communicating important features and findings, and are particularly relevant in high-dimensional and high-complexity problems. Thus statistical graphics and visualisation is a topic that I find both interesting and valuable. Finally, through my work on the analysis of orthopaedic outcome data and high-dimensional computer models, I have also developed an interest in variable selection, dimension reduction techniques, and graphical models.

Links

Contact Information

Dr J. A. Cumming
Department of Mathematical Sciences
Durham University
Science Laboratories
South Road
Durham DH1 3LE
UNITED KINGDOM

Phone: +44 (0)191 3343124
Fax: +44 (0)191 3343051

Office: CM306

Email: