Probability and Statistics
The field of Probability and Statistics encompasses a broad array of topics in pure and applied mathematics, and has applications in almost every field of scientific research. The theoretical foundations of Probability Theory were developed in the early twentieth century by Kolmogorov and other workers, and this led to an explosion of applications in every scientific field. By its nature the field is driven by real-world applications, and this is reflected in the work of the members of the Probability and Statistics group, whose research ranges from applied Statistics to inter-disciplinary research to pure mathematics.
One major area of applications is Biostatistics and Bioinformatics. Adam Ding has worked on several problems in biostatistics, including the statistical analysis of data from HIV clinical trials, analysis of multiple correlated survival times and current status data in epidemiology, and the analysis of genetic micro-array data. Michael Maliuotov has developed probabilistic models of protein dynamics, and used them to analyse molecular diffusion in the human brain.
Another major direction of research concerns estimation problems, that is how to extract useful information from noisy data. Michael Maliuotov has worked on many aspects of this question, and some of his current research topics are: discrimination of close Markov chains; the EM algorithm; sequential search for significant variables. This work has applications in multi-target estimation in the presence of noise and clutter, and molecular dynamics of proteins. Adam Ding has analysed how neural networks can be used to predict and control noisy systems, and has worked on the High-dimensional Empirical Linear Prediction (HELP) system for quality control in industrial engineering.
Another area of current interest in the group is quantum computing and quantum information theory. In this area Chris King works on quantum channel capacity problems and the role of entanglement in noisy quantum systems.