Breadcrumb
Interacting particle algorithms: theory and methodology
Supervisor: Nick Whiteley
Theme: Monte Carlo Computation
Interacting particle algorithms form one class of Monte Carlo method. They involve the simulation of a population of random samples, which mutate and interact over time, in order to approximate sequences of probability distributions arising as part of numerical integration and optimisation tasks. The algorithms have a rich probabilistic structure arising from this mutation/interaction process, which resembles simple models of genetic evolution. At the same time, this process has various practical benefits and the implementation of these algorithms can exploit cutting edge developments in parallel computing. This makes interacting particle algorithms powerful tools, especially in the context of statistical inference, where numerical integration and optimization problems abound.
There are various open questions regarding the theoretical structure of interacting particle algorithms and many challenges remain in the development of new algorithmic ideas. The aim of research in this area is to answer mathematical questions about the properties of these algorithms and contribute, ultimately, to the understanding and development of algorithms which are of practical value. Especially important and interesting topics include the analysis of how the stochasticity present in the algorithm manifests itself in the answers the algorithm provides, and how related phenomena behave over time and as the size of the population increases. This brings together elements of probability theory and statistics, connecting abstract concepts with statistical problems from the real world. It involves a combination of methodology, developing new algorithmic techniques, and theoretical study, analyzing asymptotic and other properties of the algorithms. Relevant topics which students may have already encountered in probability theory include Markov chains and martingales, and from statistics include Bayesian modelling and inference, and likelihood-based methods.