Trans-Dimensional Markov Chain Simulation for both Bayesian and Classical Model Determination

The proposed programme of research is intended to construct, investigate, develop and apply a range of novel model exploration techniques that can be used to either select or average over competing models. These methods will be based upon the idea of simulating Markov chains capable of moving between states of different dimensions corresponding to competing models under consideration. Whether the aim is to locate modes or explore model space more generally, these methods will be applicable under any statistical philosophy and will facilitate investigation of the increasingly complex (yet realistic) models required by modern science.Under the proposed programme of research, we will demonstrate the utility of these new simulation methods over a wide range of application areas that will be used to motivate and direct methodological developments. Particular areas of application include time series modelling of archaeological and geological data; analysis of epidemiological data associated with a variety of diseases of political, economic and biological importance; and variable selection in economic modelling. In each of these areas, it is intended that our work will provide significant advances in the scientific understanding of the stochastic processes under study.