Bayesian statistical computation, methodology, and applications

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Numerous applications of statistics in fields ranging from marketing, to analysis of the human genome, to cosmology deal with large amounts of data and with complex phenomena. Analysing such data is statistically and computationally challenging - naive approaches may not obtain the benefit that is possible from such data, or may produce invalid results. I use what is known as the "Bayesian'" approach to statistics to tackle such problems. In this approach, we first must formulate an appropriate model, that defines all the possibilities for what the underlying phenomenon is like, and how likely we think each is. We must then perform the computations needed to integrate the information from the observed data into this model, in order to reach conclusions or make predictions. Much of my research will be on improved methods for performing such computations, mostly based on the method of "Markov chain Monte Carlo". My aim is, on the one hand, to make it possible to tackle problems that could previously not be solved, and on the other hand, to make it easier for statisticians to routinely solve simpler problems, allowing them to concentrate on statistical issues without being distracted by computational issues. I also plan to work on improving the Bayesian approach in general, as well as on Bayesian methods that are specific to particular applications, such as analysis of the human genome.