Computer intensive statistical methods

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R is an open source implementation of the S programming language. As a member of the "R Core Team", I share authorship in it. My particular interests are in user interface issues and graphics. In particular, in one effort I am working on improving the connections between the internals of R and the source code created by the user: this will improve the usability of R and will enable studies of programmer performance. Another ongoing effort is the incorporation of 3D graphics into R, through the rgl package. In previous work, colleagues at the University of Toronto and I have shown how to evaluate the significance of millions of genetic tests in a computationally efficient way. Currently with one student I am investigating two related ideas: approximation of conditional significance, and approximation of multiple testing combinations. Another student and I are looking into choosing the most economical but informative model. A third focus of my work will be perfect simulation. Markov chain Monte Carlo is a general computational technique for sampling from an arbitrary distribution (e.g. a posterior distribution in Bayesian inference). Until late 1995, it was thought that in almost all cases this would yield samples with distributions only approximating the target distribution. Propp and Wilson (1996) showed that in some cases it is possible to get exact samples; my work and work with Green several years ago extended this to distributions on continuous and unbounded state spaces. Moreover, Propp and Wilson's ideas can be extended to other contexts such as perfect simulation of stochastic diffusions that follow stochastic differential equations. Another student and I are developing perfect simulations of maxima, minima, and barrier crossing times for "stochastic diffusions", models which are commonly used in financial modelling.