This research is focused on reference Bayesian methods (Bayesian inference with prior distributions chosen by some formal rule), mixture models, Bayes factors, and causal inference, with an emphasis on hierarchical models (including classical mixed models and their generalizations). Both parametric and nonparametric or semiparametric models are studied. Many of the results are obtained by asymptotic methods, but ``exact'' computation (typically via simulation) also play a substantial role.
Elaboration of simple statistical models has been a major theme in the discipline in the latter part of this century. Previously, models have involved a small number of parameters, the values of which have been determined from observed data. With increased computing power, more complicated statistical models involving many more parameters have become central to much current statistical activity. Yet, despite recent progress, fundamental issues remain. This research is motivated in part by problems in statistical genetics, cognitive neuroscience, and the study of criminal behavior.
