Jeffrey Hart

My interests include nonparametric function estimation, hypothesis testing in complex settings, time series analysis and Bayesian methods. Recently I have focused attention on inference problems involving a large number of small data sets. Suppose, for example, that the distribution of data within different small data sets is the same up to location and scale, with location and scale differing randomly from one data set to the next. I am interested in methods for estimating the distribution common to all data sets, and also the distribution of location and scale across data sets. I have considered both frequentist (minimum distance) and Bayesian methods for tackling this problem. Another problem involving a large number of small data sets is testing the equality of distributions across all data sets. This is like the classical k-sample problem, but with the key difference that instead of fixing k and allowing sample sizes to increase without bound, I let k tend to infinity with sample sizes fixed. Doing so leads to different and interesting asymptotics in this and other inference problems. I am also interested in simulation methods that involve generating many different models randomly rather than generating large numbers of data sets from just a few models. I call this approach BayesSim since the distribution from which models are selected is analogous to the prior distribution in Bayesian methodology.