At present, I am mainly interested in Bayesian inference in nonparametric statistics. Nonparametric models have the necessary flexibility to accommodate different types of data arising in practice. Bayesian approach has many attractive features, but what most appeals to me is its, in principle, the straightforward way of answering any inference problem by simply updating the prior opinion in the light of the sample data. In nonparametric problems such as density estimation, I evaluate the performance of Bayesian's posterior distribution for a given choice of prior in detecting the unknown true model as the sample size increases to infinity. Issues of consistency and the rate of convergence are addressed in my research. Choosing a prior in the nonparametric set up is never easy and a sensible default choice of the prior is often desirable. I suggested some general methods of construction of a default prior in the nonparametric set up such that the resulting posterior is consistent and has the best possible rate of convergence. Adaptation, namely achieving the right rate of convergence when one has competing models with different rates of convergences is one of the most important issues under study. I also studied the asymptotic behavior of the posterior distribution in non-standard parametric models such as the nonregular cases (where the density is not smooth) or when the dimension of the parameter under study increases to infinity with the sample size. In the first case, the asymptotics also helps find default priors. Normal approximations for the posterior distribution found in models with increasing dimension reduce the computational burden to a considerable extent.
Classified Research Topics:
Questions or comments to:
Subhashis Ghosal ghosal@stat.ncsu.edu
Revised November 15, 2001
Back to my home page