PLACE:  319 Snedecor

SPEAKER:
Tzee-Ming Huang
Department of Statistics, Carnegie Mellon University

TITLE:
Convergence Rates for Posterior Distributions

ABSTRACT:

The main goal of this thesis is to provide general theorems on convergence
rates of posterior distributions that can be applied to density estimation and
nonparametric regression. There have been other results on convergence rates of
posterior distributions, but what is new in this thesis is adaptive estimation.
The idea of adaptive estimation can be illustrated using an example: suppose
that the true density function or regression function is in a Sobolov space
with smoothness parameter s, then the optimal convergence rate for this
space in
the minimax sense is known to be n^-2s(1+2s). In previous results by others,
there are examples showing how to specify priors according to s in order to
achieve this optimal convergence rate. However, in the case where s is unknown,
we would like to have a prior that doesn't depend on s yet the corresponding
posterior distribution still achieves the optimal convergence rate
simultaneously for all s.  In such a case, we say that the posterior
distribution is adaptive. In this thesis, examples are given to show how
adaptive estimation can be achieved using the theorems provided here.
 
 
 

COFFEE: 3:45 p.m., 104 Snedecor