Prof. Yuefeng Wu
Department of Mathematics and Computer Science, University of Missouri-St.Louis
Title :
Hellinger Distance and Bayesian Non-Parametrics:
Hierarchical Models for Robust and Efficient Bayesian Inference
Date and Time: February 3, 2014 - 11:00am to 12:00pm
Location: Cupples I, Room 113
Abstract:
A hierarchical framework is introduced to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a
prior over non-parametric densities with the exponential of twice the Hellinger distance between a candidate and a parametric
density. By incorporating a prior over the parameters of the second density, we arrive at a hierarchical model in which a
non-parametric model is placed between parameters and the data. The parameters of the family can then be estimated as
hyperparameters in the model. In frequentist estimation, minimizing the Hellinger distance between a kernel density estimate and a
parametric family has been shown to produce estimators that are both robust to outliers and statistically efficient when the
parametric model is correct. We demonstrate that the same results are applicable when a non-parametric Bayes density estimate
replaces the kernel density estimate. We then demonstrate that robustness and efficiency also hold for the proposed hierarchical
model. The finite-sample behavior of the resulting estimates is investigated by simulation and on real world data.