Bayesian Statistics Seminar
North Carolina State University
presents
NAME: Dr. Anirban Bhattachary
AFFILIATION: Duke University
Title: Bayesian Shrinkage
Abstract:
Penalized regression methods, such as L1 regularization, are
routinely
used in high-dimensional applications, and there is a rich
literature
on optimality properties under sparsity assumptions. In
the Bayesian paradigm,
sparsity is routinely induced through
two-component
mixture priors having a probability mass at zero, but
such
priors encounter daunting computational problems in high
dimensions.
This has motivated an amazing variety of continuous
shrinkage priors,
which can be expressed as global-local scale
mixtures
of Gaussians, facilitating computation. In sharp contrast to
the
corresponding frequentist literature, very little is known about
the
properties of such priors. Focusing on a broad class of shrinkage
priors,
we provide precise results on prior and posterior
concentration.
Interestingly, we demonstrate that most commonly used
shrinkage priors,
including the Bayesian Lasso,
are suboptimal in
high-dimensional
settings. A new class of Dirichlet-Laplace (DL)
priors
are proposed, which possess optimal concentration and lead to
efficient
posterior computation exploiting results from normalized
random
measure theory.
ABSTRACT: TBA
Thursday, April, 25, 2013
4:00 - 5:00 pm
1108 SAS Hall