Abstract Details
Activity Number:
|
364
|
Type:
|
Contributed
|
Date/Time:
|
Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
|
Sponsor:
|
Section on Bayesian Statistical Science
|
Abstract - #309245 |
Title:
|
General Inequalities for Gibbs Posterior with Nonadditive Empirical Risk
|
Author(s):
|
Cheng Li*+ and Wenxin Jiang and Martin A. Tanner
|
Companies:
|
Northwestern University and Northwestern University and Northwestern University
|
Keywords:
|
Gibbs posterior ;
GMM ;
model selection ;
oracle inequalities ;
ranking ;
risk minimization
|
Abstract:
|
The Gibbs posterior is a useful tool for risk minimization, which adopts a Bayesian framework and can incorporate convenient computational algorithms such as Markov chain Monte Carlo. We derive risk bounds for the Gibbs posterior using some general nonasymptotic inequalities, which leads to nearly optimal convergence rates and optimal model selection to balance the approximation errors and the stochastic errors. These inequalities are formulated in a very general way that does not require the empirical risk to be a usual sample average over independent observations. We apply this framework to studying the convergence rate of the GMM (generalized method of moments) and deriving an oracle inequality for the ranking problem, where models are selected based on the Gibbs posterior with a nonadditive empirical risk.
|
Authors who are presenting talks have a * after their name.
Back to the full JSM 2013 program
|
2013 JSM Online Program Home
For information, contact jsm@amstat.org or phone (888) 231-3473.
If you have questions about the Continuing Education program, please contact the Education Department.
The views expressed here are those of the individual authors and not necessarily those of the JSM sponsors, their officers, or their staff.
Copyright © American Statistical Association.