JSM 2005 - Toronto

Abstract #304612

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 64
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #304612
Title: Bayesian Semiparametric Inference Based on Ranks in Linear Models
Author(s): Xiaojiang Zhan*+
Companies: Merck & Co., Inc.
Address: 1312 Forest View Dr, Avenel, NJ, 07001, United States
Keywords: linear models ; Bayesian analysis ; robust estimate ; rank estimate
Abstract:

When prior information exists, it would be desirable to incorporate it in the data analysis, even when we are using robust rank-based methods. We discuss the implementation of nonparametric rank-based procedures in the Bayesian context. We summarize the information in a sample of data via the distribution of rank-based quantity and use that distribution as a pseudo-likelihood. Meanwhile, we suppose a prior distribution for the parameter(s) of interest in the unknown function. By Bayes' theorem, we can obtain the complete posterior distribution (or the posterior distribution up to a normalizing constant) of the parameter(s) given the rank-based quantity. Statistical inference then proceeds based on this posterior distribution. Current applications are one-sample and two-sample location models as well as linear models. In this presentation, we focus on the application to linear models, especially the linear regression model.


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Revised March 2005