Bayesian Analysis

Neutral-data comparisons for Bayesian testing

Dan J. Spitzner

Full-text: Open access

Abstract

A novel approach to evidence assessment in Bayesian hypothesis testing is proposed, in the form of a "neutral-data comparison." The proposed assessment is similar to a Bayes factor, but, rather than comparing posterior to prior odds, it compares the posterior odds of the observed data to that calculated on "neutral" data, which arise as part of the elicitation of prior knowledge. The article develops a general theory of neutral-data comparisons, motivated largely by the Jeffreys-Lindley paradox, and develops methodology for specifying and working with neutral data in the context of Gaussian linear-models analysis. The proposed methodology is shown to exhibit exceptionally strong asymptotic-consistency properties in high dimensions, and, in an application example, to accommodate challenging analysis objectives using basic computational algorithms.

Article information

Source
Bayesian Anal., Volume 6, Number 4 (2011), 603-638.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339616538

Digital Object Identifier
doi:10.1214/11-BA623

Mathematical Reviews number (MathSciNet)
MR2869959

Zentralblatt MATH identifier
1330.62155

Keywords
Bayesian hypothesis testing Bayes factors Bayesian asymptotic-con-sistency model choice in high dimensions analysis of variance

Citation

Spitzner, Dan J. Neutral-data comparisons for Bayesian testing. Bayesian Anal. 6 (2011), no. 4, 603--638. doi:10.1214/11-BA623. https://projecteuclid.org/euclid.ba/1339616538


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