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March 2013 Bayesian Inference for P(X<Y) Using Asymmetric Dependent Distributions
Francisco J. Rubio, Mark F. J. Steel
Bayesian Anal. 8(1): 43-62 (March 2013). DOI: 10.1214/13-BA802


This paper studies Bayesian inference for θ=P(X<Y) in the case where the marginal distributions of X and Y belong to classes of distributions obtained by skewing scale mixtures of normals. We separately address the cases where X and Y are independent or dependent random variables. Dependencies between X and Y are modelled using a Gaussian copula. Noninformative benchmark and vague priors are provided for these scenarios and conditions for the existence of the posterior distribution of θ are presented. We show that the use of the Bayesian models proposed here is also valid in the presence of set observations. Examples using simulated and real data sets are presented.


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Francisco J. Rubio. Mark F. J. Steel. "Bayesian Inference for P(X<Y) Using Asymmetric Dependent Distributions." Bayesian Anal. 8 (1) 43 - 62, March 2013.


Published: March 2013
First available in Project Euclid: 4 March 2013

zbMATH: 1329.62141
MathSciNet: MR3036253
Digital Object Identifier: 10.1214/13-BA802

Keywords: Gaussian copula , posterior existence , set observation , skewness , stress-strength model

Rights: Copyright © 2013 International Society for Bayesian Analysis


Vol.8 • No. 1 • March 2013
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