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Paper No. 11-31

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FJ Rubio and MFJ Steel

Bayesian Inference for P (X<Y) using Asymmetric Dependent Distributions

Date: November 2011

Abstract: This paper studies the Bayesian inference for µ = 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 whereX and Y are independent or dependent random variables. Dependencies between X and Y are modelled using a Gaussian copula. Noninformative benchmark priors are provided for both scenarios and conditions for the existence of the posterior distribution of µ 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.

Keywords: Bayesian inference; Gaussian copula; posterior existence; set observation; skewness; stress-strength model.