Bayesian Analysis

Recent advances on Bayesian inference for $P(X < Y)$

Laura Ventura and Walter Racugno

Full-text: Open access

Abstract

We address the statistical problem of evaluating $R = P(X \lt Y)$, where $X$ and $Y$ are two independent random variables. Bayesian parametric inference is based on the marginal posterior density of $R$ and has been widely discussed under various distributional assumptions on $X$ and $Y$. This classical approach requires both elicitation of a prior on the complete parameter and numerical integration in order to derive the marginal distribution of $R$. In this paper, we discuss and apply recent advances in Bayesian inference based on higher-order asymptotics and on pseudo-likelihoods, and related matching priors, which allow one to perform accurate inference on the parameter of interest $R$ only, even for small sample sizes. The proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals. From a theoretical point of view, we show that the used prior is a strong matching prior. From an applied point of view, the accuracy of the proposed methodology is illustrated both by numerical studies and by real-life data concerning clinical studies.

Article information

Source
Bayesian Anal., Volume 6, Number 3 (2011), 411-428.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339616470

Digital Object Identifier
doi:10.1214/11-BA616

Mathematical Reviews number (MathSciNet)
MR2843538

Zentralblatt MATH identifier
1330.62157

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62F10: Point estimation

Keywords
Asymptotic expansions Frequentist coverage probability Matching prior Modified likelihood root Nuisance parameter ROC curve Stochastic precedence Stress-strength model Tail area probability

Citation

Ventura, Laura; Racugno, Walter. Recent advances on Bayesian inference for $P(X &lt; Y)$. Bayesian Anal. 6 (2011), no. 3, 411--428. doi:10.1214/11-BA616. https://projecteuclid.org/euclid.ba/1339616470


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