A bayesian approach to a reliability problem: Theory, analysis and interesting numerics

We consider approximate Bayesian inference about the quantity R = P [$Y_{2}>Y_{1}$] when both the random variables Y1,Y2have expectations that depend on certain explanatory variables. Our interest centers on certain characteristics of the posterior of R under Jeffreys's prior, such as its me...

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Bibliographic Details
Published in:Canadian journal of statistics 1997-06, Vol.25 (2), p.143-158
Main Authors: Guttman, Irwin, Papandonatos, George D.
Format: Article
Language:English
Subjects:
Approximation
Artificial satellites
Bayesian inference
Datasets
Estimate reliability
Estimators
Integration tables
Numerical integration
Random variables
Reliability
Simulation
Statistical variance
Steels
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Summary:We consider approximate Bayesian inference about the quantity R = P [$Y_{2}>Y_{1}$] when both the random variables Y1,Y2have expectations that depend on certain explanatory variables. Our interest centers on certain characteristics of the posterior of R under Jeffreys's prior, such as its mean, variance and percentiles. Since the posterior of R is not available in closed form, several approximation procedures are introduced, and their relative performance is assessed using two real datasets. /// Nous considérons l'inférence Bayesienne approximative pour la quantité R = P [$Y_{2}>Y_{1}$], lorsque les deux variables aléatoires Y1,Y2ont des espérances qui dépendent de certaines variables explicatives. Notre intérêt se centre sur certaines caractèristiques de la loi a posteriori de R correspondant à une loi a priori de Jeffrey, telle que sa moyenne, sa variance et ses percentiles. Etant donné que la loi a posteriori de R n'est pas disponible sous forme explicite, nous proposons plusieurs procédures d'approximation et nous évaluons leur performance relative en utilisant deux ensembles de données réelles.
ISSN:0319-5724
1708-945X
DOI:10.2307/3315728