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Nonparametric Bayes estimation in repair models
Authors:Jayaram Sethuraman  Myles Hollander
Institution:Department of Statistics, Florida State University, Tallahassee, FL 32306-4330, USA
Abstract:Consider a sequence of dependent random variables X1,X2,…,XnX1,X2,,Xn, where X1X1 has distribution F (or probability measure P  ), and the distribution of Xi+1Xi+1 given X1,…,XiX1,,Xi and other covariates and environmental factors depends on F   and the previous data, i=1,…,n-1i=1,,n-1. General repair models give rise to such random variables as the failure times of an item subject to repair. There exist nonparametric non-Bayes methods of estimating F in the literature, for instance, Whitaker and Samaniego 1989. Estimating the reliability of systems subject to imperfect repair. J. Amer. Statist. Assoc. 84, 301–309], Hollander et al. 1992. Nonparametric methods for imperfect repair models. Ann. Statist. 20, 879–896] and Dorado et al. 1997. Nonparametric estimation for a general repair model. Ann. Statist. 25, 1140–1160], etc. Typically these methods apply only to special repair models and also require repair data on N independent items until exactly only one item is left awaiting a “perfect repair”.
Keywords:Bayes methods  Dirichlet distributions  General repair models  Partition-based priors  Partition-based Dirichlet priors
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