Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 1, pp. 15--40

BAYES INFERENCE IN LIFE TESTING AND RELIABILITY VIA MARKOV CHAIN MONTE CARLO SIMULATION

By

S.K. UPADHYAY, N. VASISHTA, Banaras Hindu University, Varanasi, India

and

A.F.M. SMITH, University of London, London

(Reprinted from 2000, Volume 62, Series A, Pt. 2, pp. 203--222)

SUMMARY. The integrals involved in Bayesian inference have long served as an impediment to the wider application of these techniques in the analysis of life testing and reliability models. The computational problems are further complicated if some of the available data are censored. In addition, inference interest may focus on non-linear functions of the parameters such as the reliability functions, hazard rates, etc. The paper shows that these apparent difficulties can be overcome by simulation approaches to Bayesian computation in reliability models, using Markov chain Monte Carlo methods. We also consider the use of an important Markov chain Monte Carlo procedure, namely the Gibbs sampler, to explore posterior distributions for some commonly used life testing models and to obtain corresponding predictive data. These predictive data are then utilized for the purpose of model comparison.

AMS (1991) subject classification. 62F15, 62N03, 62N05.

Key words and phrases. Bayes statistics, simulation, Gibbs sampling, Metropolis algorithm, censored data, posterior distribution, life testing models, adaptive rejection sampling, rejection sampling, sampling-importance-resampling, measures of reliability, predictive simulation, Bayesian p-value.

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