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Conditional laplace transforms for bayesian nonparametric inference in reliabity theory

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  • P. Ammann, Larry

Abstract

In order to apply nonparametric meyhods to reliability problems, it is desibrable to have available priors over a broad class of survival distributions.In the paper, this is achieved by taking the failure rate function to be the sum oof a nonnegative stochastic process with increasing sample patjhs and a process with decreasing sample paths. This approach produces a prior which chooses an absolutely survival distribution that can have an IFR, DFR, or U-shapped failure rate. Posterior Laplace transforms of the failure rate are obtained based on survival data allows censoring. Bayes estimates of the failure rate as well as the lifetime distribution are then calculated from these posterior Laplace transforms. This approach is also applied to a competing risks model and the proportional hazards model of Cox.

Suggested Citation

  • P. Ammann, Larry, 1985. "Conditional laplace transforms for bayesian nonparametric inference in reliabity theory," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 197-212, September.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:2:p:197-212
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    Cited by:

    1. Luca La Rocca, 2008. "Bayesian Non‐Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 524-539, September.

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