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Local parametric sensitivity for mixture models of lifetime distributions

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  • Rufo, M.J.
  • Pérez, C.J.
  • Martín, J.

Abstract

Mixture models are receiving considerable significance in the last years. Practical situations in reliability and survival analysis may be addressed by using mixture models. When making inferences on them, besides the estimates of the parameters, a sensitivity analysis is necessary. In this paper, a general technique to estimate local prior sensitivities in finite mixtures of distributions from natural exponential families having quadratic variance function (NEF-QVF) is proposed. Those families include some distributions of wide use in reliability theory. An advantage of this method is that it allows a direct implementation of the sensitivity measure estimates and their errors. In addition, the samples that are drawn to estimate the parameters in the mixture model are re-used to estimate the sensitivity measures and their errors. An illustrative application based on insulating fluid failure data is shown.

Suggested Citation

  • Rufo, M.J. & Pérez, C.J. & Martín, J., 2009. "Local parametric sensitivity for mixture models of lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1238-1244.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:7:p:1238-1244
    DOI: 10.1016/j.ress.2008.05.002
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    References listed on IDEAS

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    1. E. Gutiérrez-Peña & A. Smith & José Bernardo & Guido Consonni & Piero Veronese & E. George & F. Girón & M. Martínez & G. Letac & Carl Morris, 1997. "Exponential and bayesian conjugate families: Review and extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 1-90, June.
    2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    3. Pérez, C.J. & Martín, J. & Rufo, M.J., 2006. "Sensitivity estimations for Bayesian inference models solved by MCMC methods," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1310-1314.
    4. Bohning, Dankmar & Seidel, Wilfried, 2003. "Editorial: recent developments in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 349-357, January.
    5. Bohning, Dankmar & Seidel, Wilfried & Alfo, Macro & Garel, Bernard & Patilea, Valentin & Walther, Gunther, 2007. "Advances in Mixture Models," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5205-5210, July.
    6. M. Rufo & J. Martín & C. Pérez, 2006. "Bayesian analysis of finite mixture models of distributions from exponential families," Computational Statistics, Springer, vol. 21(3), pages 621-637, December.
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    Cited by:

    1. Rufo, M.J. & Martín, J. & Pérez, C.J., 2014. "Adversarial life testing: A Bayesian negotiation model," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 118-125.
    2. M. Rufo & J. Martín & C. Pérez, 2010. "A note on the prior parameter choice in finite mixture models of distributions from exponential families," Computational Statistics, Springer, vol. 25(3), pages 537-550, September.
    3. Rufo, M.J. & Pérez, C.J. & Martín, J., 2010. "Merging experts' opinions: A Bayesian hierarchical model with mixture of prior distributions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 284-289, November.

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