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Sensitivity estimations for Bayesian inference models solved by MCMC methods

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

Abstract

The advent of Markov Chain Monte Carlo (MCMC) methods to simulate posterior distributions has virtually revolutionized the practice of Bayesian statistics. Unfortunately, sensitivity analysis in MCMC methods is a difficult task. In this paper, a computationally low-cost method to estimate local parametric sensitivities in Bayesian models is proposed. The sensitivity measure considered here is the gradient vector of a posterior quantity with respect to the parameter. The gradient vector components are estimated by using a result based on the integral/derivative interchange. The MCMC simulations used to estimate the posterior quantity can be re-used to estimate the sensitivity measures and their errors, avoiding the need for further sampling. The proposed method is easy to apply in practice as it is shown with an illustrative example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:10:p:1310-1314
    DOI: 10.1016/j.ress.2005.11.029
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    References listed on IDEAS

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    1. Hall, Charles B. & Ying, Jun & Kuo, Lynn & Lipton, Richard B., 2003. "Bayesian and profile likelihood change point methods for modeling cognitive function over time," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 91-109, February.
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    1. 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.
    2. Zhao, Tengyuan & Wang, Yu, 2020. "Non-parametric simulation of non-stationary non-gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    3. Li, Peiping & Wang, Yu, 2022. "An active learning reliability analysis method using adaptive Bayesian compressive sensing and Monte Carlo simulation (ABCS-MCS)," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    4. Marhavilas, P.K. & Koulouriotis, D.E., 2012. "A combined usage of stochastic and quantitative risk assessment methods in the worksites: Application on an electric power provider," Reliability Engineering and System Safety, Elsevier, vol. 97(1), pages 36-46.

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