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Objective Bayesian Estimation for Tweedie Exponential Dispersion Process

Author

Listed:
  • Weian Yan

    (School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, China
    School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China)

  • Shijie Zhang

    (School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, China)

  • Weidong Liu

    (School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China)

  • Yingxia Yu

    (School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, China)

Abstract

An objective Bayesian method for the Tweedie Exponential Dispersion (TED) process model is proposed in this paper. The TED process is a generalized stochastic process, including some famous stochastic processes (e.g., Wiener, Gamma, and Inverse Gaussian processes) as special cases. This characteristic model of several types of process, to be more generic, is of particular use for degradation data analysis. At present, the estimation methods of the TED model are the subjective Bayesian method or the frequentist method. However, some products may not have historical information for reference and the sample size is small, which will lead to a dilemma for the frequentist method and subjective Bayesian method. Therefore, we propose an objective Bayesian method to analyze the TED model. Furthermore, we prove that the corresponding posterior distributions have nice properties and propose Metropolis–Hastings algorithms for the Bayesian inference. To illustrate the applicability and advantages of the TED model and objective Bayesian method, we compare the objective Bayesian estimates with the subjective Bayesian estimates and the maximum likelihood estimates according to Monte Carlo simulations. Finally, a case of GaAs laser data is used to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Weian Yan & Shijie Zhang & Weidong Liu & Yingxia Yu, 2021. "Objective Bayesian Estimation for Tweedie Exponential Dispersion Process," Mathematics, MDPI, vol. 9(21), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2740-:d:666865
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    References listed on IDEAS

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    4. Weian Yan & Hassen Riahi & Karim Benzarti & Robert Chlela & Laurence Curtil & David Bigaud, 2021. "Durability and Reliability Estimation of Flax Fiber Reinforced Composites Using Tweedie Exponential Dispersion Degradation Process," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-21, February.
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    7. Weian Yan & David Bigaud & Nadare Matoiri Chaibati & Laurent Izoret, 2020. "Optimization of Accelerated Destructive Degradation Testing of Cementitious Materials for Their Performances Qualification under Aggressive Environments: The Case of Carbonation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-19, April.
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    Cited by:

    1. Yan, Weian & Xu, Xiaofan & Bigaud, David & Cao, Wenqin, 2023. "Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process," Reliability Engineering and System Safety, Elsevier, vol. 230(C).

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