Objective Bayesian Estimation for Tweedie Exponential Dispersion Process

Weian Yan, Shijie Zhang, Weidong Liu and Yingxia Yu
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Weian Yan: School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, 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

Mathematics, 2021, vol. 9, issue 21, 1-20

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.

Keywords: Tweedie Exponential Dispersion process; objective Bayesian; degradation; Metropolis–Hastings algorithm; reference prior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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