Objective Bayesian Estimation for Tweedie Exponential Dispersion Process

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 characterist...

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Autores principales:	Weian Yan, Shijie Zhang, Weidong Liu, Yingxia Yu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Tweedie Exponential Dispersion process objective Bayesian degradation Metropolis–Hastings algorithm reference prior Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b9b49570986543abae5e7311a19b3f30
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spelling	oai:doaj.org-article:b9b49570986543abae5e7311a19b3f302021-11-11T18:17:21ZObjective Bayesian Estimation for Tweedie Exponential Dispersion Process10.3390/math92127402227-7390https://doaj.org/article/b9b49570986543abae5e7311a19b3f302021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2740https://doaj.org/toc/2227-7390An 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.Weian YanShijie ZhangWeidong LiuYingxia YuMDPI AGarticleTweedie Exponential Dispersion processobjective BayesiandegradationMetropolis–Hastings algorithmreference priorMathematicsQA1-939ENMathematics, Vol 9, Iss 2740, p 2740 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Tweedie Exponential Dispersion process objective Bayesian degradation Metropolis–Hastings algorithm reference prior Mathematics QA1-939
spellingShingle	Tweedie Exponential Dispersion process objective Bayesian degradation Metropolis–Hastings algorithm reference prior Mathematics QA1-939 Weian Yan Shijie Zhang Weidong Liu Yingxia Yu Objective Bayesian Estimation for Tweedie Exponential Dispersion Process
description	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.
format	article
author	Weian Yan Shijie Zhang Weidong Liu Yingxia Yu
author_facet	Weian Yan Shijie Zhang Weidong Liu Yingxia Yu
author_sort	Weian Yan
title	Objective Bayesian Estimation for Tweedie Exponential Dispersion Process
title_short	Objective Bayesian Estimation for Tweedie Exponential Dispersion Process
title_full	Objective Bayesian Estimation for Tweedie Exponential Dispersion Process
title_fullStr	Objective Bayesian Estimation for Tweedie Exponential Dispersion Process
title_full_unstemmed	Objective Bayesian Estimation for Tweedie Exponential Dispersion Process
title_sort	objective bayesian estimation for tweedie exponential dispersion process
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b9b49570986543abae5e7311a19b3f30
work_keys_str_mv	AT weianyan objectivebayesianestimationfortweedieexponentialdispersionprocess AT shijiezhang objectivebayesianestimationfortweedieexponentialdispersionprocess AT weidongliu objectivebayesianestimationfortweedieexponentialdispersionprocess AT yingxiayu objectivebayesianestimationfortweedieexponentialdispersionprocess
_version_	1718431906853289984

Objective Bayesian Estimation for Tweedie Exponential Dispersion Process

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