广义极值回归模型下现状数据的贝叶斯估计

doi:10.16088/j.issn.1001-6600.2021060907

广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (1): 82-90.doi: 10.16088/j.issn.1001-6600.2021060907

广义极值回归模型下现状数据的贝叶斯估计

孙烨, 蒋京京, 王纯杰^*

长春工业大学数学与统计学院, 吉林长春 130012

收稿日期:2021-06-09 修回日期:2021-07-31 出版日期:2022-01-25 发布日期:2022-01-24
通讯作者: 王纯杰(1978—), 女, 辽宁灯塔人, 长春工业大学教授, 博士。E-mail: wangchunjie@ccut.edu.cn
基金资助:
国家自然科学基金(11671054)

Bayesian Estimation of Current Status Data with Generalized Extreme Value Regression Model

SUN Ye, JIANG Jingjing, WANG Chunjie^*

School of Mathematics and Statistics, Changchun University of Technology, Changchun Jilin 130012, China

Received:2021-06-09 Revised:2021-07-31 Online:2022-01-25 Published:2022-01-24

摘要/Abstract

摘要： 广义极值分布自提出以来就受到众多学者关注,它可以用于拟合某些寿命数据,在医学、工程和气象等领域应用很广泛。本文主要在区间删失I型数据,即现状数据下研究三参数广义极值模型的贝叶斯回归分析。基于广义极值分布的位置参数引入协变量,建立位置参数与生存时间的贝叶斯回归模型,并采用Gibbs抽样和MH算法相结合的MCMC方法,从各个参数的后验分布中进行抽样,得到参数的估计值。利用R软件进行数值模拟,比较极大似然估计和贝叶斯估计在有限样本下的效果,结果表明参数生存回归模型拟合效果好,模拟结果显示贝叶斯估计优于极大似然估计。将该方法用于144只雄性RFM小鼠的肺肿瘤数据分析,得到一些分析结果。

关键词: 现状数据, 广义极值分布, 极大似然估计, 贝叶斯估计, MCMC算法

Abstract: The generalized extreme value distribution has attracted the attention of many scholars since it was proposed. It can be used to fit life data and is widely used in the fields of medical sciences, engineering and meteorology. In this paper, the Bayesian regression analysis under the three-parameter generalized extreme value model is studied under the current status data. Based on the location parameter of generalized extreme value distribution, the covariate are introduced, the Bayesian regression model of location parameter and survival time are established, and the MCMC method combining with Gibbs sampling and MH algorithm is used to draw sample from the posterior distribution of each parameter. The means of the posterior samples are used as the estimated value of the parameters. R software is used for numerical simulation to compare the performance of maximum likelihood estimation and Bayesian estimation, which illustrates that the parametric survival regression model fits the data well. Simulation results indicate that Bayesian estimation outperforms the maximum likelihood estimation. Finally, this method is applied to the lung tumor data of 144 male RFM mice, and some results are obtained.

Key words: current status data, generalized extreme value distribution, maximum likelihood estimation, Bayesian estimation, MCMC algorithm

中图分类号:

O212.8

孙烨, 蒋京京, 王纯杰. 广义极值回归模型下现状数据的贝叶斯估计[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 82-90.

SUN Ye, JIANG Jingjing, WANG Chunjie. Bayesian Estimation of Current Status Data with Generalized Extreme Value Regression Model[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(1): 82-90.

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广义极值回归模型下现状数据的贝叶斯估计

Bayesian Estimation of Current Status Data with Generalized Extreme Value Regression Model

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