基于指数分布混合治愈模型的客观贝叶斯分析

肖翔; 吴懿祺; 古晞

基于指数分布混合治愈模型的客观贝叶斯分析

1.
上海工程技术大学数理与统计学院, 上海 201620
2.
上海对外经贸大学统计与信息学院, 上海 201620
3.
同济大学数学科学学院, 上海 200092

基金项目: 全国统计科学研究项目(2020LY080)

详细信息

作者简介:
肖翔：肖翔（1980−），男，讲师，硕士，研究方向为统计学. E-mail: xiaoxiang@sues.edu.cn

中图分类号: O212.1
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- 被引次数: 0
出版历程
- 收稿日期: 2021-05-17
- 刊出日期: 2022-02-23

Objective Bayesian analysis of mixture cure model based on exponential distribution

1.
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
2.
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
3.
School of Mathematical Science, Tongji University, Shanghai 200092, China

摘要

摘要: 提出基于指数分布的混合治愈模型，通过引入隐变量，利用完全似然函数比较容易计算Fisher信息矩阵，推导出参数的Jeffreys先验和reference先验，并验证后验分布的恰当性. 研究结果表明，客观贝叶斯方法对参数的估计效果很好，特别是在样本量小时比较明显.
- 混合治愈模型 /
- 客观贝叶斯分析 /
- Jeffreys先验 /
- reference先验
Abstract: A mixture cure model based on exponential distribution was proposed. By using full likelihood function and latent variables, it was easy to calculate Fisher information matrix, drive Jeffreys prior and reference priors, and the appropriateness of posterior distribution was verified. The results show that the objective Bayesian method has a good effect on parameter estimation, especially when the sample size is small.
- mixture cure model /
- objective Bayesian analysis /
- Jeffreys prior /
- reference prior

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表 1 客观贝叶斯估计下的估计偏差

Table 1. Bias under objective Bayesian estimation

$n$	先验	$p = 0.3$	$\lambda = 3$	$p = 0.3$	$\lambda = 4$	$p = 0.4$	$\lambda = 4$
20	${\pi _J}$	−0.025	0.141	−0.024	0.154	−0.008	0.085
20	${\pi _R}$	0.016	−0.095	−0.018	0.137	0.006	0.065
50	${\pi _J}$	−0.018	0.134	−0.022	0.144	−0.005	0.078
50	${\pi _R}$	0.015	0.087	−0.016	0.135	0.004	0.064

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表 2 客观贝叶斯估计下均方误差

Table 2. RMSE under objective Bayesian estimation

$n$	先验	$p = 0.3$	$\lambda = 3$	$p = 0.3$	$\lambda = 4$	$p = 0.4$	$\lambda = 4$
20	$ {\pi _J} $	0.031	0.059	0.019	0.075	0.022	0.051
20	$ {\pi _R} $	0.028	0.044	0.016	0.072	0.015	0.032
50	$ {\pi _J} $	0.027	0.056	0.018	0.071	0.022	0.048
50	$ {\pi _R} $	0.024	0.047	0.015	0.068	0.014	0.030

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表 3 客观贝叶斯估计的95%覆盖率

Table 3. 95% coverage probabilities under objective Bayesian estimation

$n$	先验	$p = 0.3$	$\lambda = 3$	$p = 0.3$	$\lambda = 4$	$p = 0.4$	$\lambda = 4$
20	$ {\pi _J} $	0.945	0.957	0.956	0.954	0.961	0.958
20	$ {\pi _R} $	0.947	0.955	0.954	0.953	0.955	0.946
50	$ {\pi _J} $	0.946	0.956	0.955	0.953	0.958	0.957
50	$ {\pi _R} $	0.947	0.954	0.952	0.952	0.953	0.947

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