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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

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[J]. 上海工程技术大学学报, 2021, 35(4): 395-400.
引用本文: 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[J]. 上海工程技术大学学报, 2021, 35(4): 395-400.
XIAO Xiang, WU Yiqi, GU Xi. Objective Bayesian analysis of mixture cure model based on exponential distribution[J]. Journal of Shanghai University of Engineering Science, 2021, 35(4): 395-400.
Citation: XIAO Xiang, WU Yiqi, GU Xi. Objective Bayesian analysis of mixture cure model based on exponential distribution[J]. Journal of Shanghai University of Engineering Science, 2021, 35(4): 395-400.

基于指数分布混合治愈模型的客观贝叶斯分析

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

Objective Bayesian analysis of mixture cure model based on exponential distribution

  • 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.
  • 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
    ${\pi _R}$ 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
    ${\pi _R}$ 0.015 0.087 −0.016 0.135 0.004 0.064
    下载: 导出CSV

    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
    $ {\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
    $ {\pi _R} $ 0.024 0.047 0.015 0.068 0.014 0.030
    下载: 导出CSV

    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} $0.9450.9570.9560.9540.9610.958
    $ {\pi _R} $0.9470.9550.9540.9530.9550.946
    50$ {\pi _J} $0.9460.9560.9550.9530.9580.957
    $ {\pi _R} $0.9470.9540.9520.9520.9530.947
    下载: 导出CSV
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    [2] 肖翔, 刘福窑. 零膨胀几何分布的参数估计[J] . 上海工程技术大学学报,2018,32(3):267 − 271. doi: 10.3969/j.issn.1009-444X.2018.03.013
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出版历程
  • 收稿日期:  2021-05-17
  • 刊出日期:  2022-02-23

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