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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (5): 695-708.doi: 10.3969/j.issn.1005-3085.2022.05.002

• • 上一篇    下一篇

数据扩充下0-1膨胀几何分布的客观贝叶斯分析及应用

肖   翔   

  1. 上海工程技术大学数理与统计学院，上海  201620
  • 出版日期:2022-10-15 发布日期:2022-12-15
  • 基金资助:
    全国统计科学研究项目(2020LY080).

Objective Bayesian Analysis and Application for Zero-and-one-inflated Geometric Distribution Using Data Augmentation

XIAO Xiang   

  1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620
  • Online:2022-10-15 Published:2022-12-15
  • Supported by:
    The National Statistical Science Research Project of China (2020LY080).

PDF (PC)

196

摘要：

在交通安全、公共卫生、风险管理等实际应用领域，经常会遇到0观测值、1观测值出现较多的样本数据。为了更深入地研究这类数据集，本文提出了0-1膨胀几何分布模型，通过设计数据扩充策略和构造完全似然函数，得到了Jeffreys先验和reference先验。设置不同的样本容量和参数真值，对不同的客观先验进行数值仿真和比较分析。最后，利用0-1膨胀几何分布模型对底特律城市交通事故死亡数据集进行了分析。研究表明，采用客观贝叶斯方法比主观贝叶斯方法能够实现更佳的拟合效果。

关键词: 0-1膨胀几何分布, 客观贝叶斯方法, Jeffreys先验, reference先验, 数据扩充

Abstract:

Count data with excess zeros and ones arise frequently in many practical application fields such as traffic safety, public health, risk management and so on. In this paper, in order to study this kind of data set more deeply, a zero-and-one-inflated geometric distribution model is proposed and considered. Jeffreys prior and reference priors are derived via data augmentation strategy and the complete likelihood function. For different sample sizes and different true values of the parameters, numerical simulation and comparative analysis are adopted to assess the performance of these different objective priors. Finally, one accidental data set from Detroit is analyzed to illustrate the practicability of the proposed model. It shows that the objective Bayesian method performs better than the subjective Bayesian method.

Key words: zero-and-one-inflated geometric distribution, objective Bayesian method, Jeffreys prior, reference prior, data augmentation

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