基于分层贝叶斯时空Poisson模型的流行病建模研究

doi:10.12341/jssms20374

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (2): 462-472.DOI: 10.12341/jssms20374

基于分层贝叶斯时空Poisson模型的流行病建模研究

梁永玉¹, 田茂再^2,3

1. 兰州财经大学统计学院, 兰州 730020;
2. 中国人民大学应用统计科学研究中心, 北京 100872;
3. 中国人民大学统计学院, 北京 100872

收稿日期:2020-09-17 修回日期:2021-08-19 出版日期:2022-02-25 发布日期:2022-03-21
通讯作者: 田茂再,Email:mztian@ruc.edu.cn.
基金资助:
国家自然科学基金（11861042），全国统计科学研究项目重点项目（2020LZ25）资助课题.

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梁永玉, 田茂再. 基于分层贝叶斯时空Poisson模型的流行病建模研究[J]. 系统科学与数学, 2022, 42(2): 462-472.

LIANG Yongyu, TIAN Maozai. Epidemic Modeling Based on Hierarchical Bayesian Spatio-Temporal Possion Model[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 462-472.

Epidemic Modeling Based on Hierarchical Bayesian Spatio-Temporal Possion Model

LIANG Yongyu¹, TIAN Maozai^2,3

1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020;
2. Center for Applied Statistics, Renmin University of China, Beijing 100872;
3. School of Statistics, Renmin University of China, Beijing 100872

Received:2020-09-17 Revised:2021-08-19 Online:2022-02-25 Published:2022-03-21

流行病的广泛传播对经济发展以及日常生活造成了巨大的冲击.因此，收集流行病相关数据并分析其发病率或感染强度的时空规律对制定相应的控制策略，经济恢复政策等方面至关重要.文章讨论了基于分层贝叶斯时空Poisson模型的流行病建模方法，具体包括数据模型，过程模型以及参数模型的不同设定，参数先验分布的讨论，模型选择等.基于这种思路对流行病的传播和发展进行分析，可以研究不同地区的空间差异性及其他协变量对流行病趋势的影响，同时也可以研究病毒传播的时空依赖性和空间效应的异方差结构.所讨论的建模方法可为相关问题研究提供理论参考.对于参数估计，可利用已有的软件WinBUGS和OpenBUGS中默认的马尔可夫链蒙特卡罗算法（MCMC）下的Gibbs抽样算法.

关键词： 分层贝叶斯模型, 时空分析, 流行病建模, Gibbs抽样

The widespread spread of the epidemic has had a huge impact on economic development and daily life. Therefore, it is of great importance for formulating corresponding control strategies and economic recovery policies to collect epidemic data and analyze the spatio-temporal patterns of incidence rate or the intensity of infection. In this paper, epidemic modeling methods based on hierarchical Bayesian spatio-temporal Poisson model are discussed, including different settings of data model, process model and parameter model, discussion of parameter prior distribution, model selection and so on. Based on this idea, we can analyze the spread and development of epidemics, study the spatial differences of different regions and the influence of other covariables on epidemic trends, and study the spatio-temporal dependence of virus transmission and the heteroscedasticity structure of spatial effects.The modeling method discussed in this paper can provide theoretical reference for the study of related problems. For parameter estimation, the Gibbs sampling algorithm under the default Markov Chain Monte Carlo algorithm (MCMC) in WinBUGS and OpenBUGS can be used.

Key words: Hierarchical Bayesian model, spatio-temporal analysis, epidemic modeling, Gibbs sampling

MR(2010)主题分类:

62C10
62F15

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