• • 上一篇    下一篇

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. 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.

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 Maozai2,3   

  1. 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.
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.

MR(2010)主题分类: 

()
[1] Buonomo B, Cerasuolo M. Analysis of a delayed SIR model with nonlinear incidence rate. Discrete Dynamics in Nature & Society, 2009, 2008(3):473-490.
[2] 马知恩, 周义仓. 传染病动力学的数学建模与研究. 北京:科学出版社, 2004. (Ma Z E, Zhou Y C. Mathematical Modeling and Research of Infectious Disease Dynamics. Beijing:Science Press, 2004.)
[3] 严阅, 陈瑜, 刘可伋, 等.基于一类时滞动力学系统对新型冠状病毒肺炎疫情的建模和预测. 中国科学:数学, 2020, 50(3):385-392. (Yan Y, Chen Y, Liu K, et al. Modeling and prediction for the trend of outbreak of NCP based on a time-delay dynamic system. Scientia Sinica $($Mathematica$)$, 2020, 50(3):385-392.)
[4] 丁志伟, 刘艳云, 孔京, 等.感染人数期望值估计及新增确诊人数趋势预测的概率模型. 运筹学学报, 2020, 24(1):1-12. (Ding Z W, Liu Y Y, Kong J, et al. Expected number of infected persons and probability model for predicting the trend of newly diagnosed persons. Journal of Operations Research, 2020, 24(1):1-12.)
[5] Besag J, York J, Mollié A. Bayesian image-restoration, with 2 applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 1991, 43(1):1-20.
[6] Kim H, Oleson J J. A Bayesian dynamic spatio-temporal interaction model:An application to prostate cancer incidence. Geographical Analysis, 2008, 40(1):77-96.
[7] Li G, Haining R, Richardson S, et al. Space-time variability in burglary risk:A Bayesian patio-temporal modelling approach. Spatial Statistics, 2014, (9):180-191.
[8] Khana D, Rossen L M, Hedegaard H, et al. A Bayesian spatial and temporal modeling approach to mapping geographic variation in mortality rates for subnational areas with R-Inla. Journal of Data Ence. Jds., 2018, 16(1):147.
[9] Kang S Y, McGree J, Baade P, et al. A case study for modelling cancer incidence using Bayesian spatio-temporal models. Australian & New Zealand Journal of Statistics, 2015, 57(3):325-345.
[10] Yin P, Mu L, Madden M, et al. Hierarchical Bayesian modeling of spatio-temporal patterns of lung cancer incidence risk in Georgia, USA:2000-2007. Journal of Geographical Systems, 2014, 16(4):387-407.
[11] Song C, He Y, Bo Y, et al. Risk assessment and mapping of hand, foot, and mouth disease at the county level in Mainland China using spatiotemporal zero-inflated Bayesian hierarchical models. International Journal of Environmental Research & Public Health, 2018, 15(7):1476-1492.
[12] Wikle C K, Anderson C J. Climatological analysis of tornado report counts using a hierarchical Bayesian spatiotemporal model. Journal of Geophysical Research:Atmospheres, 2003, 108(D24):9005.
[13] Rouamba T, Samadoulougou S, Tinto H, et al. Bayesian spatiotemporal modeling of routinely collected data to assess the effect of health programs in malaria incidence during pregnancy in Burkina Faso. Scientific Reports, 2020, 10(1):2618-2633.
[14] Carlin B, Banerjee S. Hierarchical multivariate CAR models for spatio-temporally correlated survival data. Bayesian Statistics, 2003, (7):45-64.
[15] Schrödle B, Leonhard H. A primer on disease mapping and ecological regression using INLA. Computational Statistics, 2011, 26(2):241-258.
[16] Schrödle B, Leonhard H, Riebler A, et al. Using integrated nested Laplace approximations for the evaluation of veterinary surveillance data from Switzerland:A case-study. Applied Statistics, 2011, 60(2):261-279.
[17] Richardson S, Abellan J J, Best N. Bayesian spatio-temporal analysis of joint patterns of male and female lung cancer risks in Yorkshire (UK). Statistical Methods in Medical Research, 2006, 15(4):385-407.
[18] Spiegelhalter D J, Best N G, Carlin B P, et al. Bayesian measure of model complexity and fit. Journal of Royal Statistical Society, Series B, 2002, 64(4):583-616.
[19] Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. Readings in Computer Vision, 1987, 20(5-6):25-62.
[20] Gelman A, Rubin D B. Inference from iterative simulation using multiple sequences. Statistical Science, 1992, 7(4):457-472.
[1] 赵远英,徐登可,段星德. 非线性均值方差模型的贝叶斯数据删除统计诊断[J]. 系统科学与数学, 2020, 40(1): 171-179.
[2] 黄月兰,汤银才. 变点模型下Weibull分布恒加试验的Bayes分析[J]. 系统科学与数学, 2013, 33(9): 1105-1112.
[3] 李海芬;汤银才. 对数稳定分布加速寿命试验的贝叶斯分析[J]. 系统科学与数学, 2011, 31(4): 448-457.
[4] 陈平;陈钧. ARMAX时间序列模型异常点及异常点斑片的估计和检测[J]. 系统科学与数学, 2010, 30(10): 1323-1333.
[5] 陈雪东;唐年胜. 带有不可忽略缺失数据的半参数再生散度模型的贝叶斯分析[J]. 系统科学与数学, 2010, 30(10): 1334-1350.
[6] 汤银才;侯道燕. 三参数Weibull分布参数的Bayes估计[J]. 系统科学与数学, 2009, 29(1): 109-115.
阅读次数
全文


摘要