基于Dirichlet模型的国内COVID-19疫情数据的Bayesian估计  

Bayesian Estimation of Domestic COVID-19 Epidemic Data Based on Dirichlet Model

作　　者：杨云源 杨新平 张洁 YANG Yunyuan;YANG Xinping;ZHANG Jie(School of Geography and Tourism Management,Chuxiong Normal University,Chuxiong 675000,Yunnan;School of Mathematics and Statistics,Chuxiong Normal University,Chuxiong 675000,Yunnan;Chuxiong Medical College,Chuxiong 675000,Yunnan)

机构地区：[1]楚雄师范学院地理科学与旅游管理学院,云南楚雄675000 [2]楚雄师范学院数学与统计学院,云南楚雄675000 [3]楚雄医药高等专科学校,云南楚雄675000

出　　处：《四川师范大学学报（自然科学版）》2020年第6期838-846,共9页Journal of Sichuan Normal University（Natural Science）

基　　金：云南省高校联合基金面上项目(2017FH001-068);云南省教育厅资助项目(2017ZZX018)。

摘　　要：对累计治愈病例数、现有重症病例数、累计病死病例数、现有轻症病例数的点估计与区间估计进行计算,在Bayesian框架下建立Dirichlet模型,共264个逐日概率指标(治愈概率、重症概率、病死概率及轻症概率)作为参数,通过MCMC方法完成参数的Bayesian估计,最后分别计算COVID-19逐日4个总量指标的点估计及区间估计.结果发现:264条MC链均收敛于各自的后验分布,最大MC误差与标准差的比值百分数仅为0.77455%;除病死概率可信区间带略宽外,其他3个概率的可信区间带与点估计曲线几乎重合,逐日4个概率点估计最大误差限为3.07%;截至2020-03-28,4个总量指标点估计值分别为75447.80、742.0045、3299.885、1948.745例,与样本值几乎相等;95%CI分别为:(75301.20,75594.39)、(689.8810,796.0826)、(3189.937,3409.833)、(1864.045,2035.075).In this paper,we calculate the point estimation and interval estimation of cumulative number of cured cases,number of existing severe cases,cumulative number of dead cases and cumulative number of mild cases.The Dirichlet model is established under the Bayesian framework,with 264 daily probability indexes(cure probability,severe probability,death probability and light disease probability) as parameters.Bayesian estimation of the parameters is completed by MCMC method,and the point estimation and interval estimation of the four total indexes of COVID-19 day by day are calculated.Results:All the 264 MC.chains converge to their posterior distribution,with the percentage of the ratio of the largest MC error to the standard deviation is only 0.774 55%.Except for the wide confidence interval of death probability,the confidence intervals of the three other probabilities almost coincide with the point estimation curve,and the maximum error limit of the four probabilities is 3.07%.Until March 28 th,2020,the estimated values of the four indicators are 75 447.80,742.004 5,3 299.885,1 948.745,respectively.These values are almost equal to the sample values and95% CI are(75 301.20,75 594.39),(689.881 0,796.082 6),(3 189.937,3 409.833),(1 864.045,2 035.075),respectively.

关 键 词：COVID-19国内疫情数据 多项分布 Dirichlet分布 GIBBS抽样 区间估计 

分 类 号：O212.4[理学—概率论与数理统计]