基于0-1膨胀二项分布的客观贝叶斯分析  

OBJECTIVE BAYESIAN ANALYSIS BASED ON ZERO-AND-ONE-INFLATED BINOMIAL DISTRIBUTION

作　　者：吴懿祺 肖翔 古晞[2] Wu Yiqi;Xiao Xiang;Gu Xi(School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;School of Mathematical Science,Tongji University,Shanghai 200092,China)

机构地区：[1]上海工程技术大学数理与统计学院,上海201620 [2]同济大学数学科学学院,上海200092

出　　处：《计算机应用与软件》2024年第4期46-52,59,共8页Computer Applications and Software

基　　金：全国统计科学研究项目(2020LY080);上海市大学生创新训练计划项目(cs2021003)。

摘　　要：在医疗卫生、金融证券等应用领域,经常会同时出现零观测值、一观测值较多的情况。为更好地拟合这类数据,提出一种0-1膨胀二项分布模型并进行客观贝叶斯分析。采用数据扩充策略,基于完全似然函数,得到Jeffreys先验和reference先验。采用WinBUGS软件和R软件进行数值模拟,设定不同的样本量和参数真值,对不同的无信息先验进行评估。对2020年1月28日与2月22日COVID-19死亡人数进行分析,结果表明,在小样本情形下基于客观贝叶斯先验π_(R3)下的拟合效果比π_(R1)和π_(R2)要好。Count data with excess zeros and ones arise frequently in various fields such as medical health,finance and securities.To better fit such data,a zero-and one-inflated binomial distribution model is proposed and the objective Bayesian analysis is carried.Based on data augmentation strategy and the complete likelihood function,the Jeffreys prior and the reference priors were derived for this model.For different sample sizes and different true values of the parameters,simulations were adopted to assess the performance of the different uninformed priors through WinBUGS and R software.We analyze the death toll of COVID-19 on January 28 and February 22,2020.The results show that the fitting effect based on objective Bayesian prior π_(R3) is better than π_(R1) and π_(R2) in the case of small sample.

关 键 词：0-1膨胀二项分布 客观贝叶斯 Jeffreys先验 reference先验 数据扩充 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]