基于连续比例Logistic回归模型的贝叶斯判别分析  

A Bayesian discriminant analysis method based on continuous ratioLogistic regression models

作　　者：乔姝 万树文[1] QIAO Shu;WAN Shuwen(Department of Applied Mathematics,Nanjing University of Finance&Economics,Nanjing 210023,Jiangsu,China)

机构地区：[1]南京财经大学应用数学学院,江苏南京210023

出　　处：《云南大学学报（自然科学版）》2024年第4期601-609,共9页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11001119).

摘　　要：针对传统贝叶斯判别分析方法处理实际问题的局限性,提出一种基于连续比例Logistic回归模型的贝叶斯判别分析方法.首先基于连续比例Logistic回归模型建立半参数密度比模型,通过经验似然法估计模型的参数,并使用贝叶斯定理计算后验概率进行分类预测.然后对比新方法与传统方法的回判正确率,统计模拟表明当总体数据符合正态分布时,2者判别能力相当,否则,提出的新方法能够更好地判别不同的数据特征.最后运用新方法分析真实的数据集,验证了新方法在分类预测中的准确性和稳健性,与传统方法相比,更适用于实际应用中多元分类问题的建模和预测.A Bayesian discriminant analysis method based on a continuous ratio Logistic regression model is proposed to address the limitations of the traditional Bayesian discriminant analysis method in dealing with practical problems.Firstly,a semiparametric density ratio model is established based on the continuous ratio Logistic regression model,and the parameters of the model are estimated by the empirical likelihood method,and the posterior probabilities are calculated using Bayes'theorem for classification prediction.Statistical simulations then compare the correct rate of judgement between the new method and the traditional method.Statistical simulations show that the discriminative power of the two is comparable when the overall data conforms to a normal distribution,otherwise,the proposed new method can better discriminate different data characteristics.Finally,the new method is applied to analysis real data sets to verify the accuracy and robustness of the new method in classification prediction,which is more suitable for modelling and prediction of multivariate classification problems in practical applications compared with the traditional method.

关 键 词：贝叶斯判别分析法 半参数法 密度比模型 连续比例Logistic回归模型 经验似然 

分 类 号：O212.7[理学—概率论与数理统计]