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| 判别分析两类资料的贝叶斯线性判别分析法 |
| Liu Huigang1,Hu Chunyan2, Hu Liangping2,3*(1. School of Basic Medical Sciences, Capital Medical University, Beijing 100069,China; |
| 投稿时间：2025-06-24 修订日期：2025-06-24 |
| DOI： |
| 中文关键词: 贝叶斯定理 线性判别分析 朴素贝叶斯判别分析 判别准则 后验概率 |
| 英文关键词:Bayes’ theorem Linear discriminant analysis (LDA) Naive Bayesian discriminant analysis Discriminant criterion Posterior probability |
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| 中文摘要: |
| 【】本文目的是介绍与两类资料的贝叶斯线性典型判别分析有关的基本概念、计算方法、两个实例及其用SAS实现计算的方法。基本概念包括线性判别分析、贝叶斯定理、贝叶斯判别分析、朴素贝叶斯判别分析、判别准则与分类规则；计算方法涉及问题设定、贝叶斯判别准则、后验概率计算、初始判别函数、最终的线性判别函数和分类规则；两个实例中的资料分别是“甲型血友病必然的携带者和非携带者两项定量指标的测定结果”和“正常人和白血病患者两项定量指标的测定结果”；借助SAS软件,对两个实例中的数据进行两类资料的贝叶斯线性判别分析,并分别给出了回代判别与交叉验证判别的总误判率。 |
| 英文摘要: |
| 【】The purpose of this paper was to introduce the fundamental concepts, computational methods, two practical examples, and their implementation using SAS software in the context ofBayesian linear discriminant analysis for two-class data. The fundamental concepts includedlinear discriminant analysis (LDA), Bayes’ theorem, Bayesian discriminant analysis, naive Bayesian discriminant analysis, discriminant criteria, and classification rules. The computational methods coveredproblem formulation, Bayesian discriminant criteria, posterior probability calculation, initial discriminant functions, final linear discriminant functions, and classification rules. The two datasets used in the examples were “Quantitative measurements of two indicators in obligatory carriers vs. non-carriers of hemophilia A” and “Quantitative measurements of two indicators in healthy individuals vs. leukemia patients.” Using SAS,Bayesian linear discriminant analysis for two-class datawas performed on both datasets, and thetotal misclassification rateswere reported for bothresubstitution (reclassification) and cross-validation. |
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