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| 判别分析多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: 贝叶斯线性判别分析 先验概率 后验概率 损失函数 似然函数 |
| 英文关键词:Bayesian linear discriminant analysis Prior probability Posterior probability Loss function Likelihood function |
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| 中文摘要: |
| 【】本文目的是介绍与多类资料的贝叶斯线性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。基本概念包括先验概率、后验概率、最优分类方法、损失函数和似然函数；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“从三个总体中各抽取5位患者四项定量指标的测定结果”和“从三类铀矿中分别随机抽取7、8、9个样品九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多类资料的贝叶斯线性判别分析,并分别给出回代判别与交叉验证判别的总误判率。 |
| 英文摘要: |
| 【】This paper aimed to introduce the fundamental concepts, computational methods, two practical examples, and their implementation using SAS software forBayesian linear discriminant analysis of multi-class data. The key concepts includedprior probability, posterior probability, optimal classification methods, loss functions, and likelihood functions. The computational methodology coveredproblem formulation, Bayesian discriminant criteria, posterior probability calculation, initial discriminant functions, final linear discriminant functions, and classification rules. Two datasets were analyzed: The first dataset was measurements of four quantitative indicators from five patients randomly selected from each of three populations, and the second dataset was measurements of nine quantitative indicators from 7, 8, and 9 samples randomly collected from three types of uranium ores, respectively. Using SAS,Bayesian linear discriminant analysis for multi-class datawas performed on both datasets, with thetotal misclassification ratesreported for bothresubstitution and cross-validationprocedures. |
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