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| 判别分析多类资料的贝叶斯二次型判别分析法 |
| 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: 贝叶斯判别分析 二次型判别函数 回代判别 交叉验证判别 测试集 |
| 英文关键词:Bayesian discriminant analysis Quadratic discriminant function Resubstitution Cross-validation Test set |
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| 中文摘要: |
| 【】本文目的是介绍与多类资料的贝叶斯二次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。基本概念包括协方差矩阵、协方差矩阵的齐性检验、回代判别、交叉验证判别、训练集和测试集；计算方法涉及假设、贝叶斯判别准则、判别函数的推导和分类规则；两个实例中的资料分别是“三个层段的样品5个定量指标的测定结果”和“美国三大制造商生产的早餐麦片相关数据”；借助SAS软件,对两个实例中的数据进行多类资料的贝叶斯二次型判别分析,进而分别给出回代判别和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 application examples, and their implementation using SAS software forBayesian quadratic discriminant analysis of multi-class data. Key concepts includedcovariance matrices, homogeneity tests of covariance matrices, resubstitution, cross-validation, training sets, and test sets. The computational methodology coveredassumptions, Bayesian discriminant criteria, derivation of discriminant functions, and classification rules. Two datasets were analyzed: The first dataset was the measurements of five quantitative indicators from samples in three stratigraphic layers; the second dataset was nutritional data of breakfast cereals produced by three major U.S. manufacturers. Using SAS,Bayesian quadratic discriminant analysis for multi-class datawas performed, withtotal misclassification ratesreported for bothresubstitution and cross-validationprocedures. |
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