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| 判别分析两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: 二次型 贝叶斯判别分析 多元正态分布 特征向量 判别准则 |
| 英文关键词:Quadratic form Bayesian discriminant analysis multivariate normal distribution eigenvector discriminant criterion |
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| 中文摘要: |
| 【】本文的目的是介绍与两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。基本概念包括二次型判别函数、概率密度函数、多元正态分布、特征维度和特征向量；计算方法涉及假设、贝叶斯判别准则、初始判别函数、二次型判别函数和分类规则；两个实例中的资料分别是“野生和养殖龟的八种骨骼指的测定结果”和“阿拉斯加和加拿大的淡水和海水中鲑鱼的增长环的直径”；借助SAS软件,对两个实例中的数据进行两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 two-class data. Key concepts included thequadratic discriminant function, probability density function, multivariate normal distribution, eigenvalues, and eigenvectors. The computational methodology coveredassumptions, Bayesian discriminant criteria, initial discriminant functions, quadratic discriminant functions, and classification rules. Two datasets were analyzed: The first dataset was measurements of eight skeletal indices in wild vs. farmed turtles, and the second dataset was growth ring diameters in salmon from freshwater (Alaska) and marine (Canada) habitats. Using SAS,Bayesian quadratic discriminant analysis for two-class datawas performed, withtotal misclassification ratesreported for bothresubstitution and cross-validationprocedures. |
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