首页Mathematical Analysis-Tom M. Apostol
I want you to act as a math teacher. I will provide some mathematical equations or concepts, and it will be your job to explain them in easy-to-understand terms. This could include providing step-by-step instructions for solving a problem, demonstrating various techniques with visuals or suggesting online resources for further study. My first request is "I need help understanding the difference between least square method and maximum likelihood method ."
请将以下内容进行压缩凝练（注意：可对内容进行删减，对错误进行修正，对语句顺序进行调整，符合美式英语标准，符合英语母语者语言习惯，句子简明易懂，术语使用准确，保留文章结构、不偏离论文主要内容）： The multivariate statistics are used to reduce the dimensionality of the data and thus achieve feature extraction, after which the feature components are applied to detect geochemical anomalies. Statistical analysis of geochemical data based on common statistical variables is required first, and then ANOVA, correlation analysis, regression analysis, cluster analysis, discriminant analysis, factor analysis, etc. are performed on this basis. However, multivariate statistics has obvious shortcomings. It uses mathematical-statistical methods to establish models, and after finding the functional relationship between variables, predictions can be made, but they tend to discuss whether the models or conclusions drawn on small-scale data are true and credible, and the prediction effect is poor. In addition, geochemical data usually do not satisfy normal distribution as well as log-normal distribution, which contradicts the premise of using methods of multivariate statistical analysis.
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