Mathematical Sciences: Statistical Theory for Classification

数学科学：分类统计理论

• 批准号: 9401296
• 负责人: John Hartigan
• 金额: $ 20.4万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401296&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Theory; Classification

The proposal develops classification based approaches to prediction and statistical inference. Examples of statistical problems considered are change point problems, histograms, mode identification, reticulate evolution, and quantization of probability ditributions. A particular classification problem studied is the problem of types, the family of classes that most succinctly describes a primitive given family of classes. One way of predicting the future is by recognising circumstances that are similar to circumstances already experienced, that is, by placing the present circumstances in some established class of circumstances, from which we can infer other aspects of th future. Our method of classifying experience will determine how we predict the future. Thus we need to study classification to study prediction. We can't simply seize on some scheme of classification and use it permanently; we must develop new classifications adapting to the success or failure of predictions. Thus classification is needed for practical probability judgments, and practical probability judgments are needed for classification.

该提案开发了基于分类的预测和统计推断方法。所考虑的统计问题的示例包括变化点问题、直方图、模式识别、网状演化和概率分布的量化。研究的一个特定分类问题是类型问题，即最简洁地描述原始给定类族的类族。 预测未来的一种方法是认识到与已经经历过的情况相似的情况，即将当前情况置于某种既定的情况类别中，从中我们可以推断出未来的其他方面。我们对经验进行分类的方法将决定我们如何预测未来。因此我们需要研究分类来研究预测。我们不能简单地抓住某种分类方案并永久使用它；我们必须开发适应预测成功或失败的新分类。因此，实用的概率判断需要分类，分类也需要实用的概率判断。