充分统计量的贝叶斯定义及其应用

Bayes' Definition of Sufficient Statistics and Its Application

充分统计量在简化统计问题中是一个非常重要的概念 .在经典统计中 ,它的定义是使用数学期望来叙述的 ,用到的数学知识较多且不易理解 ,而使用Bayes统计的观点定义充分统计量 ,从而证明有关充分统计量的等价命题 ,为判断一个统计量的充分性提供了简单有效的方法 .

Sufficient statistic is a very important concept in studying the statistical problems. In the classical statistics, its definition is described by means of expectation, which involves much mathematical knowledge and can not be easily understood. In this paper this concept is redefined from the point of view of Bayes' statistics and an equivalent proposition is proved by this definition. A simple and efficient method determing whether or not a statistic is sufficient.