二项分布的几种经验Bayes估计方法

讨论了4种二项分布的经验贝叶斯估计,并通过实例比较了这4种方法的优缺点.其中参数化方法缺点是要注意先验分布的选择;最小熵方法的缺点是只能采用数值解法;线性经验贝叶斯方法的优点是不需求出先验分布,结果简明,便于应用,缺点是需要估计局限于样本x的线性函数;条件期望法的优点是不必考虑先验分布的类型、参数等,只需要有充分多的“经验”样本.

Several empirical Bayes Estimations on binomial distribution

In this paper,four kinds of empirical estimations on binomial distribution are discussed.The advantages and disadvantages of the estimations are contrasted by examples.If a,b>0,the parametric method takes active.But in practice a<0 or b<0,we must consider the choice of prior distribution.To the minimum entroy method,it is difficult to solve equation,the only method we can adopt is numerical method.The advantage of linear empirical Bayes method is that the prior distribution is not necessary to be given and the result is clear and easy to apply.While the estimations are to be confined to be linear functions of the sample X,as to conditional expectation method,it is not concerned about the prior distribution's types,parameters and so on.We only need to have enough empirical samples.