基于Jeffreys验前的Bayes方差估计修正

Modification of Bayesian Variance Estimation Based on Jeffreys Prior

分析了基于Jeffreys验前的经典Bayes方差估计以及考虑验前信息可信度情况下Bayes方差估计存在的问题,在一般情况下,其方差估计要大于验前子样和验后子样的方差,这显然是不合理的.这是采用Jeffreys验前和正态共轭分布假设时存在的固有问题.为了解决这一问题,提出了方差估计的修正公式,经过计算验证,其值在验前子样和验后子样方差之间,说明修正公式是合理的.

The problem of Bayesian variance estimation based on Jeffreys prior is analyzed,including classical Bayesian estimation and the variance estimation based on the credibility of prior information.In general cases,Bayesian variance estimation will be greater than the variances of prior sample and test sample,which is obviously unreasonable.This is the intrinsic issue under the assumptions of Jeffreys prior and normal conjugate distribution.In order to settle the issue,the modified formulas for variance estimation are proposed,whose values lie between the variances of prior sample and test sample.So the modified formulas are reasonable.