正态分布在不同先验下的Bayes估计及风险比较

Bayes estimation and risk comparison of two prior distribution at the normal distribution

本文讨论在均值未知,方差已知的正态分布情况下通过在共轭先验以及Jeffreys先验二种先验下的Bayes估计问题,在平方损失函数下和线性损失函数下Bayes风险的比较.数据计算可以看出,在Jeffreys先验下的Bayes风险要比在共轭先验下的Bayes风险要大,但是当样本量增大时,两者的后验风险越来越靠近.

This article discusses in the average value unknown, in variance knownnormal distribution situation through in conjugate prior as well as Jeffreys priortwo kind of prior under Bayes estimate question, under square loss function and under linear loss function Bayes risk comparison. Form the data may see, risk must have to be bigger in the Jeffreys prior than in the conjugate prior, but when the sample size increases, both after examines the risk more and more to approach.