不同先验信息下成功概率的Bayes估计

参数的Bayes估计取决于先验分布和损失函数。在平方损失下,参数的Bayes估计是后验分布的均值。在无信息先验、Jeffreys先验和平方损失下,给出两点分布成功概率的估计,比较了其无偏性、方差、均方误差与风险,并进行了数值仿真实验。结果表明:无信息先验分布下的估计优于Jeffreys先验分布下的估计,无信息先验分布下估计的均方误差小于Jeffreys先验分布下的估计的均方误差,无信息先验分布下估计的风险小于Jeffreys先验分布下的估计的风险。

Bayes estimation of success probability under different priors information

Bayes estimation of parameter depends on the prior distribution and the loss function .Bayes estimation is the mean of the posterior distribution under the square loss .The paper first provided the Bayes es-timation of success probability under the condition of zero information priori , Jeffreys priori and square loss , and then compared the properties of unbiasedness , variance and MSE and risks , and the numerical simulation was also experimented .The result showed that the estimation under zero information priori is better than the es-timation under Jeffreys priori .The MSE of the estimation under non-informative priori is smaller than the esti-mation under Jeffreys priori and the risk of the estimation under non-informative priori is better than the estima-tion under Jeffreys priori .