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正态情形下后验均值的收缩
Bayes estimation with a normal conditional distribution and an unknown prior distribution is considered. It is shown that the posterior mean always shrinks the observation toward a local maximum of the marginal distribution of the observation. For any symmetric, unimodal prior distribution itis shown that the posterior mean lies between the observation and the prior mean.
《线性回归模型中经验贝叶斯估计量的使用》公式订正条目
In (18) the quantity summed in the numerator should read and the definition of At should read (β – βi+h)/(2h). In (19) a plus sign should be inserted on the right hand side after β Exactly corresponding changes should be made in the numerator of (21) and in the definition of Ci In (30) the last term on the right hand side should read (x-x¯)2E(β-β)2.
点估计中的若干经验贝叶斯方法
In point estimation with a squared-error loss function the Bayes estimator is the posterior mean. In the empirical Bayes approach we must construct a consistent sequence of estimators for this posterior mean using past experience. This construction is done here for four general families of conditional distributions which include as special cases: the Poisson, the gamma, the normal and the uniform.
点估计中的若干经验贝叶斯技术
In point estimation with a squared-error loss function the Bayes estimator is the posterior mean. In the empirical Bayes approach we must construct a consistent sequence of estimators for this posterior mean using past experience. This construction is done here for four general families of conditional distributions which include as special cases: the Poisson, the gamma, the normal and the uniform.
经验贝叶斯估计量的 ε 渐近最优性
Robbins (1964) gives conditions under which empirical Beyes estimators are asymptotically optimal. The conditions require the loss function to be bounded in the parameter. This does not hold in some important situations including the squared error loss. Here we give weaker conditions and prove a weaker result, ε asymptotic optimality, which is equivalent to asymptotic optimality in practical situations.
经验贝叶斯方法：估计先验分布
There is a random variable A distributed according to a specific but unknown prior distribution G from an appropriate class GP. The random variable Λ = λ is unobrvable but another random variable X = x, distributed with known conditional distribution function F(x∣λ), is observable. We construct estimators Gn(λ) of G(λ) such that lim E[{Gn(λ) − G(λ)}2]=0 and we use Gn(λ) to estimate the posterior distribution G(λ∣x) and hence to construct consistent estimators of posterior…