推 ddiigg:可不可以請教一下是哪一本書有提到呢？ 04/19 17:43
Suppose we have two independent observations
X1～N(μ1, σ1^2) X2～N(μ2, σ2^2)
where σ1, σ2 are known, and μ1, μ2 are independent.
Suppose prior densities for μ1, μ2 are
μ1～N(v1, υ1^2) μ2～N(v2, υ2^2)
where v1, υ1^2, v2, υ2^2 are known.
Find Bayes estimators for μ1, μ2 subject to the quadratic loss function
L(μ1*, μ2*)=(μ1*-μ1)^2 + (μ2*-μ2)^2
====
書上有這樣的範例推導
If X1, X2,... Xn iid ～N(μ, σ^2) where σ^2 is known and μ～N(v, υ^2)
then Bayes estimator for μ is
_
nX v
-- + --
σ^2 υ^2
------------
n 1
-- + --
σ^2 υ^2
我現在很疑惑, 因為 L 看起來像是兩個獨立的平方和, 不知道本題跟書上範例差在哪裡?
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