[問題] Bayes procedure和Frequentist test問題
想要請教大家下面這道題目:
Use the binomial model for X with n=25; 0<θ<1, A={a1,a2} where a1 means:“
say θ<=0.2”and a2 means:”say θ>0.2”.
a)Let the loss be L(a1,θ)= 0, ifθ<=0.2 or 5, ifθ>0.2
L(a2,θ)= 10, ifθ<=0.2 or 0, ifθ>0.2
Find the Bayes procedure for a Beta prior with α=6 and β=18
b)Consider the following class of decision procedures:
t(x)=a2 if and only if X>C where C can be any value in {0,1,2,…,n-1}
Find C such that the defined procedure is a frequentist test of size α=0.05
c)Show that there is a Beta prior such that the corresponding Bayes procedure
is the frequentist test in (b).
d)Assume the prior is Uniform on the interval 0 to 1. Show that there is a
very drastic modification of the loss function above which makes the
frequentist test in (b) a Bayes procedure wrt this prior.
下面是我現在遇到困難的地方~
a)我有解出到 Bayes Procedure t(x)=a1 iff 1/3<=P(θ<=0.2|x)
a2 otherwise
不知道要如何把x解出來
b)從這條式子P(X>C|θ=0.2)<=0.05有解出C=8
不知道對不對
c)是指說改變Beta(α,β)中的α和β讓Bayes procedure 變成 frequentist test嗎?
d)就完全沒有頭緒了
可以請大家給點想法嗎?
謝謝大家^^
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