[問題] 一題Bayes estimate
Let X be a single observation frome a geometric distribution with density
P(X=x|Θ) = (1-θ)(θ^x) for x=0,1,2,3,... & 0≦θ＜1 .
Want to estimate θ. with loss function L(θ,d)=(θ-d)^2
1/3 , if θ=0
Prior distribution P(θ)= {
2/3 , if θ=3/4
我現在想要算posterior density 麻煩幫大家看我有沒有哪邊算錯
P(Θ,X) P(X|Θ) P(θ)
P(Θ|X=x) =--------- = -----------------
P(X) Σ P(X|Θ) P(θ) 這邊是貝氏定理
θ
(1-θ)θ^x P(θ)
=---------------------------------------
(1-0)0^x (1/3) + (1-3/4)(3/4)^x (2/3) 分母左邊=0
0 if θ=0
= {
1 if θ=3/4
如果這條件機率沒算錯，接下來繼續算posterior mean
E(Θ|X=x) = ΣθP(Θ|X=x) = 0 0 + (3/4)(1) = 3/4
θ
麻煩各位了
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※ 文章網址: https://www.ptt.cc/bbs/Statistics/M.1466768762.A.84B.html
※ 編輯: lin6613 (106.1.3.60), 06/24/2016 19:47:01
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