※ [本文轉錄自 Statistics 看板 #1NRHrwXB ]作者: lin6613 (lin) 看板: Statistics標題: [問題] 一題Bayes estimate時間: Fri Jun 24 19:45:59 2016 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=0Prior 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 meanE(Θ|X=x) = ΣθP(Θ|X=x) = 0 0 + (3/4)(1) = 3/4 θ麻煩各位了--※ 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※ lin6613:轉錄至看板 Math 06/25 10:23※ 發信站: 批踢踢實業坊(ptt.cc)※ 轉錄者: lin6613 (106.1.3.60), 07/10/2016 16:15:05