MCMC
涓殑
Metropolis Hastings
鎶芥牱娉?/p>
2012
骞?/p>
03
鏈?/p>
09
鏃?/p>
鈦?/p>
Script
鈦?/p>
瀛楀彿
灏忎腑澶?/p>
鈦?/p>
鏆傛棤璇勮
鈦?/p>
闃呰
1,823
娆?/p>
[
鐐瑰嚮鍔犲叆鍦ㄧ嚎鏀惰棌澶?/p>
]
Metropolis Hasting
锛堜笅闈㈢畝绉?/p>
MH
锛夋槸钂欑壒鍗＄綏椹皵绉戝か閾句腑涓�绉嶉噸瑕佺殑
鎶芥牱
鏂规硶銆傛湰鏂囩畝
瑕佷粙缁?/p>
MH
绠楁硶锛屽苟缁欏嚭涓�涓疄渚嬨�?/p>
MH
绠楁硶鍦ㄥ弬鏁扮┖闂撮殢鏈哄彇鍊硷紝浣滀负璧峰鐐广�傛寜鐓у弬鏁扮殑姒傜巼鍒嗗竷鐢熸垚闅忔満鐨勫弬鏁帮紝鎸夌収杩?/p>
涓�绯诲垪鍙傛暟鐨勭粍鍚堬紝璁＄畻褰撳墠鐐圭殑姒傜巼瀵嗗害銆備緷鎹綋鍓嶇偣鍜岃捣濮嬬偣姒傜巼瀵嗗害姣斿�兼槸鍚﹀ぇ浜?/p>
(
0,1
)
涔嬮棿鐨勯殢鏈烘暟鏉ュ垽鏂槸鍚︿繚鐣欏綋鍓嶇偣銆?/p>
鑻ュ綋鍓嶇偣鐨勬鐜囧瘑搴﹀ぇ浜庤闅忔満鏁帮紝
灏辩О杩欑鐘?/p>
鎬佷负鎺ュ彈鐘舵�侊紝
姝ゆ椂锛屽湪婊¤冻鍙傛暟姒傜巼鍒嗗竷鐨勫墠鎻愪笅锛岀户缁殢鏈烘娊鍙栧弬鏁扮殑缁勫悎锛?/p>
浣滀负涓嬩竴
鐐癸紝璁＄畻涓嬩竴鐐圭殑姒傜巼瀵嗗害锛屽苟璁＄畻涓嬩竴鐐规鐜囧瘑搴﹀拰姒傜巼瀵嗗害鐨勬瘮鍊硷紝骞剁户缁惊鐜�?/p>
鑻ュ綋
鍓嶇偣涓嶈兘琚帴鍙楋紝
鍒欑户缁湪婊¤冻鍙傛暟姒傜巼鍒嗗竷鐨勫墠鎻愪笅锛?/p>
缁х画鐢熸垚闅忔満鏁帮紝
浣滀负鏂扮殑鍙傛暟缁?/p>
鍚堬紝鐩村埌鍙傛暟缁勫悎鑳藉琚帴鍙椾负姝€�?/p>
涓嬮潰鏄敤
MCMC
MH
鎶芥牱
娉曠敓鎴愭弧瓒充竴瀹氭潯浠朵簩鍏冩鎬佸垎甯冪殑渚嬪瓙锛屼緵鎰熷叴瓒ｇ殑鍚屼粊鍙傝�冦�?/p>
闂锛?/p>
##
瀵逛簬涓�涓簩鍏冩鎬佸垎甯冿紝缁欏畾杈撳叆鏁版嵁鐐瑰悜閲?/p>
x
锛?/p>
x
鍖呭惈涓や釜鍏冪礌锛?/p>
x1
锛?/p>
x2
锛?/p>
锛屽钩
鍧囧�煎弬鏁板悜閲?/p>
mu
锛?/p>
x1
锛?/p>
x2
锛?/p>
锛屽拰
sigma
锛堟柟宸煩闃碉級
锛屽啓鍑轰簩鍏冩鎬佸垎甯冪殑姒傜巼瀵嗗害鍑芥暟銆?/p>
璇ラ棶棰樺紩鑷細
http
://
users.aims.ac.za
/~
ioana
/
鐢变簬鏈汉瀵?/p>
MCMC
鐞嗚В涓嶆繁锛屽涓�浜涙蹇电殑鐞嗚В闅惧厤鍑虹幇閿欒锛屾湜璇昏�呰兘澶熸壒璇勫緱闃呰锛?/p>
鑻ュ彂鐜伴棶棰橈紝璇峰強鏃跺憡鐭ユ湰浜恒�?/p>
##
瑙ｇ瓟锛?/p>
mvdnorm <- function(x, mu, sigma){
#
浠?/p>
x
鍑忓幓
mu
x.minus.mu <- x - mu
exp.arg
<- -0.5 * sum(x.minus.mu * solve(sigma, x.minus.mu))
# det(sigma) sigma
鐨勮鍒楀紡
return( 1 / (2 * pi * sqrt(det(sigma))) * exp(exp.arg) )
}
##
闂浜?/p>
##
鍋囪浜屽厓姝ｆ�佸垎甯冪殑鍙傛暟濡備笅锛?/p>
##
涓や釜缁村害鐨勫钩鍧囧�煎垎鍒负
2
锛?/p>
3
#
鍗忔柟宸煩闃典负
# 4 1
# 1 4
#
灏濊瘯鐢ㄨ挋鐗瑰崱娲涢┈灏旂澶摼
Metropolis
Hastings
鎶芥牱娉曠敓鎴愬悗楠屽垎甯冿紝杩涜
10000
娆￠殢
鏈烘娊鏍凤紝骞惰绠楅殢鏈虹偣鐨勬帴鍙楃巼銆?/p>
#
绛旓細鎸夌収棰樻剰锛屾湁
mu <- c(2 ,3)
sigma <- matrix(c(4, 1, 1, 4), nrow = 2)
#
闄愬埗
sampler
鍦ㄧ┖闂寸殑绉诲姩閫熺巼锛屾暟鍊艰秺澶э紝鍙樺寲瓒婂揩锛岃鏁板�肩殑璁惧畾寰呰繘涓�姝ヨ璁恒�?/p>
sd.proposal <- 2
##
璁惧畾妯℃嫙鐨勬鏁?/p>