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1、第 24卷null 第 8期Vo.l 24null null No. 8重庆理工大学学报(自然科学)Journal ofChongqingUniversity ofTechnology(Natural Science)2010年 8月Aug. 2010null null l : 2010- 06- 01 : i v 2010M nulld 9 0b2) x - , M q q(x1, x2)V4 p s 9 8 x* | x / B b3) x* ,9 ! x* - xt- 1 1 :null= p(x* )p(xt- 1) =f(x* )f(xt- 1 )null null 4) T nul
2、l 1,5 7 xt = x* ,i R 2); null 1,5 null q | xt = x* ,7 1- null q | xt = x* ,i R 2)b1. 2null Gibbs Gibbs Z E K * Geman7 1984M 4 , MetropolisnullHastings B + y f bGibbs Z E | _ bW s s , s GibbsM _ - ,+ Y a M b 8 E :L X= (x1, x2, , xn) Rn B _ b7 (n- 1) M X- jX- j = (x1, , xj- 1, xj+ 1, , xn ),i : xj |X-
3、 j H q f(xj |X- j ),5 G ibbs E / U :x1(t) f(x1 |x2(t- 1), x3(t- 1), , xn (t- 1)x2(t) f(x2 | x1(t), x3(t- 1), , xn(t- 1)xn(t) f(xn | x1(t),x2(t), x3(t), ,xn-1(t)null null Gibbs Z E | s B H q s 3 , s f ,E s V ? 4 b1. 3null _ r T K Z E _ V M s b s , E _ Z E _ f b = s , ! (null, ) f(x, y), (x, y)# D, ni
4、jV U(i, j) 0 Dij | ,5 Dij pij = nullDijf(x, y)dxdyb: L = nullpij =nijn, nV U | 9 , E _ ,5 !2 = i j(nullpij - pij )2pij !2(m) :m= (R- 1) (C - 1); R, Cs Y V U s b null f / , Td 9 W ,5 V U ? | V s f(x, y), f / _ b2null M 2. 1null M G ibbs Z E , s B H qs ,V L C s b s ,L ! X Np (, ), , X =105荣腾中,等:多维复杂分布
5、的MCMC抽样(x1, x2, , xp )%b7 X i= xi,X- i = (x1, x2, , xi- 1, xi+ 1 , xp )%,Xi |X - i Np ( i|- i, i|- i ), i| - i = i +cov(X i,X- i) - 1- i (X - i - - i), i|- i = ii -cov(X i,X- i) - 1- i cov(X - i,Xi),y N f(Xi |X - i) N(i| - i, i|- i), i= 1, 2, , pb Gibbs E , / :1)7 X=X (t- 1)b2)V f(Xi |X- i) 3 Xi ! x
6、( t)i , X xi b3) T i p,| i= i+ 1,R 2)b4) X(t)= (x( t)1 , x(t)2 , , x( t)p )b = s X= (x1, x2)%N(1, 2, #21,#22, ) , | 1 = 0, #1 = 1, 2 = 3, #2 = 2,= - 0. 77, G ibbs E , S 1 000 , : 9 , T :12= - 0. 004 63. 006 7, = 1. 022 8 - 1. 578 5- 1. 578 5 4. 076 7,= - 0. 773 0null null 9 T 9 ,T (x1, x2) m , m 1 U
7、 ,V 9 V A x1, x2 W A M 1 b图 1null x1, x2间的散点图2. 2null s s ,6 B 4 L C s , MCMC E ,V Z L | H q b ! X =(x1, x2, , xp )% f(x1, x2, , xp ), x1, x2, ,xi M , xi+ 1, xi+ 2, , xp M b: null= (x1, x2, , xi )%, = (xi+ 1, xi+ 2, xp )%, | , null M , | null , M b X 2 gibbs L C b / s ,i s :f(x, y) = n!(n- x)!x!yx+
8、null- 1(1- y)n-x+ %- 1,x = 0, 1, , n, null y # 0, 1A s 1 ,7 I n H q s / T :f(x | y = p, n) & n!(n- x)!x!px (1- p)n-xf(y | null, %) & ynull- 1(1- y)%- 1 x|y B(n, y), y |x Beta(x+ null, n- x+ %)b | n= 20, null= 1. 5, %= 2 y0 = 1/2, Gibbs / U :1) x0 V = s B(n, y0)= B(20, 1/2) M b2) yt+ 1 V Beta(x+ null, n- x+ %)= Beta(xt +1. 5, 20- xt+ 2) | M b3) xt+ 1 V = s B(n, y1 )= B(20, yt ) M ,R 2)b (x, y) m m 2 U bV m 2V A | y xv V = s , xH s , yH s b106 重庆理工大学学报图 2null (x, y)散点图3null V s T V A , MCMC E 9 E , . d Z E , s bMCMC E v % 5 B 1 7
