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temp
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#RJMCMC抽样
w=NULL;mu=NULL;Isigma=NULL;k_arr=NULL;
for(chou in 1:20000)
{
#更新w
par=rep(0,k);#replicates the values in x
for(i in 1:k)
{par[i]=delta+N[i];}
w0=t(rdirichlet(1,par));
#Dirichlet distribution
#rdirichlet(n, alpha)
#n number of random variables to be generated.
#alpha vector of Dirichlet hyper parameter.
#更新mu
for(j in 1:k)
{
mub=(Isigma0[j]*sum((ifelse(z==j,1,0))*y)+kai*kesi)/(Isigma0[j]*N[j]+kai);
sigmab=1/(Isigma0[j]*N[j]+kai);
mu0[j]=rnorm(1,mub,sigmab);
}
#更新Isigma
for(j in 1:k)
{
Isigma0[j]=rgamma(1,alpha+N[j]/2,1/(beta+sum((ifelse(z==j,1,0))*((y-mu0[j])^2))/2));
}
#更新z,N
#Z为潜变量
p=matrix(0,n,k);
for(j in 1:k)
{
p[,j]=w0[j]*sqrt(Isigma0[j])*exp(-(y-mu0[j])^2*Isigma0[j]/2);
}
z=max.col(p);
#max.col
#Find the maximum position for each row of a matrix,
for(i in 1:k)
{
N[i]=sum(ifelse(z==i,1,0));
}
#更新beta
temp=0;
for(j in 1:k)
{
temp=temp+Isigma0[j];
}
beta=rgamma(1,g+k*alpha,h+temp);
#更新k
k_sel=ceiling(k*runif(1));#随机取一个数用于合并或拆分
if (k>1) #合并
{
u=runif(1);#抽0～1的一个随机数
if (u<die[k])#判断是否合并
{
mu_sort=sort(mu0);#均值按升序排列
k_new=which(sort.list(mu0)==k_sel);#找到选取的点在升序中的位置
if(k_new==1)#选取在升序中与选取点邻近的点
{
k_old=sort.list(mu0)[k_new+1];
}else{
k_old=ifelse(k_new==k,sort.list(mu0)[k_new-1],ifelse(u<0.5,sort.list(mu0)[k_new-1],sort.list(mu0)[k_new+1]));
}
w_j=w0[k_sel]+w0[k_old];#更新w
mu_j=(w0[k_sel]*mu0[k_sel]+w0[k_old]*mu0[k_old])/w_j;#更新mu
Isigma_j=((w0[k_sel]*(mu0[k_sel]^2+Isigma0[k_sel]^(-1))+w0[k_old]*(mu0[k_old]^2+Isigma0[k_old]^(-1)))/w_j-mu_j^2)^(-1);#更新Isigma
if(max(k_sel,k_old)==k)
{
w_0=rep(0,(k-1));
w_0[1:(max(k_sel,k_old)-1)]=w0[1:(max(k_sel,k_old)-1)];
w_0[min(k_sel,k_old)]=w_j;#调整w
mu_0=rep(0,(k-1));
mu_0[1:(max(k_sel,k_old)-1)]=mu0[1:(max(k_sel,k_old)-1)];
mu_0[min(k_sel,k_old)]=mu_j;#调整mu
Isigma_0=rep(0,(k-1));
Isigma_0[1:(max(k_sel,k_old)-1)]=Isigma0[1:(max(k_sel,k_old)-1)];
Isigma_0[min(k_sel,k_old)]=Isigma_j;#调整Isigma
}
else{
w_0=rep(0,(k-1));
w_0[1:(max(k_sel,k_old)-1)]=w0[1:(max(k_sel,k_old)-1)];
w_0[min(k_sel,k_old)]=w_j;
w_0[max(k_sel,k_old):(k-1)]=w0[(max(k_sel,k_old)+1):k];#调整w
mu_0=rep(0,(k-1));
mu_0[1:(max(k_sel,k_old)-1)]=mu0[1:(max(k_sel,k_old)-1)];
mu_0[min(k_sel,k_old)]=mu_j;
mu_0[max(k_sel,k_old):(k-1)]=mu0[(max(k_sel,k_old)+1):k];#调整mu
Isigma_0=rep(0,(k-1));
Isigma_0[1:(max(k_sel,k_old)-1)]=Isigma0[1:(max(k_sel,k_old)-1)];
Isigma_0[min(k_sel,k_old)]=Isigma_j;
Isigma_0[max(k_sel,k_old):(k-1)]=Isigma0[(max(k_sel,k_old)+1):k];#调整Isigma
}
z_0=z;temp_1=which(z==k_sel);Palloc=1;
if(length(temp_1)!=0)
{
z_0[temp_1]=min(k_sel,k_old);
Palloc_1=prod((w0[k_sel]*sqrt(Isigma0[k_sel])*exp(-Isigma0[k_sel]*++
(y[temp_1]-mu0[k_sel])^2/2)/++
(w0[k_sel]*sqrt(Isigma0[k_sel])*++
exp(-Isigma0[k_sel]*(y[temp_1]-mu0[k_sel])^2/2)+++
w0[k_old]*sqrt(Isigma0[k_old])*exp(-Isigma0[k_old]*(y[temp_1]-mu0[k_old])^2/2))));
Palloc=Palloc*Palloc_1;
}
temp_2=which(z==k_old);
if(length(temp_2)!=0)
{
z_0[temp_2]=min(k_sel,k_old);
Palloc_2=prod((w0[k_old]*sqrt(Isigma0[k_old])*exp(-Isigma0[k_old]*++
(y[temp_2]-mu0[k_old])^2/2)/++
(w0[k_sel]*sqrt(Isigma0[k_sel])*++
exp(-Isigma0[k_sel]*(y[temp_2]-mu0[k_sel])^2/2)+++
w0[k_old]*sqrt(Isigma0[k_old])*exp(-Isigma0[k_old]*(y[temp_2]-mu0[k_old])^2/2))));
Palloc=Palloc*Palloc_2;
}
if (max(k_sel,k_old)<k)#调整z
{
for (i in (max(k_sel,k_old)+1):k)
{
temp=which(z==i);
if (length(temp)!=0) z_0(temp)=i-1;
}
}
u1=rbeta(1,2,2);u2=rbeta(1,2,2);u3=rbeta(1,1,1);#计算合并的接受概率
tempratio=w_j^(sum(ifelse(z==k_sel,1,0))+sum(ifelse(z==k_old,1,0)))*beta(1,(k-1))*gamma(alpha)*(Isigma0[k_sel]*Isigma0[k_old]/++
Isigma_j)^(1-alpha)/k/sqrt(kai/2/pi)/exp(-kai*(mu0[k_sel]^2+mu0[k_old]^2-mu_j^2)/2)/beta^alpha/++
exp(-beta*(Isigma0[k_sel]+Isigma0[k_old]-Isigma_j))/w0[k_sel]^(sum(ifelse(z==k_sel,1,0)))/w0[k_old]^(sum(ifelse(z==k_old,1,0)));
tempratio=ifelse(is.na(tempratio),100,tempratio);
ac_c=tempratio*bor[k-1]*Palloc*dbeta(u1,2,2)*dbeta(u2,2,2)*dbeta(u3,1,1)/die[k]/++
(w_j*abs(mu0[k_sel]-mu0[k_old])*Isigma_j)*(u2*(1-u2^2)*u3*(1-u3)*Isigma0[k_sel]*Isigma0[k_old]);
u=runif(1);
if(u<min(1,ac_c))#判断是否接受新的参数
{
k=k-1;mu0=mu_0;w0=w_0;Isigma0=Isigma_0;z=z_0;
}
}
else{ #进行拆分
u1=rbeta(1,2,2);u2=rbeta(1,2,2);u3=rbeta(1,1,1);
w_j1=w0[k_sel]*u1;w_j2=w0[k_sel]*(1-u1);#更新w
mu_j1=mu0[k_sel]-u2*sqrt(w_j2/w_j1)/sqrt(Isigma0[k_sel]);#更新mu
mu_j2=mu0[k_sel]+u2*sqrt(w_j1/w_j2)/sqrt(Isigma0[k_sel]);
Isigma_j1=1/(u3*(1-u2^2)*w0[k_sel]/(w_j1*Isigma0[k_sel]));#更新Isigma
Isigma_j2=1/((1-u3)*(1-u2^2)*w0[k_sel]/(w_j2*Isigma0[k_sel]));
label_var_pre=rep(0,(k-1));
label_var_pre[1:(k_sel-1)]=mu0[1:(k_sel-1)];
label_var_pre[k_sel:(k-1)]=mu0[(k_sel+1):k];
label_var_pre_sort=sort(label_var_pre);#升序排列
new_com_1=p_w*w_j1+q_w*mu_j1+(1-p_w-q_w)*Isigma_j1;
new_com_2=p_w*w_j2+q_w*mu_j2+(1-p_w-q_w)*Isigma_j2;
if (sum(ifelse(label_var_pre_sort<new_com_1,1,0))==sum(ifelse(label_var_pre_sort<new_com_2,1,0)))
{
if (k_sel<k)
{
w_0=rep(0,(k+1));
w_0[1:(k_sel-1)]=w0[1:(k_sel-1)];w_0[k_sel]=w_j1;w_0[k_sel+1]=w_j2;w_0[(k_sel+2):(k+1)]=w0[(k_sel+1):k];
mu_0=rep(0,(k+1));
mu_0[1:(k_sel-1)]=mu0[1:(k_sel-1)];mu_0[k_sel]=mu_j1;mu_0[k_sel+1]=mu_j2;mu_0[(k_sel+2):(k+1)]=mu0[(k_sel+1):k];
Isigma_0=rep(0,(k+1));
Isigma_0[1:(k_sel-1)]=Isigma0[1:(k_sel-1)];Isigma_0[k_sel]=Isigma_j1;Isigma_0[k_sel+1]=Isigma_j2;Isigma_0[(k_sel+2):(k+1)]=Isigma0[(k_sel+1):k];
z_0=z;
for(i in (k_sel+1):k)
{
temp=which(z==i);
if(length(temp)!=0) z_0[temp]=i+1;
}
}else
{
w_0=rep(0,(k+1));
w_0[1:(k_sel-1)]=w0[1:(k_sel-1)];w_0[k_sel]=w_j1;w_0[k_sel+1]=w_j2;
mu_0=rep(0,(k+1));
mu_0[1:(k_sel-1)]=mu0[1:(k_sel-1)];mu_0[k_sel]=mu_j1;mu_0[k_sel+1]=mu_j2;
Isigma_0=rep(0,(k+1));
Isigma_0[1:(k_sel-1)]=Isigma0[1:(k_sel-1)];Isigma_0[k_sel]=Isigma_j1;Isigma_0[k_sel+1]=Isigma_j2;
z_0=z;
}
temp=which(z==k_sel);U=runif(length(temp));
z_0[temp]=k_sel+ifelse((U<(w_j2*sqrt(Isigma_j2)*exp(-Isigma_j2*(y[temp]-mu_j2)^2/2)/(w_j1*sqrt(Isigma_j1)*exp(-Isigma_j1*++
(y[temp]-mu_j1)^2/2)+w_j2*sqrt(Isigma_j2)*exp(-Isigma_j2*(y[temp]-mu_j2)^2/2)))),1,0);
Palloc=1;temp_1=which(z_0==k_sel);
if(length(temp_1)!=0)
{
Palloc_1=prod((w_j1*sqrt(Isigma_j1)*exp(-Isigma_j1*(y[temp_1]-mu_j1)^2/2)/++
(w_j1*sqrt(Isigma_j1)*exp(-Isigma_j1*(y[temp_1]-mu_j1)^2/2)+++
w_j2*sqrt(Isigma_j2)*exp(-Isigma_j2*(y[temp_1]-mu_j2)^2/2))));
Palloc=Palloc*Palloc_1;
}
temp_2=which(z_0==(k_sel+1));
if(length(temp_2)!=0)
{
Palloc_2=prod((w_j2*sqrt(Isigma_j2)*exp(-Isigma_j2*(y[temp_2]-mu_j2)^2/2)/++
(w_j1*sqrt(Isigma_j1)*exp(-Isigma_j1*(y[temp_2]-mu_j1)^2/2)+++
w_j2*sqrt(Isigma_j2)*exp(-Isigma_j2*(y[temp_2]-mu_j2)^2/2))));
Palloc=Palloc*Palloc_2;
}
temp=which(z==k_sel);
tempratio=w0[k_sel]^(sum(ifelse(z==k_sel,1,0))+sum(ifelse(z==(k_sel+1),1,0)))*beta(1,k)*gamma(alpha)*(Isigma_j1*Isigma_j2/++
Isigma0[k_sel])^(1-alpha)/(k+1)/sqrt(kai/2/pi)/exp(-kai*(mu_j1^2+mu_j2^2-mu0[k_sel]^2)/2)/beta^alpha/++
exp(-beta*(Isigma_j1+Isigma_j2-Isigma0[k_sel]))/w_j1^(sum(ifelse(z_0==k_sel,1,0)))/w_j2^(sum(ifelse(z==(k_sel+1),1,0)));
tempratio=ifelse(is.na(tempratio),1/100,tempratio);
ac_s=d_k[k+1]/(b_k[k]*Palloc*dbeta(u1,2,2)*dbeta(u2,2,2)*dbeta(u3,1,1))*w0[k_sel]*abs(mu_j1-mu_j2)*Isigma0[k_sel]/(u2*++ #计算拆分的接受概率
(1-u2^2)*u3*(1-u3)*Isigma_j1*Isigma_j2)/tempratio;
u=runif(1);
if(u<min(1,ac_s))#判断是否接受新的参数
{
k=k+1;mu0=mu_0;w0=w_0;Isigma0=Isigma_0;z=z_0;
}
}
}
}else #k=1,直接进行拆分
{
u1=rbeta(1,2,2);u2=rbeta(1,2,2);u3=rbeta(1,1,1);w_1=w0*u1;w_2=w0*(1-u1);
mu_1=mu0-u2*sqrt(w_2/w_1)/sqrt(Isigma0);mu_2=mu0+u2*sqrt(w_1/w_2)/sqrt(Isigma0);
Isigma_1=1/(u3*(1-u2^2)*w0/(w_1*Isigma0));Isigma_2=1/((1-u3)*(1-u2^2)*w0/(w_2*Isigma0));
mu_0=rep(0,2);
mu_0[1]=mu_1;mu_0[2]=mu_2;
Isigma_0=rep(0,2);
Isigma_0[1]=Isigma_1;Isigma_0[2]=Isigma_2;
w_0=rep(0,2);
w_0[1]=w_1;w_0[2]=w_2;
U=runif(length(y));
z_0=1+ifelse((U<(w_0[2]*sqrt(Isigma_0[2])*exp(-Isigma_0[2]*(y-mu_0[2])^2/2)/++
(w_0[1]*sqrt(Isigma_0[1])*exp(-Isigma_0[1]*(y-mu_0[1])^2/2)+++
w_0[2]*sqrt(Isigma_0[2])*exp(-Isigma_0[2]*(y-mu_0[2])^2/2)))),1,0);
Palloc=1;
for(i in 1:2)
{
temp=which(z_0==i);
if(length(temp)!=0)
{
Palloc_0=prod((w_0[i]*sqrt(Isigma_0[i])*exp(-Isigma_0[i]*++
(y[temp]-mu_0[i])^2/2)/(w_0[1]*sqrt(Isigma_0[1])*exp(-Isigma_0[1]*++
(y[temp]-mu_0[1])^2/2)+w_0[2]*sqrt(Isigma_0[2])*exp(-Isigma_0[2]*++
(y[temp]-mu_0[2])^2/2))));
Palloc=Palloc*Palloc_0;
}
}
tempratio=beta(1,k)*gamma(alpha)*(Isigma_1*Isigma_2/Isigma0)^(1-alpha)/(k+1)/sqrt(kai/2/pi)/exp(-kai*(mu_1^2+mu_2^2-mu0^2)/2)/++
beta^alpha/exp(-beta*(Isigma_1+Isigma_2-Isigma0))/w_1^(sum(ifelse(z_0==1,1,0)))/w_2^(sum(ifelse(z_0==2,1,0)));
tempratio=ifelse(is.na(tempratio),1/100,tempratio);
ac_s=die[k+1]/(bor[k]*Palloc*dbeta(u1,2,2)*dbeta(u2,2,2)*dbeta(u3,1,1))*++
w0*abs(mu_1-mu_2)*Isigma0/(u2*(1-u2^2)*u3*(1-u3)*Isigma_1*Isigma_2)/tempratio;
u=runif(1);
if(u<min(1,ac_s))
{k=k+1;mu0=mu_0;w0=w_0;Isigma0=Isigma_0;z=z_0;}
}
###########################
#生成或删除一个成分
N=rep(0,k);#计算属于第i类点的个数
for(i in 1:k){
N[i]=sum(ifelse(z==i,1,0));
}
k_empty=which(N==0);
if(k>1) {#生成或删除一个成分
u=runif(1);
if(u<bor[k]){#<--生成一个成分
w_birth=rbeta(1,1,k);mu_birth=rnorm(1,kesi,sqrt(1/kai));Isigma_birth=rgamma(alpha,1/beta);
B=1/beta(k*delta,delta)*w_birth^(delta-1)*(1-w_birth)^(length(y)+k*delta-k)*(k+1)*++
die[k+1]/(length(k_empty)+1)/bor[k]/dbeta(w_birth,1,k)*(1-w_birth)^k;
u=runif(1);
if(u<min(1,B))#判断是否接受
{
k=k+1;
w_0=rep(0,(k+1));
w_0[1:k]=w0*(1-w_birth);w_0[k+1]=w_birth;w0=w_0;
mu_0=rep(0,(k+1));
mu_0[1:k]=mu0;mu_0[k+1]=mu_birth;mu0=mu_0;
Isigma_0=rep(0,(k+1));
Isigma_0[1:k]=Isigma0;Isigma_0[k+1]=Isigma_birth;Isigma0=Isigma_0;
}
}#生成一个成分-->
else{#<--删除一个成分
if(length(k_empty)!=0){
k_death=k_empty[ceiling(length(k_empty)*runif(1))];
B_B=beta((k-1)*delta,delta)/w0[k_death]^(delta-1)/(1-w0[k_death])^(length(y)+(k-1)*(delta-1))/k*++
bor[k-1]*length(k_empty)/die[k]*dbeta(w0[k_death],1,k-1)/(1-w0[k_death])^(k-1);
u=runif(1);
if(u<min(1,B_B))
{
w_0=rep(0,(k-1));
w_0[1:(k_death-1)]=w0[1:(k_death-1)];
w_0[k_death:(k-1)]=w0[(k_death+1):k];
w_0=w_0/(1-w0[k_death]);
mu_0=rep(0,(k-1));
mu_0[1:(k_death-1)]=mu0[1:(k_death-1)];
mu_0[k_death:(k-1)]=mu0[(k_death+1):k];
Isigma_0=rep(0,(k-1));
Isigma_0[1:(k_death-1)]=Isigma0[1:(k_death-1)];
Isigma_0[k_death:(k-1)]=Isigma0[(k_death+1):k];
if(k_death<k)
{
for(i in (k_death+1):k)
{
temp=which(z==i);
if(length(temp)!=0) z[temp]=i-1;
}
}
k=k-1;
}
}
} #删除一个成分-->
}#生成或删除一个成分-->
else{#<--当k=1时,直接生成一个成分
w_birth=rbeta(1,1,k);mu_birth=rnorm(1,kesi,sqrt(1/kai));Isigma_birth=rgamma(alpha,1/beta);
B=1/beta(k*delta,delta)*w_birth^(delta-1)*(1-w_birth)^(length(y)+k*delta-k)*(k+1)*++
die[k+1]/(length(k_empty)+1)/bor[k]/dbeta(w_birth,1,k)*(1-w_birth)^k;
u=runif(1);
if(u<min(1,B)){#<--判断是否接受
k=k+1;
w_0=rep(0,(k+1));
w_0[1:k]=w0*(1-w_birth);w_0[k+1]=w_birth;w0=w_0;
mu_0=rep(0,(k+1));
mu_0[1:k]=mu0;mu_0[k+1]=mu_birth;mu0=mu_0;
Isigma_0=rep(0,(k+1));
Isigma_0[1:k]=Isigma0;Isigma_0[k+1]=Isigma_birth;Isigma0=Isigma_0;
}#判断是否接受-->
}#当k=1时,直接生成一个成分-->
}