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mFB_code.R
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mFB_code.R
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########################################################################################################################################################################################################################
#Load Packages
########################################################################################################################################################################################################################
library(truncnorm)
library(lattice)
library(nlme)
library(MCMCpack)
library(combinat)
########################################################################################################################################################################################################################
#Load Data
########################################################################################################################################################################################################################
data=read.csv("Training_data.csv")
data_validation=read.csv("Validation_data.csv")
set.seed(1) #set seed so each run matches reported results
########################################################################################################################################################################################################################
#Functions for model fitting
########################################################################################################################################################################################################################
posterior_mu_theta=function(Theta,sigma_theta_2,mu_0,sigma_0_2)
{
mu_0_star=(sigma_theta_2*mu_0)/(sigma_theta_2 + N*sigma_0_2) + (sigma_0_2*sum(Theta))/(sigma_theta_2 + N*sigma_0_2)
sigma_0_star_2=(sigma_theta_2*sigma_0_2)/(sigma_theta_2 + N*sigma_0_2)
list(mu_0_star=mu_0_star,sigma_0_star_2=sigma_0_star_2)
}
posterior_sigma_theta_2=function(Theta,mu_theta,a_theta,b_theta)
{
a_theta_star=a_theta + N/2
b_theta_star=b_theta + sum((Theta-mu_theta)^2)/2
list(a_theta_star=a_theta_star,b_theta_star=b_theta_star)
}
posterior_sigma_2=function(Y,t,D,J,Theta,I,gamma,Tau)
{
a_sigma=sum(J)/2
temp_I=rep(c(rep(0,n_0),I),J)
temp_gamma=rep(c(rep(0,n_0),gamma),J)
temp_gamma[is.na(temp_gamma)]=0
temp_Tau=rep(c(rep(0,n_0),Tau),J)
temp_Tau[is.na(temp_Tau)]=0
Theta_star=rep(Theta,J)+temp_gamma*(t-temp_Tau)*as.numeric(t>temp_Tau)
b_sigma=sum((Y-Theta_star)^2)/2
list(a_sigma=a_sigma,b_sigma=b_sigma)
}
posterior_mu_gamma=function(I,gamma,sigma_gamma_2,mu_1,sigma_1_2)
{
n_I=sum(I)
mu_1_star=(sigma_gamma_2*mu_1)/(sigma_gamma_2 + n_I*sigma_1_2) + (sigma_1_2*sum(log(gamma),na.rm=T))/(sigma_gamma_2 + n_I*sigma_1_2)
sigma_1_star_2=(sigma_gamma_2*sigma_1_2)/(sigma_gamma_2 + n_I*sigma_1_2)
list(mu_1_star=mu_1_star,sigma_1_star_2=sigma_1_star_2)
}
posterior_sigma_gamma_2=function(I,gamma,mu_gamma,a_gamma,b_gamma)
{
n_I=sum(I)
a_gamma_star=a_gamma+n_I/2
b_gamma_star=b_gamma+sum((log(gamma)-mu_gamma)^2,na.rm=T)/2
list(a_gamma_star=a_gamma_star,b_gamma_star=b_gamma_star)
}
posterior_theta=function(Y_i,t_i,D_i,J_i,mu_theta,sigma_theta_2,sigma_2,I_i,gamma_i,tau_i)
{
Y_star_i=Y_i
if(is.na(I_i)==FALSE & I_i==1)
{
Y_star_i=Y_i-gamma_i*(t_i-tau_i)*as.numeric(t_i>tau_i)
}
mu_theta_star=(sigma_2*mu_theta)/(sigma_2 + J_i*sigma_theta_2) + (sigma_theta_2*sum(Y_star_i))/(sigma_2 + J_i*sigma_theta_2)
sigma_theta_star_2=(sigma_2*sigma_theta_2)/(sigma_2 + J_i*sigma_theta_2)
list(mu_theta_star=mu_theta_star,sigma_theta_star_2=sigma_theta_star_2)
}
log_likelihood_cases=function(Y_i,t_i,J_i,sigma_2,Theta_i,I_i,gamma_i,tau_i)
{
log_pr=NA
if(I_i==0)
{
log_pr=log((2*pi*sigma_2)^(-J_i/2)) + (-sum((Y_i-Theta_i)^2)/(2*sigma_2))
}
if(I_i==1)
{
log_pr=log((2*pi*sigma_2)^(-J_i/2)) + (-sum((Y_i-Theta_i-gamma_i*(t_i-tau_i)*as.numeric(t_i>tau_i))^2)/(2*sigma_2))
}
log_pr
}
update_I=function(Y_i,t_i,J_i,d_i,mu_gamma,sigma_gamma_2,mu_tau,sigma_tau_2,Tau_star,sigma_2,Theta_i,I_i,gamma_i,tau_i,Pi)
{
#new_I=NA
new_gamma=NA
new_tau=NA
if(I_i==0)
{
gamma_star=exp(rnorm(1,mean=mu_gamma,sd=sqrt(sigma_gamma_2)))
tau_star=rtruncnorm(1,a=d_i-Tau_star,b=d_i,mean=d_i-mu_tau,sd=sqrt(sigma_tau_2))
temp_log_r=log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=1,gamma_i=gamma_star,tau_i=tau_star)-log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=0,gamma_i=NA,tau_i=NA)
log_r=min(temp_log_r+log(Pi)-log(1-Pi),log(1))
u=runif(1,min=0,max=1)
new_I=as.numeric(log(u)<log_r)
if(new_I==1)
{
new_gamma=gamma_star
new_tau=tau_star
}
}
if(I_i==1)
{
temp_log_r=log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=0,gamma_i=NA,tau_i=NA)-log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=1,gamma_i=gamma_i,tau_i=tau_i)
log_r=min(temp_log_r+log(1-Pi)-log(Pi),log(1))
u=runif(1,min=0,max=1)
new_I=1-as.numeric(log(u)<log_r)
if(new_I==1)
{
new_gamma=gamma_i
new_tau=tau_i
}
}
list(new_I=new_I,new_gamma=new_gamma,new_tau=new_tau)
}
update_gamma=function(Y_i,t_i,J_i,mu_gamma,sigma_gamma_2,sigma_2,Theta_i,I_i,gamma_i,tau_i,delta_gamma)
{
new_gamma=NA
gamma_accepted=NA
new_I=0
new_tau=NA
if(I_i==1)
{
gamma_star=exp(rnorm(1,mean=log(gamma_i),sd=delta_gamma))
log_temp_r1=log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=1,gamma_i=gamma_star,tau_i=tau_i)-log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=1,gamma_i=gamma_i,tau_i=tau_i)
log_temp_r2=log(dlnorm(x=gamma_star,meanlog=mu_gamma,sdlog=sqrt(sigma_gamma_2)))-log(dlnorm(x=gamma_i,meanlog=mu_gamma,sdlog=sqrt(sigma_gamma_2)))
log_temp_r3=log(dlnorm(x=gamma_i,meanlog=log(gamma_star),sdlog=delta_gamma))-log(dlnorm(x=gamma_star,meanlog=log(gamma_i),sdlog=delta_gamma))
log_r=min(log_temp_r1+log_temp_r2+log_temp_r3,log(1))
u=runif(1,min=0,max=1)
new_gamma=as.numeric(log(u)<log_r)*gamma_star + (1-as.numeric(log(u)<log_r))*gamma_i
gamma_accepted=as.numeric(log(u)<log_r)
new_I=I_i
new_tau=tau_i
}
list(new_gamma=new_gamma,gamma_accepted=gamma_accepted,new_I=new_I,new_tau=new_tau)
}
update_tau=function(Y_i,t_i,J_i,d_i,sigma_2,mu_tau,sigma_tau_2,Theta_i,I_i,gamma_i,tau_i,delta_tau,Tau_star)
{
new_gamma=NA
new_I=0
new_tau=NA
tau_accepted=NA
if(I_i==1)
{
tau_star=rtruncnorm(1,a=d_i-Tau_star,b=d_i,mean=tau_i,sd=delta_tau)
log_temp_r1=log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=1,gamma_i=gamma_i,tau_i=tau_star)-log_likelihood_cases(Y_i,t_i,J_i,sigma_2,Theta_i,I_i=1,gamma_i=gamma_i,tau_i=tau_i)
log_temp_r2=log(dtruncnorm(x=tau_star,a=d_i-Tau_star,b=d_i,mean=d_i-mu_tau,sd=sqrt(sigma_tau_2)))-log(dtruncnorm(x=tau_i,a=d_i-Tau_star,b=d_i,mean=d_i-mu_tau,sd=sqrt(sigma_tau_2)))
log_temp_r3=log(dtruncnorm(x=tau_i,a=d_i-Tau_star,b=d_i,mean=tau_star,sd=delta_tau))-log(dtruncnorm(x=tau_star,a=d_i-Tau_star,b=d_i,mean=tau_i,sd=delta_tau))
log_r=min(log_temp_r1+log_temp_r2+log_temp_r3,log(1))
u=runif(1,min=0,max=1)
new_tau=as.numeric(log(u)<log_r)*tau_star + (1-as.numeric(log(u)<log_r))*tau_i
tau_accepted=as.numeric(log(u)<log_r)
new_I=I_i
new_gamma=gamma_i
}
list(new_gamma=new_gamma,tau_accepted=tau_accepted,new_I=new_I,new_tau=new_tau)
}
update_mu_tau=function(Tau,I,d,D,mu_tau,sigma_tau_2,delta_mu_tau,mu_2,sigma_2_2,Tau_star)
{
n_I=sum(I)
mu_tau_star=rnorm(1,mean=mu_tau,sd=delta_mu_tau)
log_temp1=sum(log(dtruncnorm(x=Tau[I==1],a=d[D==1][I==1]-Tau_star,b=d[D==1][I==1],mean=d[D==1][I==1]-mu_tau_star,sd=sqrt(sigma_tau_2)))) + log(dnorm(x=mu_tau_star,mean=mu_2,sd=sqrt(sigma_2_2)))
log_temp2=sum(log(dtruncnorm(x=Tau[I==1],a=d[D==1][I==1]-Tau_star,b=d[D==1][I==1],mean=d[D==1][I==1]-mu_tau,sd=sqrt(sigma_tau_2)))) + log(dnorm(x=mu_tau,mean=mu_2,sd=sqrt(sigma_2_2)))
log_r=min(log_temp1 - log_temp2,log(1))
u=runif(1,min=0,max=1)
new_mu_tau=as.numeric(log(u)<log_r)*mu_tau_star + (1-as.numeric(log(u)<log_r))*mu_tau
mu_tau_accepted=as.numeric(log(u)<log_r)
list(new_mu_tau=new_mu_tau,mu_tau_accepted=mu_tau_accepted)
}
update_sigma_tau=function(Tau,I,d,D,mu_tau,sigma_tau_2,delta_sigma_tau,a_tau,b_tau,Tau_star)
{
n_I=sum(I)
sigma_tau_2_star=rtruncnorm(1,a=0,b=Inf,mean=sigma_tau_2,sd=delta_sigma_tau)
log_temp1=sum(log(dtruncnorm(x=Tau[I==1],a=d[D==1][I==1]-Tau_star,b=d[D==1][I==1],mean=d[D==1][I==1]-mu_tau,sd=sqrt(sigma_tau_2_star)))) + log(dinvgamma(x=sigma_tau_2_star,shape=a_tau,scale=b_tau))
log_temp2=sum(log(dtruncnorm(x=Tau[I==1],a=d[D==1][I==1]-Tau_star,b=d[D==1][I==1],mean=d[D==1][I==1]-mu_tau,sd=sqrt(sigma_tau_2)))) + log(dinvgamma(x=sigma_tau_2,shape=a_tau,scale=b_tau))
log_temp3=log(dtruncnorm(x=sigma_tau_2,a=0,b=Inf,mean=sigma_tau_2_star,sd=delta_sigma_tau))-log(dtruncnorm(x=sigma_tau_2_star,a=0,b=Inf,mean=sigma_tau_2,sd=delta_sigma_tau))
log_r=min(log_temp1 - log_temp2 + log_temp3,log(1))
u=runif(1,min=0,max=1)
new_sigma_tau_2=as.numeric(log(u)<log_r)*sigma_tau_2_star + (1-as.numeric(log(u)<log_r))*sigma_tau_2
sigma_tau_accepted=as.numeric(log(u)<log_r)
list(new_sigma_tau_2=new_sigma_tau_2,sigma_tau_accepted=sigma_tau_accepted)
}
#I_matrix is a matrix of indicator variables of dimension (n-n_0) X K
update_mu_I=function(I_matrix,mu_I,eta_I,delta_mu_I)
{
mu_I_star=rnorm(1,mean=mu_I,sd=delta_mu_I)
log_temp1=log_p_all_I_mu_eta(I_matrix,mu_I_star,eta_I) + log_p_mu_I(mu_I_star)
log_temp2=log_p_all_I_mu_eta(I_matrix,mu_I,eta_I) + log_p_mu_I(mu_I)
log_r=min(log_temp1 - log_temp2,log(1))
u=runif(1,min=0,max=1)
new_mu_I=as.numeric(log(u)<log_r)*mu_I_star + (1-as.numeric(log(u)<log_r))*mu_I
mu_I_accepted=as.numeric(log(u)<log_r)
list(new_mu_I=new_mu_I,mu_I_accepted=mu_I_accepted)
}
#I_matrix is a matrix of indicator variables of dimension (n-n_0) X K
log_p_all_I_mu_eta=function(I_matrix,mu_I,eta_I)
{
temp=rep(NA,nrow(I_matrix))
for(l in 1:nrow(I_matrix))
{
temp[l]=log_p_I_mu_eta(I_matrix[l,],mu_I,eta_I)
}
sum(temp)
}
#I_vector is a vector of indicator variables
log_p_I_mu_eta=function(I_vector,mu_I,eta_I)
{
R=array(1,c(K,K))
R[lower.tri(R,diag=TRUE)]=0
#Normaliztion constant
I_full=find_all_comb(K)
c=0
for(l in 1:nrow(I_full))
{
temp1=sum(I_full[l,])
temp2=array(I_full[l,],c(K,1))
temp3=mu_I*temp1 + eta_I*(t(temp2)%*%R%*%temp2)
c=c+exp(temp3)
}
#Observed data
temp1=sum(I_vector)
temp2=array(I_vector,c(K,1))
mu_I*temp1 + eta_I*(t(temp2)%*%R%*%temp2) - log(c)
}
#K>1
find_all_comb=function(K)
{
temp1=array(0,c(K+1,K))
temp1[lower.tri(temp1,diag=FALSE)]=1
temp2=temp1[1,]
for(k in 2:K)
{
temp3=unique(permn(temp1[k,]))
l_temp3=length(temp3)
for(l in 1:l_temp3)
{
temp2=rbind(temp2,temp3[[l]])
}
}
temp2=rbind(temp2,temp1[K+1,])
array(temp2,dimnames=NULL,c(nrow(temp2),ncol(temp2)))
}
log_p_mu_I=function(mu_I)
{
temp1=log(dbeta(x=exp(mu_I)/(1+exp(mu_I)),shape1=p_1,shape2=p_2))
temp2=log(1+exp(mu_I))
temp1 + mu_I - 2*temp2
}
update_eta_I=function(I_matrix,mu_I,eta_I,delta_eta_I)
{
eta_I_star_parameters=get_beta_parameters(eta_I,delta_eta_I)
eta_I_star=rbeta(1,shape1=eta_I_star_parameters$a,shape2=eta_I_star_parameters$b)
log_temp1=log_p_all_I_mu_eta(I_matrix,mu_I,eta_I_star) + log(dbeta(eta_I_star,shape1=p_3,shape2=p_4))
log_temp2=log_p_all_I_mu_eta(I_matrix,mu_I,eta_I) + log(dbeta(eta_I,shape1=p_3,shape2=p_4))
temp_beta_parameters1=get_beta_parameters(eta_I_star,delta_eta_I)
temp_beta_parameters2=get_beta_parameters(eta_I,delta_eta_I)
log_temp3=log(dbeta(eta_I,shape1=temp_beta_parameters1$a,shape2=temp_beta_parameters1$b)) - log(dbeta(eta_I_star,shape1=temp_beta_parameters2$a,shape2=temp_beta_parameters2$b))
log_r=min(log_temp1 - log_temp2 + log_temp3,log(1))
u=runif(1,min=0,max=1)
new_eta_I=as.numeric(log(u)<log_r)*eta_I_star + (1-as.numeric(log(u)<log_r))*eta_I
eta_I_accepted=as.numeric(log(u)<log_r)
list(new_eta_I=new_eta_I,eta_I_accepted=eta_I_accepted)
}
get_beta_parameters=function(mean_eta_I,std_dev_eta_I)
{
var_eta_I=std_dev_eta_I^2
a=mean_eta_I + (mean_eta_I^2)/var_eta_I - (mean_eta_I^3)/var_eta_I
b=a*(1/mean_eta_I - 1)
list(a=a, b=b)
}
get_p1=function(mu_I,eta_I)
{
c_inv=1+3*exp(mu_I)+3*exp(2*mu_I+eta_I)+exp(3*mu_I+3*eta_I)
(exp(mu_I)+2*exp(2*mu_I+eta_I)+exp(3*mu_I+3*eta_I))/c_inv
}
get_p2_I_1=function(I_1,mu_I,eta_I)
{
c_inv=1+3*exp(mu_I)+3*exp(2*mu_I+eta_I)+exp(3*mu_I+3*eta_I)
p_I_1=(exp(mu_I)+2*exp(2*mu_I+eta_I)+exp(3*mu_I+3*eta_I))/c_inv
num=(exp(mu_I*(I_1+1)+eta_I*I_1) + exp(mu_I*(I_1+2)+eta_I*(2*I_1 + 1)))/c_inv
dem=p_I_1*I_1 + (1-p_I_1)*(1-I_1)
num/dem
}
get_p3_I_1_2=function(I_1,I_2,mu_I,eta_I)
{
F_I_3=mu_I + eta_I*(I_1 + I_2)
exp(F_I_3)/(1+exp(F_I_3))
}
########################################################################################################################################################################################################################
#Analyze Training Data (pg 6 Supplementary Materials)
########################################################################################################################################################################################################################
#Get sample size
N=length(unique(data$ID)) #total number of patients
n_0=length(unique(data$ID[(data$D==0)])) #number of control patients
#Extract vectors
D=data$D[(data$obs_number==1)] #case/control status
d=data$d[(data$obs_number==1)] #diagnosis/follow-up times
J=data$J[(data$obs_number==1)] #number of screening visits
K=3 #Number of biomarkers in the study
#Specify fixed parameters
p_1=30
p_2=30
p_3=5
p_4=45
#Biomarker 1
mu_0_1=2
sigma_0_1_2=0.1
a_theta_1=2
b_theta_1=0.05
mu_1_1=log(16)
sigma_1_1_2=0.1
a_gamma_1=4
b_gamma_1=0.1
Tau_star_1=2
mu_2_1=1
sigma_2_1_2=0.1
a_tau_1=10
b_tau_1=(0.75^2)*(a_tau_1+1)
#Biomarker 2
mu_0_2=3
sigma_0_2_2=0.1
a_theta_2=2
b_theta_2=0.05
mu_1_2=log(16)
sigma_1_2_2=0.05
a_gamma_2=2*2
b_gamma_2=0.05*2
Tau_star_2=2
mu_2_2=1
sigma_2_2_2=0.1
a_tau_2=10
b_tau_2=(0.75^2)*(a_tau_2+1)
#Biomarker 3
mu_0_3=2
sigma_0_3_2=0.1
a_theta_3=2
b_theta_3=0.05
mu_1_3=log(16)
sigma_1_3_2=0.05
a_gamma_3=2*2
b_gamma_3=0.05*2
Tau_star_3=2
mu_2_3=1
sigma_2_3_2=0.1
a_tau_3=10
b_tau_3=(0.75^2)*(a_tau_1+1)
S=10000
delta_gamma_set=0.1
delta_tau_set=0.5
delta_mu_tau_set=0.75
delta_sigma_tau_set=0.3
delta_mu_I_set=0.2
delta_eta_I_set=0.02
###########################Initialize parameters from priors for first chain
temp_p=rbeta(n=1,shape1=p_1,shape2=p_2)
mu_I_out=log(temp_p/(1-temp_p))
eta_I_out=rbeta(n=1,shape1=p_3,shape2=p_4)
#biomarker 1
mu_theta_1_out=rnorm(1,mean=mu_0_1,sd=sqrt(sigma_0_1_2))
sigma_theta_1_2_out=rinvgamma(1,shape=a_theta_1,scale=b_theta_1)
Theta_1_out=array(rnorm(N,mean=mu_theta_1_out,sd=sigma_theta_1_2_out),c(N,1))
I_1_out=array(rbinom(3*(N-n_0),size=1,prob=0.5),c(N-n_0,3))
mu_gamma_1_out=rnorm(1,mean=mu_1_1,sd=sqrt(sigma_1_1_2))
sigma_gamma_1_2_out=rinvgamma(1,shape=a_gamma_1,scale=b_gamma_1)
mu_tau_1_out=1
sigma_tau_1_2_out=(0.75)^2
gamma_1_out=array(exp(rnorm(3*(N-n_0),mean=mu_gamma_1_out,sd=sqrt(sigma_gamma_1_2_out))),c(N-n_0,3))
gamma_1_out[I_1_out[,1]==0,1]=NA
gamma_1_out[I_1_out[,2]==0,2]=NA
gamma_1_out[I_1_out[,3]==0,3]=NA
Tau_1_out=array(rtruncnorm(n=3*(N-n_0),a=d[D==1]-Tau_star_1,b=d[D==1],mean=d[D==1]-mu_tau_1_out,sd=sqrt(sigma_tau_1_2_out)),c(N-n_0,3))
Tau_1_out[I_1_out[,1]==0,1]=NA
Tau_1_out[I_1_out[,2]==0,2]=NA
Tau_1_out[I_1_out[,3]==0,3]=NA
sigma_1_2_out=0.1
#biomarker 2
mu_theta_2_out=rnorm(1,mean=mu_0_2,sd=sqrt(sigma_0_2_2))
sigma_theta_2_2_out=rinvgamma(1,shape=a_theta_2,scale=b_theta_2)
Theta_2_out=array(rnorm(N,mean=mu_theta_2_out,sd=sigma_theta_2_2_out),c(N,1))
I_2_out=array(rbinom(3*(N-n_0),size=1,prob=0.5),c(N-n_0,3))
mu_gamma_2_out=rnorm(1,mean=mu_1_2,sd=sqrt(sigma_1_2_2))
sigma_gamma_2_2_out=rinvgamma(1,shape=a_gamma_2,scale=b_gamma_2)
mu_tau_2_out=1
sigma_tau_2_2_out=(0.75)^2
gamma_2_out=array(exp(rnorm(3*(N-n_0),mean=mu_gamma_2_out,sd=sqrt(sigma_gamma_2_2_out))),c(N-n_0,3))
gamma_2_out[I_2_out[,1]==0,1]=NA
gamma_2_out[I_2_out[,2]==0,2]=NA
gamma_2_out[I_2_out[,3]==0,3]=NA
Tau_2_out=array(rtruncnorm(n=3*(N-n_0),a=d[D==1]-Tau_star_1,b=d[D==1],mean=d[D==1]-mu_tau_2_out,sd=sqrt(sigma_tau_2_2_out)),c(N-n_0,3))
Tau_2_out[I_2_out[,1]==0,1]=NA
Tau_2_out[I_2_out[,2]==0,2]=NA
Tau_2_out[I_2_out[,3]==0,3]=NA
sigma_2_2_out=0.1
#biomarker 3
mu_theta_3_out=rnorm(1,mean=mu_0_3,sd=sqrt(sigma_0_3_2))
sigma_theta_3_2_out=rinvgamma(1,shape=a_theta_3,scale=b_theta_3)
Theta_3_out=array(rnorm(N,mean=mu_theta_3_out,sd=sigma_theta_3_2_out),c(N,1))
I_3_out=array(rbinom(3*(N-n_0),size=1,prob=0.5),c(N-n_0,3))
mu_gamma_3_out=rnorm(1,mean=mu_1_3,sd=sqrt(sigma_1_3_2))
sigma_gamma_3_2_out=rinvgamma(1,shape=a_gamma_3,scale=b_gamma_3)
mu_tau_3_out=1
sigma_tau_3_2_out=(0.75)^2
gamma_3_out=array(exp(rnorm(3*(N-n_0),mean=mu_gamma_3_out,sd=sqrt(sigma_gamma_3_2_out))),c(N-n_0,3))
gamma_3_out[I_3_out[,1]==0,1]=NA
gamma_3_out[I_3_out[,2]==0,2]=NA
gamma_3_out[I_3_out[,3]==0,3]=NA
Tau_3_out=array(rtruncnorm(n=3*(N-n_0),a=d[D==1]-Tau_star_3,b=d[D==1],mean=d[D==1]-mu_tau_3_out,sd=sqrt(sigma_tau_3_2_out)),c(N-n_0,3))
Tau_3_out[I_3_out[,1]==0,1]=NA
Tau_3_out[I_3_out[,2]==0,2]=NA
Tau_3_out[I_3_out[,3]==0,3]=NA
sigma_3_2_out=0.1
#Update parameters
for(i in 1:S)
{
#MU_THETA_1
mu_theta_parameters=posterior_mu_theta(Theta=Theta_1_out[,i],sigma_theta_2=sigma_theta_1_2_out[i],mu_0=mu_0_1,sigma_0_2=sigma_0_1_2)
mu_theta_1_out=c(mu_theta_1_out,rnorm(1,mean=mu_theta_parameters$mu_0_star,sd=sqrt(mu_theta_parameters$sigma_0_star_2)))
#MU_THETA_2
mu_theta_parameters=posterior_mu_theta(Theta=Theta_2_out[,i],sigma_theta_2=sigma_theta_2_2_out[i],mu_0=mu_0_2,sigma_0_2=sigma_0_2_2)
mu_theta_2_out=c(mu_theta_2_out,rnorm(1,mean=mu_theta_parameters$mu_0_star,sd=sqrt(mu_theta_parameters$sigma_0_star_2)))
#MU_THETA_3
mu_theta_parameters=posterior_mu_theta(Theta=Theta_3_out[,i],sigma_theta_2=sigma_theta_3_2_out[i],mu_0=mu_0_3,sigma_0_2=sigma_0_3_2)
mu_theta_3_out=c(mu_theta_3_out,rnorm(1,mean=mu_theta_parameters$mu_0_star,sd=sqrt(mu_theta_parameters$sigma_0_star_2)))
#SIGMA_THETA_1
sigma_theta_parameters=posterior_sigma_theta_2(Theta=Theta_1_out[,i],mu_theta=mu_theta_1_out[i+1],a_theta=a_theta_1,b_theta=b_theta_1)
sigma_theta_1_2_out=c(sigma_theta_1_2_out,rinvgamma(1,shape=sigma_theta_parameters$a_theta_star,scale=sigma_theta_parameters$b_theta_star))
#SIGMA_THETA_2
sigma_theta_parameters=posterior_sigma_theta_2(Theta=Theta_2_out[,i],mu_theta=mu_theta_2_out[i+1],a_theta=a_theta_2,b_theta=b_theta_2)
sigma_theta_2_2_out=c(sigma_theta_2_2_out,rinvgamma(1,shape=sigma_theta_parameters$a_theta_star,scale=sigma_theta_parameters$b_theta_star))
#SIGMA_THETA_3
sigma_theta_parameters=posterior_sigma_theta_2(Theta=Theta_3_out[,i],mu_theta=mu_theta_3_out[i+1],a_theta=a_theta_3,b_theta=b_theta_3)
sigma_theta_3_2_out=c(sigma_theta_3_2_out,rinvgamma(1,shape=sigma_theta_parameters$a_theta_star,scale=sigma_theta_parameters$b_theta_star))
#SIGMA_1
sigma_parameters=posterior_sigma_2(Y=data$Y1,t=data$t,D=D,J=J,Theta=Theta_1_out[,i],I=I_1_out[,3*i],gamma=gamma_1_out[,3*i],Tau=Tau_1_out[,3*i])
sigma_1_2_out=c(sigma_1_2_out,rinvgamma(1,shape=sigma_parameters$a_sigma,scale=sigma_parameters$b_sigma))
#SIGMA_2
sigma_parameters=posterior_sigma_2(Y=data$Y2,t=data$t,D=D,J=J,Theta=Theta_2_out[,i],I=I_2_out[,3*i],gamma=gamma_2_out[,3*i],Tau=Tau_2_out[,3*i])
sigma_2_2_out=c(sigma_2_2_out,rinvgamma(1,shape=sigma_parameters$a_sigma,scale=sigma_parameters$b_sigma))
#SIGMA_3
sigma_parameters=posterior_sigma_2(Y=data$Y3,t=data$t,D=D,J=J,Theta=Theta_3_out[,i],I=I_3_out[,3*i],gamma=gamma_3_out[,3*i],Tau=Tau_3_out[,3*i])
sigma_3_2_out=c(sigma_3_2_out,rinvgamma(1,shape=sigma_parameters$a_sigma,scale=sigma_parameters$b_sigma))
#MU_I
temp_I_matrix=cbind(I_1_out[,3*i],I_2_out[,3*i],I_3_out[,3*i])
mu_I_output=update_mu_I(temp_I_matrix,mu_I_out[i],eta_I_out[i],delta_mu_I_set)
mu_I_out=c(mu_I_out,mu_I_output$new_mu_I)
#ETA_I
temp_I_matrix=cbind(I_1_out[,3*i],I_2_out[,3*i],I_3_out[,3*i])
eta_I_output=update_eta_I(temp_I_matrix,mu_I_out[i+1],eta_I_out[i],delta_eta_I_set)
eta_I_out=c(eta_I_out,eta_I_output$new_eta_I)
#MU_GAMMA_1
mu_gamma_parameters=posterior_mu_gamma(I=I_1_out[,3*i],gamma=gamma_1_out[,3*i],sigma_gamma_2=sigma_gamma_1_2_out[i],mu_1=mu_1_1,sigma_1_2=sigma_1_1_2)
mu_gamma_1_out=c(mu_gamma_1_out,rnorm(1,mean=mu_gamma_parameters$mu_1_star,sd=sqrt(mu_gamma_parameters$sigma_1_star_2)))
#MU_GAMMA_2
mu_gamma_parameters=posterior_mu_gamma(I=I_2_out[,3*i],gamma=gamma_2_out[,3*i],sigma_gamma_2=sigma_gamma_2_2_out[i],mu_1=mu_1_2,sigma_1_2=sigma_1_2_2)
mu_gamma_2_out=c(mu_gamma_2_out,rnorm(1,mean=mu_gamma_parameters$mu_1_star,sd=sqrt(mu_gamma_parameters$sigma_1_star_2)))
#MU_GAMMA_3
mu_gamma_parameters=posterior_mu_gamma(I=I_3_out[,3*i],gamma=gamma_3_out[,3*i],sigma_gamma_2=sigma_gamma_3_2_out[i],mu_1=mu_1_3,sigma_1_2=sigma_1_3_2)
mu_gamma_3_out=c(mu_gamma_3_out,rnorm(1,mean=mu_gamma_parameters$mu_1_star,sd=sqrt(mu_gamma_parameters$sigma_1_star_2)))
#SIGMA_GAMMA_1
sigma_gamma_parameters=posterior_sigma_gamma_2(I=I_1_out[,3*i],gamma=gamma_1_out[,3*i],mu_gamma=mu_gamma_1_out[i+1],a_gamma=a_gamma_1,b_gamma=b_gamma_1)
sigma_gamma_1_2_out=c(sigma_gamma_1_2_out,rinvgamma(1,shape=sigma_gamma_parameters$a_gamma_star,scale=sigma_gamma_parameters$b_gamma_star))
#SIGMA_GAMMA_2
sigma_gamma_parameters=posterior_sigma_gamma_2(I=I_2_out[,3*i],gamma=gamma_2_out[,3*i],mu_gamma=mu_gamma_2_out[i+1],a_gamma=a_gamma_2,b_gamma=b_gamma_2)
sigma_gamma_2_2_out=c(sigma_gamma_2_2_out,rinvgamma(1,shape=sigma_gamma_parameters$a_gamma_star,scale=sigma_gamma_parameters$b_gamma_star))
#SIGMA_GAMMA_3
sigma_gamma_parameters=posterior_sigma_gamma_2(I=I_3_out[,3*i],gamma=gamma_3_out[,3*i],mu_gamma=mu_gamma_3_out[i+1],a_gamma=a_gamma_3,b_gamma=b_gamma_3)
sigma_gamma_3_2_out=c(sigma_gamma_3_2_out,rinvgamma(1,shape=sigma_gamma_parameters$a_gamma_star,scale=sigma_gamma_parameters$b_gamma_star))
#MU_TAU_1
mu_tau_output=update_mu_tau(Tau=Tau_1_out[,3*i],I=I_1_out[,3*i],d=d,D=D,mu_tau=mu_tau_1_out[i],sigma_tau_2=sigma_tau_1_2_out[i],delta_mu_tau=delta_mu_tau_set,mu_2=mu_2_1,sigma_2_2=sigma_2_1_2,Tau_star=Tau_star_1)
mu_tau_1_out=c(mu_tau_1_out,mu_tau_output$new_mu_tau)
#MU_TAU_2
mu_tau_output=update_mu_tau(Tau=Tau_2_out[,3*i],I=I_2_out[,3*i],d=d,D=D,mu_tau=mu_tau_2_out[i],sigma_tau_2=sigma_tau_2_2_out[i],delta_mu_tau=delta_mu_tau_set,mu_2=mu_2_2,sigma_2_2=sigma_2_2_2,Tau_star=Tau_star_2)
mu_tau_2_out=c(mu_tau_2_out,mu_tau_output$new_mu_tau)
#MU_TAU_3
mu_tau_output=update_mu_tau(Tau=Tau_3_out[,3*i],I=I_3_out[,3*i],d=d,D=D,mu_tau=mu_tau_3_out[i],sigma_tau_2=sigma_tau_3_2_out[i],delta_mu_tau=delta_mu_tau_set,mu_2=mu_2_3,sigma_2_2=sigma_2_3_2,Tau_star=Tau_star_3)
mu_tau_3_out=c(mu_tau_3_out,mu_tau_output$new_mu_tau)
#SIGMA_TAU_1
sigma_tau_output=update_sigma_tau(Tau=Tau_1_out[,3*i],I=I_1_out[,3*i],d=d,D=D,mu_tau=mu_tau_1_out[i+1],sigma_tau_2=sigma_tau_1_2_out[i],delta_sigma_tau=delta_sigma_tau_set,a_tau=a_tau_1,b_tau=b_tau_1,Tau_star=Tau_star_1)
sigma_tau_1_2_out=c(sigma_tau_1_2_out,sigma_tau_output$new_sigma_tau_2)
#SIGMA_TAU_2
sigma_tau_output=update_sigma_tau(Tau=Tau_2_out[,3*i],I=I_2_out[,3*i],d=d,D=D,mu_tau=mu_tau_2_out[i+1],sigma_tau_2=sigma_tau_2_2_out[i],delta_sigma_tau=delta_sigma_tau_set,a_tau=a_tau_2,b_tau=b_tau_2,Tau_star=Tau_star_2)
sigma_tau_2_2_out=c(sigma_tau_2_2_out,sigma_tau_output$new_sigma_tau_2)
#SIGMA_TAU_3
sigma_tau_output=update_sigma_tau(Tau=Tau_3_out[,3*i],I=I_3_out[,3*i],d=d,D=D,mu_tau=mu_tau_3_out[i+1],sigma_tau_2=sigma_tau_3_2_out[i],delta_sigma_tau=delta_sigma_tau_set,a_tau=a_tau_3,b_tau=b_tau_3,Tau_star=Tau_star_3)
sigma_tau_3_2_out=c(sigma_tau_3_2_out,sigma_tau_output$new_sigma_tau_2)
Theta_1_new=rep(NA,N)
Theta_2_new=rep(NA,N)
Theta_3_new=rep(NA,N)
I_1_new_1=rep(NA,N-n_0)
I_1_new_2=rep(NA,N-n_0)
I_1_new_3=rep(NA,N-n_0)
I_2_new_1=rep(NA,N-n_0)
I_2_new_2=rep(NA,N-n_0)
I_2_new_3=rep(NA,N-n_0)
I_3_new_1=rep(NA,N-n_0)
I_3_new_2=rep(NA,N-n_0)
I_3_new_3=rep(NA,N-n_0)
gamma_1_new_1=rep(NA,N-n_0)
gamma_1_new_2=rep(NA,N-n_0)
gamma_1_new_3=rep(NA,N-n_0)
gamma_2_new_1=rep(NA,N-n_0)
gamma_2_new_2=rep(NA,N-n_0)
gamma_2_new_3=rep(NA,N-n_0)
gamma_3_new_1=rep(NA,N-n_0)
gamma_3_new_2=rep(NA,N-n_0)
gamma_3_new_3=rep(NA,N-n_0)
Tau_1_new_1=rep(NA,N-n_0)
Tau_1_new_2=rep(NA,N-n_0)
Tau_1_new_3=rep(NA,N-n_0)
Tau_2_new_1=rep(NA,N-n_0)
Tau_2_new_2=rep(NA,N-n_0)
Tau_2_new_3=rep(NA,N-n_0)
Tau_3_new_1=rep(NA,N-n_0)
Tau_3_new_2=rep(NA,N-n_0)
Tau_3_new_3=rep(NA,N-n_0)
for(j in 1:n_0)
{
#THETA_1_j
theta_j_parameters=posterior_theta(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_1_out[i+1],sigma_theta_2=sigma_theta_1_2_out[i+1],sigma_2=sigma_1_2_out[i+1],I_i=NA,gamma_i=NA,tau_i=NA)
Theta_1_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_2_j
theta_j_parameters=posterior_theta(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_2_out[i+1],sigma_theta_2=sigma_theta_2_2_out[i+1],sigma_2=sigma_2_2_out[i+1],I_i=NA,gamma_i=NA,tau_i=NA)
Theta_2_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_3_j
theta_j_parameters=posterior_theta(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_3_out[i+1],sigma_theta_2=sigma_theta_3_2_out[i+1],sigma_2=sigma_3_2_out[i+1],I_i=NA,gamma_i=NA,tau_i=NA)
Theta_3_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
}
for(j in (n_0+1):N)
{
#THETA_1_j
theta_j_parameters=posterior_theta(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_1_out[i+1],sigma_theta_2=sigma_theta_1_2_out[i+1],sigma_2=sigma_1_2_out[i+1],I_i=I_1_out[j-n_0,3*i],gamma_i=gamma_1_out[j-n_0,3*i],tau_i=Tau_1_out[j-n_0,3*i])
Theta_1_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_2_j
theta_j_parameters=posterior_theta(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_2_out[i+1],sigma_theta_2=sigma_theta_2_2_out[i+1],sigma_2=sigma_2_2_out[i+1],I_i=I_2_out[j-n_0,3*i],gamma_i=gamma_2_out[j-n_0,3*i],tau_i=Tau_2_out[j-n_0,3*i])
Theta_2_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_3_j
theta_j_parameters=posterior_theta(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_3_out[i+1],sigma_theta_2=sigma_theta_3_2_out[i+1],sigma_2=sigma_3_2_out[i+1],I_i=I_3_out[j-n_0,3*i],gamma_i=gamma_3_out[j-n_0,3*i],tau_i=Tau_3_out[j-n_0,3*i])
Theta_3_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#I_1
F_temp=mu_I_out[i+1] + eta_I_out[i+1]*(I_2_out[j-n_0,3*i] + I_3_out[j-n_0,3*i])
Pi_1_input=exp(F_temp)/(1+exp(F_temp))
I_output=update_I(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],mu_gamma=mu_gamma_1_out[i+1],sigma_gamma_2=sigma_gamma_1_2_out[i+1],mu_tau=mu_tau_1_out[i+1],sigma_tau_2=sigma_tau_1_2_out[i+1],Tau_star=Tau_star_1,sigma_2=sigma_1_2_out[i+1],Theta_i=Theta_1_new[j],I_i=I_1_out[j-n_0,3*i],gamma_i=gamma_1_out[j-n_0,3*i],tau_i=Tau_1_out[j-n_0,3*i],Pi=Pi_1_input)
I_1_new_1[j-n_0]=I_output$new_I
Tau_1_new_1[j-n_0]=I_output$new_tau
gamma_1_new_1[j-n_0]=I_output$new_gamma
#I_2
F_temp=mu_I_out[i+1] + eta_I_out[i+1]*(I_1_new_1[j-n_0] + I_3_out[j-n_0,3*i])
Pi_2_input=exp(F_temp)/(1+exp(F_temp))
I_output=update_I(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],mu_gamma=mu_gamma_2_out[i+1],sigma_gamma_2=sigma_gamma_2_2_out[i+1],mu_tau=mu_tau_2_out[i+1],sigma_tau_2=sigma_tau_2_2_out[i+1],Tau_star=Tau_star_2,sigma_2=sigma_2_2_out[i+1],Theta_i=Theta_2_new[j],I_i=I_2_out[j-n_0,3*i],gamma_i=gamma_2_out[j-n_0,3*i],tau_i=Tau_2_out[j-n_0,3*i],Pi=Pi_2_input)
I_2_new_1[j-n_0]=I_output$new_I
Tau_2_new_1[j-n_0]=I_output$new_tau
gamma_2_new_1[j-n_0]=I_output$new_gamma
#I_3
F_temp=mu_I_out[i+1] + eta_I_out[i+1]*(I_1_new_1[j-n_0] + I_2_new_1[j-n_0])
Pi_3_input=exp(F_temp)/(1+exp(F_temp))
I_output=update_I(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],mu_gamma=mu_gamma_3_out[i+1],sigma_gamma_2=sigma_gamma_3_2_out[i+1],mu_tau=mu_tau_3_out[i+1],sigma_tau_2=sigma_tau_3_2_out[i+1],Tau_star=Tau_star_3,sigma_2=sigma_3_2_out[i+1],Theta_i=Theta_3_new[j],I_i=I_3_out[j-n_0,3*i],gamma_i=gamma_3_out[j-n_0,3*i],tau_i=Tau_3_out[j-n_0,3*i],Pi=Pi_3_input)
I_3_new_1[j-n_0]=I_output$new_I
Tau_3_new_1[j-n_0]=I_output$new_tau
gamma_3_new_1[j-n_0]=I_output$new_gamma
#GAMMA_1
gamma_output=update_gamma(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],mu_gamma=mu_gamma_1_out[i+1],sigma_gamma_2=sigma_gamma_1_2_out[i+1],sigma_2=sigma_1_2_out[i+1],Theta_i=Theta_1_new[j],I_i=I_1_new_1[j-n_0],gamma_i=gamma_1_new_1[j-n_0],tau_i=Tau_1_new_1[j-n_0],delta_gamma=delta_gamma_set)
gamma_1_new_2[j-n_0]=gamma_output$new_gamma
I_1_new_2[j-n_0]=gamma_output$new_I
Tau_1_new_2[j-n_0]=gamma_output$new_tau
#GAMMA_2
gamma_output=update_gamma(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],mu_gamma=mu_gamma_2_out[i+1],sigma_gamma_2=sigma_gamma_2_2_out[i+1],sigma_2=sigma_2_2_out[i+1],Theta_i=Theta_2_new[j],I_i=I_2_new_1[j-n_0],gamma_i=gamma_2_new_1[j-n_0],tau_i=Tau_2_new_1[j-n_0],delta_gamma=delta_gamma_set)
gamma_2_new_2[j-n_0]=gamma_output$new_gamma
I_2_new_2[j-n_0]=gamma_output$new_I
Tau_2_new_2[j-n_0]=gamma_output$new_tau
#GAMMA_3
gamma_output=update_gamma(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],mu_gamma=mu_gamma_3_out[i+1],sigma_gamma_2=sigma_gamma_3_2_out[i+1],sigma_2=sigma_3_2_out[i+1],Theta_i=Theta_3_new[j],I_i=I_3_new_1[j-n_0],gamma_i=gamma_3_new_1[j-n_0],tau_i=Tau_3_new_1[j-n_0],delta_gamma=delta_gamma_set)
gamma_3_new_2[j-n_0]=gamma_output$new_gamma
I_3_new_2[j-n_0]=gamma_output$new_I
Tau_3_new_2[j-n_0]=gamma_output$new_tau
#TAU_1
tau_output=update_tau(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],sigma_2=sigma_1_2_out[i+1],mu_tau=mu_tau_1_out[i+1],sigma_tau_2=sigma_tau_1_2_out[i+1],Theta_i=Theta_1_new[j],I_i=I_1_new_2[j-n_0],gamma_i=gamma_1_new_2[j-n_0],tau_i=Tau_1_new_2[j-n_0],delta_tau=delta_tau_set,Tau_star=Tau_star_1)
I_1_new_3[j-n_0]=tau_output$new_I
Tau_1_new_3[j-n_0]=tau_output$new_tau
gamma_1_new_3[j-n_0]=tau_output$new_gamma
#TAU_2
tau_output=update_tau(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],sigma_2=sigma_2_2_out[i+1],mu_tau=mu_tau_2_out[i+1],sigma_tau_2=sigma_tau_2_2_out[i+1],Theta_i=Theta_2_new[j],I_i=I_2_new_2[j-n_0],gamma_i=gamma_2_new_2[j-n_0],tau_i=Tau_2_new_2[j-n_0],delta_tau=delta_tau_set,Tau_star=Tau_star_2)
I_2_new_3[j-n_0]=tau_output$new_I
Tau_2_new_3[j-n_0]=tau_output$new_tau
gamma_2_new_3[j-n_0]=tau_output$new_gamma
#TAU_1
tau_output=update_tau(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],sigma_2=sigma_3_2_out[i+1],mu_tau=mu_tau_3_out[i+1],sigma_tau_2=sigma_tau_3_2_out[i+1],Theta_i=Theta_3_new[j],I_i=I_3_new_2[j-n_0],gamma_i=gamma_3_new_2[j-n_0],tau_i=Tau_3_new_2[j-n_0],delta_tau=delta_tau_set,Tau_star=Tau_star_3)
I_3_new_3[j-n_0]=tau_output$new_I
Tau_3_new_3[j-n_0]=tau_output$new_tau
gamma_3_new_3[j-n_0]=tau_output$new_gamma
}
Theta_1_out=cbind(Theta_1_out,Theta_1_new)
Theta_2_out=cbind(Theta_2_out,Theta_2_new)
Theta_3_out=cbind(Theta_3_out,Theta_3_new)
I_1_out=cbind(I_1_out,I_1_new_1,I_1_new_2,I_1_new_3)
I_2_out=cbind(I_2_out,I_2_new_1,I_2_new_2,I_2_new_3)
I_3_out=cbind(I_3_out,I_3_new_1,I_3_new_2,I_3_new_3)
gamma_1_out=cbind(gamma_1_out,gamma_1_new_1,gamma_1_new_2,gamma_1_new_3)
gamma_2_out=cbind(gamma_2_out,gamma_2_new_1,gamma_2_new_2,gamma_2_new_3)
gamma_3_out=cbind(gamma_3_out,gamma_3_new_1,gamma_3_new_2,gamma_3_new_3)
Tau_1_out=cbind(Tau_1_out,Tau_1_new_1,Tau_1_new_2,Tau_1_new_3)
Tau_2_out=cbind(Tau_2_out,Tau_2_new_1,Tau_2_new_2,Tau_2_new_3)
Tau_3_out=cbind(Tau_3_out,Tau_3_new_1,Tau_3_new_2,Tau_3_new_3)
print(i)
}
###########################Initialize parameters from priors for second chain
temp_p=rbeta(n=1,shape1=p_1,shape2=p_2)
mu_I_out_2=log(temp_p/(1-temp_p))
eta_I_out_2=rbeta(n=1,shape1=p_3,shape2=p_4)
#Biomarker 1
mu_theta_1_out_2=rnorm(1,mean=mu_0_1,sd=sqrt(sigma_0_1_2))
sigma_theta_1_2_out_2=rinvgamma(1,shape=a_theta_1,scale=b_theta_1)
Theta_1_out_2=array(rnorm(N,mean=mu_theta_1_out_2,sd=sigma_theta_1_2_out_2),c(N,1))
I_1_out_2=array(rbinom(3*(N-n_0),size=1,prob=0.5),c(N-n_0,3))
mu_gamma_1_out_2=rnorm(1,mean=mu_1_1,sd=sqrt(sigma_1_1_2))
sigma_gamma_1_2_out_2=rinvgamma(1,shape=a_gamma_1,scale=b_gamma_1)
mu_tau_1_out_2=2
sigma_tau_1_2_out_2=(2)^2
gamma_1_out_2=array(exp(rnorm(3*(N-n_0),mean=mu_gamma_1_out_2,sd=sqrt(sigma_gamma_1_2_out_2))),c(N-n_0,3))
gamma_1_out_2[I_1_out_2[,1]==0,1]=NA
gamma_1_out_2[I_1_out_2[,2]==0,2]=NA
gamma_1_out_2[I_1_out_2[,3]==0,3]=NA
Tau_1_out_2=array(rtruncnorm(n=3*(N-n_0),a=d[D==1]-Tau_star_1,b=d[D==1],mean=d[D==1]-mu_tau_1_out_2,sd=sqrt(sigma_tau_1_2_out_2)),c(N-n_0,3))
Tau_1_out_2[I_1_out_2[,1]==0,1]=NA
Tau_1_out_2[I_1_out_2[,2]==0,2]=NA
Tau_1_out_2[I_1_out_2[,3]==0,3]=NA
sigma_1_2_out_2=1
#Biomarker 2
mu_theta_2_out_2=rnorm(1,mean=mu_0_2,sd=sqrt(sigma_0_2_2))
sigma_theta_2_2_out_2=rinvgamma(1,shape=a_theta_2,scale=b_theta_2)
Theta_2_out_2=array(rnorm(N,mean=mu_theta_2_out_2,sd=sigma_theta_2_2_out_2),c(N,1))
I_2_out_2=array(rbinom(3*(N-n_0),size=1,prob=0.5),c(N-n_0,3))
mu_gamma_2_out_2=rnorm(1,mean=mu_1_2,sd=sqrt(sigma_1_2_2))
sigma_gamma_2_2_out_2=rinvgamma(1,shape=a_gamma_2,scale=b_gamma_2)
mu_tau_2_out_2=0.5
sigma_tau_2_2_out_2=1
gamma_2_out_2=array(exp(rnorm(3*(N-n_0),mean=mu_gamma_2_out_2,sd=sqrt(sigma_gamma_2_2_out_2))),c(N-n_0,3))
gamma_2_out_2[I_2_out_2[,1]==0,1]=NA
gamma_2_out_2[I_2_out_2[,2]==0,2]=NA
gamma_2_out_2[I_2_out_2[,3]==0,3]=NA
Tau_2_out_2=array(rtruncnorm(n=3*(N-n_0),a=d[D==1]-Tau_star_1,b=d[D==1],mean=d[D==1]-mu_tau_2_out_2,sd=sqrt(sigma_tau_2_2_out_2)),c(N-n_0,3))
Tau_2_out_2[I_2_out_2[,1]==0,1]=NA
Tau_2_out_2[I_2_out_2[,2]==0,2]=NA
Tau_2_out_2[I_2_out_2[,3]==0,3]=NA
sigma_2_2_out_2=3
#biomarker 3
mu_theta_3_out_2=rnorm(1,mean=mu_0_3,sd=sqrt(sigma_0_3_2))
sigma_theta_3_2_out_2=rinvgamma(1,shape=a_theta_3,scale=b_theta_3)
Theta_3_out_2=array(rnorm(N,mean=mu_theta_3_out_2,sd=sigma_theta_3_2_out_2),c(N,1))
I_3_out_2=array(rbinom(3*(N-n_0),size=1,prob=0.5),c(N-n_0,3))
mu_gamma_3_out_2=rnorm(1,mean=mu_1_3,sd=sqrt(sigma_1_3_2))
sigma_gamma_3_2_out_2=rinvgamma(1,shape=a_gamma_3,scale=b_gamma_3)
mu_tau_3_out_2=1
sigma_tau_3_2_out_2=(0.75)^2
gamma_3_out_2=array(exp(rnorm(3*(N-n_0),mean=mu_gamma_3_out_2,sd=sqrt(sigma_gamma_3_2_out_2))),c(N-n_0,3))
gamma_3_out_2[I_3_out_2[,1]==0,1]=NA
gamma_3_out_2[I_3_out_2[,2]==0,2]=NA
gamma_3_out_2[I_3_out_2[,3]==0,3]=NA
Tau_3_out_2=array(rtruncnorm(n=3*(N-n_0),a=d[D==1]-Tau_star_3,b=d[D==1],mean=d[D==1]-mu_tau_3_out_2,sd=sqrt(sigma_tau_3_2_out_2)),c(N-n_0,3))
Tau_3_out_2[I_3_out_2[,1]==0,1]=NA
Tau_3_out_2[I_3_out_2[,2]==0,2]=NA
Tau_3_out_2[I_3_out_2[,3]==0,3]=NA
sigma_3_2_out_2=1
#Update parameters
for(i in 1:S)
{
#MU_THETA_1
mu_theta_parameters=posterior_mu_theta(Theta=Theta_1_out_2[,i],sigma_theta_2=sigma_theta_1_2_out_2[i],mu_0=mu_0_1,sigma_0_2=sigma_0_1_2)
mu_theta_1_out_2=c(mu_theta_1_out_2,rnorm(1,mean=mu_theta_parameters$mu_0_star,sd=sqrt(mu_theta_parameters$sigma_0_star_2)))
#MU_THETA_2
mu_theta_parameters=posterior_mu_theta(Theta=Theta_2_out_2[,i],sigma_theta_2=sigma_theta_2_2_out_2[i],mu_0=mu_0_2,sigma_0_2=sigma_0_2_2)
mu_theta_2_out_2=c(mu_theta_2_out_2,rnorm(1,mean=mu_theta_parameters$mu_0_star,sd=sqrt(mu_theta_parameters$sigma_0_star_2)))
#MU_THETA_3
mu_theta_parameters=posterior_mu_theta(Theta=Theta_3_out_2[,i],sigma_theta_2=sigma_theta_3_2_out_2[i],mu_0=mu_0_3,sigma_0_2=sigma_0_3_2)
mu_theta_3_out_2=c(mu_theta_3_out_2,rnorm(1,mean=mu_theta_parameters$mu_0_star,sd=sqrt(mu_theta_parameters$sigma_0_star_2)))
#SIGMA_THETA_1
sigma_theta_parameters=posterior_sigma_theta_2(Theta=Theta_1_out_2[,i],mu_theta=mu_theta_1_out_2[i+1],a_theta=a_theta_1,b_theta=b_theta_1)
sigma_theta_1_2_out_2=c(sigma_theta_1_2_out_2,rinvgamma(1,shape=sigma_theta_parameters$a_theta_star,scale=sigma_theta_parameters$b_theta_star))
#SIGMA_THETA_2
sigma_theta_parameters=posterior_sigma_theta_2(Theta=Theta_2_out_2[,i],mu_theta=mu_theta_2_out_2[i+1],a_theta=a_theta_2,b_theta=b_theta_2)
sigma_theta_2_2_out_2=c(sigma_theta_2_2_out_2,rinvgamma(1,shape=sigma_theta_parameters$a_theta_star,scale=sigma_theta_parameters$b_theta_star))
#SIGMA_THETA_3
sigma_theta_parameters=posterior_sigma_theta_2(Theta=Theta_3_out_2[,i],mu_theta=mu_theta_3_out_2[i+1],a_theta=a_theta_3,b_theta=b_theta_3)
sigma_theta_3_2_out_2=c(sigma_theta_3_2_out_2,rinvgamma(1,shape=sigma_theta_parameters$a_theta_star,scale=sigma_theta_parameters$b_theta_star))
#SIGMA_1
sigma_parameters=posterior_sigma_2(Y=data$Y1,t=data$t,D=D,J=J,Theta=Theta_1_out_2[,i],I=I_1_out_2[,3*i],gamma=gamma_1_out_2[,3*i],Tau=Tau_1_out_2[,3*i])
sigma_1_2_out_2=c(sigma_1_2_out_2,rinvgamma(1,shape=sigma_parameters$a_sigma,scale=sigma_parameters$b_sigma))
#SIGMA_2
sigma_parameters=posterior_sigma_2(Y=data$Y2,t=data$t,D=D,J=J,Theta=Theta_2_out_2[,i],I=I_2_out_2[,3*i],gamma=gamma_2_out_2[,3*i],Tau=Tau_2_out_2[,3*i])
sigma_2_2_out_2=c(sigma_2_2_out_2,rinvgamma(1,shape=sigma_parameters$a_sigma,scale=sigma_parameters$b_sigma))
#SIGMA_3
sigma_parameters=posterior_sigma_2(Y=data$Y3,t=data$t,D=D,J=J,Theta=Theta_3_out_2[,i],I=I_3_out_2[,3*i],gamma=gamma_3_out_2[,3*i],Tau=Tau_3_out_2[,3*i])
sigma_3_2_out_2=c(sigma_3_2_out_2,rinvgamma(1,shape=sigma_parameters$a_sigma,scale=sigma_parameters$b_sigma))
#MU_I
temp_I_matrix=cbind(I_1_out_2[,3*i],I_2_out_2[,3*i],I_3_out_2[,3*i])
mu_I_output=update_mu_I(temp_I_matrix,mu_I_out_2[i],eta_I_out_2[i],delta_mu_I_set)
mu_I_out_2=c(mu_I_out_2,mu_I_output$new_mu_I)
#ETA_I
temp_I_matrix=cbind(I_1_out_2[,3*i],I_2_out_2[,3*i],I_3_out_2[,3*i])
eta_I_output=update_eta_I(temp_I_matrix,mu_I_out_2[i+1],eta_I_out_2[i],delta_eta_I_set)
eta_I_out_2=c(eta_I_out_2,eta_I_output$new_eta_I)
#MU_GAMMA_1
mu_gamma_parameters=posterior_mu_gamma(I=I_1_out_2[,3*i],gamma=gamma_1_out_2[,3*i],sigma_gamma_2=sigma_gamma_1_2_out_2[i],mu_1=mu_1_1,sigma_1_2=sigma_1_1_2)
mu_gamma_1_out_2=c(mu_gamma_1_out_2,rnorm(1,mean=mu_gamma_parameters$mu_1_star,sd=sqrt(mu_gamma_parameters$sigma_1_star_2)))
#MU_GAMMA_2
mu_gamma_parameters=posterior_mu_gamma(I=I_2_out_2[,3*i],gamma=gamma_2_out_2[,3*i],sigma_gamma_2=sigma_gamma_2_2_out_2[i],mu_1=mu_1_2,sigma_1_2=sigma_1_2_2)
mu_gamma_2_out_2=c(mu_gamma_2_out_2,rnorm(1,mean=mu_gamma_parameters$mu_1_star,sd=sqrt(mu_gamma_parameters$sigma_1_star_2)))
#MU_GAMMA_3
mu_gamma_parameters=posterior_mu_gamma(I=I_3_out_2[,3*i],gamma=gamma_3_out_2[,3*i],sigma_gamma_2=sigma_gamma_3_2_out_2[i],mu_1=mu_1_3,sigma_1_2=sigma_1_3_2)
mu_gamma_3_out_2=c(mu_gamma_3_out_2,rnorm(1,mean=mu_gamma_parameters$mu_1_star,sd=sqrt(mu_gamma_parameters$sigma_1_star_2)))
#SIGMA_GAMMA_1
sigma_gamma_parameters=posterior_sigma_gamma_2(I=I_1_out_2[,3*i],gamma=gamma_1_out_2[,3*i],mu_gamma=mu_gamma_1_out_2[i+1],a_gamma=a_gamma_1,b_gamma=b_gamma_1)
sigma_gamma_1_2_out_2=c(sigma_gamma_1_2_out_2,rinvgamma(1,shape=sigma_gamma_parameters$a_gamma_star,scale=sigma_gamma_parameters$b_gamma_star))
#SIGMA_GAMMA_2
sigma_gamma_parameters=posterior_sigma_gamma_2(I=I_2_out_2[,3*i],gamma=gamma_2_out_2[,3*i],mu_gamma=mu_gamma_2_out_2[i+1],a_gamma=a_gamma_2,b_gamma=b_gamma_2)
sigma_gamma_2_2_out_2=c(sigma_gamma_2_2_out_2,rinvgamma(1,shape=sigma_gamma_parameters$a_gamma_star,scale=sigma_gamma_parameters$b_gamma_star))
#SIGMA_GAMMA_3
sigma_gamma_parameters=posterior_sigma_gamma_2(I=I_3_out_2[,3*i],gamma=gamma_3_out_2[,3*i],mu_gamma=mu_gamma_3_out_2[i+1],a_gamma=a_gamma_3,b_gamma=b_gamma_3)
sigma_gamma_3_2_out_2=c(sigma_gamma_3_2_out_2,rinvgamma(1,shape=sigma_gamma_parameters$a_gamma_star,scale=sigma_gamma_parameters$b_gamma_star))
#MU_TAU_1
mu_tau_output=update_mu_tau(Tau=Tau_1_out_2[,3*i],I=I_1_out_2[,3*i],d=d,D=D,mu_tau=mu_tau_1_out_2[i],sigma_tau_2=sigma_tau_1_2_out_2[i],delta_mu_tau=delta_mu_tau_set,mu_2=mu_2_1,sigma_2_2=sigma_2_1_2,Tau_star=Tau_star_1)
mu_tau_1_out_2=c(mu_tau_1_out_2,mu_tau_output$new_mu_tau)
#MU_TAU_2
mu_tau_output=update_mu_tau(Tau=Tau_2_out_2[,3*i],I=I_2_out_2[,3*i],d=d,D=D,mu_tau=mu_tau_2_out_2[i],sigma_tau_2=sigma_tau_2_2_out_2[i],delta_mu_tau=delta_mu_tau_set,mu_2=mu_2_2,sigma_2_2=sigma_2_2_2,Tau_star=Tau_star_2)
mu_tau_2_out_2=c(mu_tau_2_out_2,mu_tau_output$new_mu_tau)
#MU_TAU_3
mu_tau_output=update_mu_tau(Tau=Tau_3_out_2[,3*i],I=I_3_out_2[,3*i],d=d,D=D,mu_tau=mu_tau_3_out_2[i],sigma_tau_2=sigma_tau_3_2_out_2[i],delta_mu_tau=delta_mu_tau_set,mu_2=mu_2_3,sigma_2_2=sigma_2_3_2,Tau_star=Tau_star_3)
mu_tau_3_out_2=c(mu_tau_3_out_2,mu_tau_output$new_mu_tau)
#SIGMA_TAU_1
sigma_tau_output=update_sigma_tau(Tau=Tau_1_out_2[,3*i],I=I_1_out_2[,3*i],d=d,D=D,mu_tau=mu_tau_1_out_2[i+1],sigma_tau_2=sigma_tau_1_2_out_2[i],delta_sigma_tau=delta_sigma_tau_set,a_tau=a_tau_1,b_tau=b_tau_1,Tau_star=Tau_star_1)
sigma_tau_1_2_out_2=c(sigma_tau_1_2_out_2,sigma_tau_output$new_sigma_tau_2)
#SIGMA_TAU_2
sigma_tau_output=update_sigma_tau(Tau=Tau_2_out_2[,3*i],I=I_2_out_2[,3*i],d=d,D=D,mu_tau=mu_tau_2_out_2[i+1],sigma_tau_2=sigma_tau_2_2_out_2[i],delta_sigma_tau=delta_sigma_tau_set,a_tau=a_tau_2,b_tau=b_tau_2,Tau_star=Tau_star_2)
sigma_tau_2_2_out_2=c(sigma_tau_2_2_out_2,sigma_tau_output$new_sigma_tau_2)
#SIGMA_TAU_3
sigma_tau_output=update_sigma_tau(Tau=Tau_3_out_2[,3*i],I=I_3_out_2[,3*i],d=d,D=D,mu_tau=mu_tau_3_out_2[i+1],sigma_tau_2=sigma_tau_3_2_out_2[i],delta_sigma_tau=delta_sigma_tau_set,a_tau=a_tau_3,b_tau=b_tau_3,Tau_star=Tau_star_3)
sigma_tau_3_2_out_2=c(sigma_tau_3_2_out_2,sigma_tau_output$new_sigma_tau_2)
Theta_1_new=rep(NA,N)
Theta_2_new=rep(NA,N)
Theta_3_new=rep(NA,N)
I_1_new_1=rep(NA,N-n_0)
I_1_new_2=rep(NA,N-n_0)
I_1_new_3=rep(NA,N-n_0)
I_2_new_1=rep(NA,N-n_0)
I_2_new_2=rep(NA,N-n_0)
I_2_new_3=rep(NA,N-n_0)
I_3_new_1=rep(NA,N-n_0)
I_3_new_2=rep(NA,N-n_0)
I_3_new_3=rep(NA,N-n_0)
gamma_1_new_1=rep(NA,N-n_0)
gamma_1_new_2=rep(NA,N-n_0)
gamma_1_new_3=rep(NA,N-n_0)
gamma_2_new_1=rep(NA,N-n_0)
gamma_2_new_2=rep(NA,N-n_0)
gamma_2_new_3=rep(NA,N-n_0)
gamma_3_new_1=rep(NA,N-n_0)
gamma_3_new_2=rep(NA,N-n_0)
gamma_3_new_3=rep(NA,N-n_0)
Tau_1_new_1=rep(NA,N-n_0)
Tau_1_new_2=rep(NA,N-n_0)
Tau_1_new_3=rep(NA,N-n_0)
Tau_2_new_1=rep(NA,N-n_0)
Tau_2_new_2=rep(NA,N-n_0)
Tau_2_new_3=rep(NA,N-n_0)
Tau_3_new_1=rep(NA,N-n_0)
Tau_3_new_2=rep(NA,N-n_0)
Tau_3_new_3=rep(NA,N-n_0)
for(j in 1:n_0)
{
#THETA_1_j
theta_j_parameters=posterior_theta(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_1_out_2[i+1],sigma_theta_2=sigma_theta_1_2_out_2[i+1],sigma_2=sigma_1_2_out_2[i+1],I_i=NA,gamma_i=NA,tau_i=NA)
Theta_1_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_2_j
theta_j_parameters=posterior_theta(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_2_out_2[i+1],sigma_theta_2=sigma_theta_2_2_out_2[i+1],sigma_2=sigma_2_2_out_2[i+1],I_i=NA,gamma_i=NA,tau_i=NA)
Theta_2_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_3_j
theta_j_parameters=posterior_theta(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_3_out_2[i+1],sigma_theta_2=sigma_theta_3_2_out_2[i+1],sigma_2=sigma_3_2_out_2[i+1],I_i=NA,gamma_i=NA,tau_i=NA)
Theta_3_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
}
for(j in (n_0+1):N)
{
#THETA_1_j
theta_j_parameters=posterior_theta(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_1_out_2[i+1],sigma_theta_2=sigma_theta_1_2_out_2[i+1],sigma_2=sigma_1_2_out_2[i+1],I_i=I_1_out_2[j-n_0,3*i],gamma_i=gamma_1_out_2[j-n_0,3*i],tau_i=Tau_1_out_2[j-n_0,3*i])
Theta_1_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_2_j
theta_j_parameters=posterior_theta(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_2_out_2[i+1],sigma_theta_2=sigma_theta_2_2_out_2[i+1],sigma_2=sigma_2_2_out_2[i+1],I_i=I_2_out_2[j-n_0,3*i],gamma_i=gamma_2_out_2[j-n_0,3*i],tau_i=Tau_2_out_2[j-n_0,3*i])
Theta_2_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#THETA_3_j
theta_j_parameters=posterior_theta(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],D_i=D[j],J_i=J[j],mu_theta=mu_theta_3_out_2[i+1],sigma_theta_2=sigma_theta_3_2_out_2[i+1],sigma_2=sigma_3_2_out_2[i+1],I_i=I_3_out_2[j-n_0,3*i],gamma_i=gamma_3_out_2[j-n_0,3*i],tau_i=Tau_3_out_2[j-n_0,3*i])
Theta_3_new[j]=rnorm(1,mean=theta_j_parameters$mu_theta_star,sd=sqrt(theta_j_parameters$sigma_theta_star_2))
#I_1
F_temp=mu_I_out_2[i+1] + eta_I_out_2[i+1]*(I_2_out_2[j-n_0,3*i] + I_3_out_2[j-n_0,3*i])
Pi_1_input=exp(F_temp)/(1+exp(F_temp))
I_output=update_I(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],mu_gamma=mu_gamma_1_out_2[i+1],sigma_gamma_2=sigma_gamma_1_2_out_2[i+1],mu_tau=mu_tau_1_out_2[i+1],sigma_tau_2=sigma_tau_1_2_out_2[i+1],Tau_star=Tau_star_1,sigma_2=sigma_1_2_out_2[i+1],Theta_i=Theta_1_new[j],I_i=I_1_out_2[j-n_0,3*i],gamma_i=gamma_1_out_2[j-n_0,3*i],tau_i=Tau_1_out_2[j-n_0,3*i],Pi=Pi_1_input)
I_1_new_1[j-n_0]=I_output$new_I
Tau_1_new_1[j-n_0]=I_output$new_tau
gamma_1_new_1[j-n_0]=I_output$new_gamma
#I_2
F_temp=mu_I_out_2[i+1] + eta_I_out_2[i+1]*(I_1_new_1[j-n_0] + I_3_out_2[j-n_0,3*i])
Pi_2_input=exp(F_temp)/(1+exp(F_temp))
I_output=update_I(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],mu_gamma=mu_gamma_2_out_2[i+1],sigma_gamma_2=sigma_gamma_2_2_out_2[i+1],mu_tau=mu_tau_2_out_2[i+1],sigma_tau_2=sigma_tau_2_2_out_2[i+1],Tau_star=Tau_star_2,sigma_2=sigma_2_2_out_2[i+1],Theta_i=Theta_2_new[j],I_i=I_2_out_2[j-n_0,3*i],gamma_i=gamma_2_out_2[j-n_0,3*i],tau_i=Tau_2_out_2[j-n_0,3*i],Pi=Pi_2_input)
I_2_new_1[j-n_0]=I_output$new_I
Tau_2_new_1[j-n_0]=I_output$new_tau
gamma_2_new_1[j-n_0]=I_output$new_gamma
#I_3
F_temp=mu_I_out_2[i+1] + eta_I_out_2[i+1]*(I_1_new_1[j-n_0] + I_2_new_1[j-n_0])
Pi_3_input=exp(F_temp)/(1+exp(F_temp))
I_output=update_I(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],mu_gamma=mu_gamma_3_out_2[i+1],sigma_gamma_2=sigma_gamma_3_2_out_2[i+1],mu_tau=mu_tau_3_out_2[i+1],sigma_tau_2=sigma_tau_3_2_out_2[i+1],Tau_star=Tau_star_3,sigma_2=sigma_3_2_out_2[i+1],Theta_i=Theta_3_new[j],I_i=I_3_out_2[j-n_0,3*i],gamma_i=gamma_3_out_2[j-n_0,3*i],tau_i=Tau_3_out_2[j-n_0,3*i],Pi=Pi_3_input)
I_3_new_1[j-n_0]=I_output$new_I
Tau_3_new_1[j-n_0]=I_output$new_tau
gamma_3_new_1[j-n_0]=I_output$new_gamma
#GAMMA_1
gamma_output=update_gamma(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],mu_gamma=mu_gamma_1_out_2[i+1],sigma_gamma_2=sigma_gamma_1_2_out_2[i+1],sigma_2=sigma_1_2_out_2[i+1],Theta_i=Theta_1_new[j],I_i=I_1_new_1[j-n_0],gamma_i=gamma_1_new_1[j-n_0],tau_i=Tau_1_new_1[j-n_0],delta_gamma=delta_gamma_set)
gamma_1_new_2[j-n_0]=gamma_output$new_gamma
I_1_new_2[j-n_0]=gamma_output$new_I
Tau_1_new_2[j-n_0]=gamma_output$new_tau
#GAMMA_2
gamma_output=update_gamma(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],mu_gamma=mu_gamma_2_out_2[i+1],sigma_gamma_2=sigma_gamma_2_2_out_2[i+1],sigma_2=sigma_2_2_out_2[i+1],Theta_i=Theta_2_new[j],I_i=I_2_new_1[j-n_0],gamma_i=gamma_2_new_1[j-n_0],tau_i=Tau_2_new_1[j-n_0],delta_gamma=delta_gamma_set)
gamma_2_new_2[j-n_0]=gamma_output$new_gamma
I_2_new_2[j-n_0]=gamma_output$new_I
Tau_2_new_2[j-n_0]=gamma_output$new_tau
#GAMMA_3
gamma_output=update_gamma(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],mu_gamma=mu_gamma_3_out_2[i+1],sigma_gamma_2=sigma_gamma_3_2_out_2[i+1],sigma_2=sigma_3_2_out_2[i+1],Theta_i=Theta_3_new[j],I_i=I_3_new_1[j-n_0],gamma_i=gamma_3_new_1[j-n_0],tau_i=Tau_3_new_1[j-n_0],delta_gamma=delta_gamma_set)
gamma_3_new_2[j-n_0]=gamma_output$new_gamma
I_3_new_2[j-n_0]=gamma_output$new_I
Tau_3_new_2[j-n_0]=gamma_output$new_tau
#TAU_1
tau_output=update_tau(Y_i=data$Y1[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],sigma_2=sigma_1_2_out_2[i+1],mu_tau=mu_tau_1_out_2[i+1],sigma_tau_2=sigma_tau_1_2_out_2[i+1],Theta_i=Theta_1_new[j],I_i=I_1_new_2[j-n_0],gamma_i=gamma_1_new_2[j-n_0],tau_i=Tau_1_new_2[j-n_0],delta_tau=delta_tau_set,Tau_star=Tau_star_1)
I_1_new_3[j-n_0]=tau_output$new_I
Tau_1_new_3[j-n_0]=tau_output$new_tau
gamma_1_new_3[j-n_0]=tau_output$new_gamma
#TAU_2
tau_output=update_tau(Y_i=data$Y2[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],sigma_2=sigma_2_2_out_2[i+1],mu_tau=mu_tau_2_out_2[i+1],sigma_tau_2=sigma_tau_2_2_out_2[i+1],Theta_i=Theta_2_new[j],I_i=I_2_new_2[j-n_0],gamma_i=gamma_2_new_2[j-n_0],tau_i=Tau_2_new_2[j-n_0],delta_tau=delta_tau_set,Tau_star=Tau_star_2)
I_2_new_3[j-n_0]=tau_output$new_I
Tau_2_new_3[j-n_0]=tau_output$new_tau
gamma_2_new_3[j-n_0]=tau_output$new_gamma
#TAU_1
tau_output=update_tau(Y_i=data$Y3[(data$ID==j)],t_i=data$t[(data$ID==j)],J_i=J[j],d_i=d[j],sigma_2=sigma_3_2_out_2[i+1],mu_tau=mu_tau_3_out_2[i+1],sigma_tau_2=sigma_tau_3_2_out_2[i+1],Theta_i=Theta_3_new[j],I_i=I_3_new_2[j-n_0],gamma_i=gamma_3_new_2[j-n_0],tau_i=Tau_3_new_2[j-n_0],delta_tau=delta_tau_set,Tau_star=Tau_star_3)
I_3_new_3[j-n_0]=tau_output$new_I
Tau_3_new_3[j-n_0]=tau_output$new_tau
gamma_3_new_3[j-n_0]=tau_output$new_gamma
}
Theta_1_out_2=cbind(Theta_1_out_2,Theta_1_new)
Theta_2_out_2=cbind(Theta_2_out_2,Theta_2_new)
Theta_3_out_2=cbind(Theta_3_out_2,Theta_3_new)
I_1_out_2=cbind(I_1_out_2,I_1_new_1,I_1_new_2,I_1_new_3)
I_2_out_2=cbind(I_2_out_2,I_2_new_1,I_2_new_2,I_2_new_3)
I_3_out_2=cbind(I_3_out_2,I_3_new_1,I_3_new_2,I_3_new_3)
gamma_1_out_2=cbind(gamma_1_out_2,gamma_1_new_1,gamma_1_new_2,gamma_1_new_3)
gamma_2_out_2=cbind(gamma_2_out_2,gamma_2_new_1,gamma_2_new_2,gamma_2_new_3)
gamma_3_out_2=cbind(gamma_3_out_2,gamma_3_new_1,gamma_3_new_2,gamma_3_new_3)
Tau_1_out_2=cbind(Tau_1_out_2,Tau_1_new_1,Tau_1_new_2,Tau_1_new_3)
Tau_2_out_2=cbind(Tau_2_out_2,Tau_2_new_1,Tau_2_new_2,Tau_2_new_3)
Tau_3_out_2=cbind(Tau_3_out_2,Tau_3_new_1,Tau_3_new_2,Tau_3_new_3)
print(i)
}