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comp_cmfdr.R
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comp_cmfdr.R
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##### Comparison between LSMM and cmfdr #####
# Figures S60 in Supplementary Document
library(LSMM)
library(pROC)
library(MASS)
library(locfdr)
library(pgnorm)
source("performance.R")
# function to generate data
generate_data <- function(M, L, K, alpha, Z.perc, A.perc, beta0, b, omega, sigma2){
# design matrix of fixed effects
Z <- rep(0, M*L)
indexZ <- sample(M*L, M*L*Z.perc)
Z[indexZ] <- 1
Z <- matrix(Z, M, L)
# design matrix of random effects
A <- rep(0, M*K)
indexA <- sample(M*K, M*K*A.perc)
A[indexA] <- 1
A <- matrix(A, M, K)
# eta (latent variable which indicate whether the annotation is relevant to the phenotype)
eta <- rep(0, K)
indexeta <- sample(K, K*omega)
eta[indexeta] <- 1
# beta (random effects)
beta <- rep(0, K)
beta[indexeta] <- rnorm(K*omega, 0, sqrt(sigma2))
# gamma (latent variable which indicate whether the SNP is associated with the phenotype)
pi1 <- sigma(beta0 + Z %*% b + A %*% beta)
gamma <- rep(0, M)
indexgamma <- (runif(M) < pi1)
gamma[indexgamma] <- 1
# Pvalue
Pvalue <- runif(M)
Pvalue[indexgamma] <- rbeta(sum(indexgamma), alpha, 1)
return( list(Z = Z, A = A, Pvalue = Pvalue, beta = beta, pi1 = pi1, eta = eta,
gamma = gamma))
}
# sigmoid function
sigma <- function(x){
y <- 1/(1+exp(-x))
return (y)
}
# Functions in cmfdr
run_cmlocfdr=function(Pvalue=1,P,X,bases_X=FALSE,K=2,knots=NULL,
nIter=160,thin=1,burnIn=10,SSA=1,SSG=1,MA=3,MG=3,theoNULL=FALSE,mu,inits=NULL){
library(pgnorm)
library(locfdr)
library(splines)
## Inputs:
## P: N vector of P-values or Z scores based on the input from mainfile.R;
## X: N x Q matrix of covariates
## nIter: Number of MCMC iterations
## thin: thinning rate
## burnIn: burn-in number
## SSA: increase step-size for alpha draw
## SS: increase step-size for gamma draw
## MA: num of multiple try for alpha
## MG: num of multiple try for gamma
## mu: origin of gamma distribution, do not change; not used for generalized normal
if (Pvalue==1){ # input P value
N=length(P)
snpid=1:N
all.complete=complete.cases(cbind(P,X))
X=X[all.complete,]
P=P[all.complete]
P[P==0]=min(P[P>0]);P[P==1]=max(P[P<1])
Z=-qnorm(P/2);N=length(Z)
if(!colnames(X)[1]=="Intcpt"){X=cbind(Intcpt=1,X)}
}else{
Z=P; #input Z score;
}
X_bases=NULL
if(!is.null(bases_X)){
for(p in 1:length(bases_X)){
X_p=X[,bases_X[p]]
range=c(min(X_p),max(X_p))
delta=(range[2]-range[1])/200
grid=seq(range[1],range[2]+delta,by=delta)
knots=c(min(grid),quantile(X_p,.5),quantile(X_p,.67),max(grid))
phi.mat=bs(grid,knots=knots[2:(length(knots)-1)],degree=3,intercept=FALSE,
Boundary.knots=c(knots[1],knots[length(knots)]))
for(k in 1:(K+3)){
phi.mat[,k]=phi.mat[,k]/(sum(phi.mat[,k])*delta)
}
#plot(grid,phi.mat[,1],type="l",ylab="density",xlab="annotation score")
#title(main="density basis functions")
#for(k in 2:K){
# lines(grid,phi.mat[,k],type="l",col=k+1,lwd=.5)
#}
Phi.mat=phi.mat
for(k in 1:(K+3)){
for(j in 1:length(grid)){Phi.mat[j,k]=sum(phi.mat[grid<=grid[j],k]*delta)}
}
#plot(grid,Phi.mat[,2],type="l")
#lines(grid,Phi.mat[,3],type="l",col=k)
X_bases_p=array(NA,dim=c(length(X_p),2))
for(g in 1:length(grid)){
#print(c(p,g))
if(length(X_p[abs(X_p-grid[g])<=delta/2])>0){
tmp=dim(rbind(X_bases_p[abs(X_p-grid[g])<=delta/2,]))[1]
X_bases_p[abs(X_p-grid[g])<=delta/2,]=cbind(rep(Phi.mat[g,2],tmp),rep(Phi.mat[g,3],tmp))
}
}
X_bases=cbind(X_bases,X_bases_p)
}
name=colnames(X)[bases_X[1]]
colnames(X_bases)=rep(1:2,length(bases_X))
colnames(X_bases)[1:2]=c(paste(name,"_1",sep=""),paste(name,"_2",sep=""))
if(length(bases_X)>1){
for(p in 2:length(bases_X)){
name=colnames(X)[bases_X[p]]
colnames(X_bases)[(2*(p-1)+1):(2*(p-1)+2)]=c(paste(name,"_1",sep=""),paste(name,"_2",sep=""))
}
}
colnames(X_bases)
X=cbind(Intcpt=1,X_bases,X[,-c(1,bases_X)])
}
save(file="data_inputs.R",Z,X,N)
MCMCfit=cmlFDR_GammaDist(Z,X,nIter=nIter,burnIn=burnIn,thin=thin,SSA=SSA,SSG=SSG,MA=MA,MG=MG,mu=mu,
theoNULL=theoNULL,inits=inits)
ALPHA_array=MCMCfit[[1]]
BETA_array=MCMCfit[[2]]
GAMMA_array=MCMCfit[[3]]
SIGMA_SQ_array=MCMCfit[[4]]
first=1
Alpha=ALPHA_array[[first]]
Beta=BETA_array[[first]]
Gamma=GAMMA_array[[first]]
if(theoNULL==FALSE){Sigma_sq=SIGMA_SQ_array[[first]]}
for(j in (first+1):length(ALPHA_array)){
Alpha=Alpha+ALPHA_array[[j]]
Beta=Beta+BETA_array[[j]]
Gamma=Gamma+GAMMA_array[[j]]
if(theoNULL==FALSE){Sigma_sq=Sigma_sq+SIGMA_SQ_array[[j]]}
}
Alpha=cbind(Alpha/length(first:length(ALPHA_array)))
Beta=Beta/length(first:length(ALPHA_array))
Gamma=cbind(Gamma/length(first:length(ALPHA_array)))
if(theoNULL==FALSE){Sigma_sq=Sigma_sq/length(first:length(ALPHA_array))}
if(theoNULL==TRUE){Sigma_sq=1}
f0<-2*dnorm(abs(Z),mean=0,sd=Sigma_sq^.5)
f1<-f0
for (i in 1:length(Z)){
X_i=rbind(X[i,])
f1[i]<-2*dgamma(abs(Z[i])-.68,shape=exp(X_i%*%Alpha),rate=Beta)
}
p0=1;
p1=exp(X%*%Gamma)
pi0=p0/(p0+p1)
pi1=1-pi0
cmfdr=pi0*f0/(pi0*f0+pi1*f1)
X_mean=rbind(apply(X,2,mean))
f1=2*dpgnorm(Z,p=Beta,mean=0,sigma=exp(X_mean%*%Alpha)*sqrt(gamma(3/Beta)/gamma(1/Beta)))
p1=exp(X_mean%*%Gamma)
pi0=p0/(p0+p1)
pi1=1-pi0
fdr=pi0*f0/(pi0*f0+pi1*f1)
z.locfdr=locfdr(c(Z,-Z),nulltype=1,plot=0)
efron_fdr=z.locfdr$fdr[1:length(Z)]
results=list()
results[[1]]=MCMCfit[[1]]
results[[2]]=MCMCfit[[2]]
results[[3]]=MCMCfit[[3]]
results[[4]]=MCMCfit[[4]]
results[[5]]=MCMCfit[[5]]
results[[6]]=array(NA,dim=c(N,3))
results[[6]][,1]=efron_fdr
results[[6]][,2]=fdr
results[[6]][,3]=cmfdr
return(results)
}
cmlFDR_GammaDist=function (Z,X,nIter=1100,burnIn=100,thin=5,initNULL=0.95,simulate=FALSE,
SSA=1,SSG=1,MA=3,MG=3,mu=0.68,theoNULL=FALSE,inits=NULL)
{
#SSA:scale the diagnal of the covariance matrix in MH of Alpha draw to increase/decrease the step size
#SSG:scale the diagnal of the covariance matrix in MH of Gamma draw to increase/decrease the step size
###########################
#Load packages/functions
###########################
library(tmvtnorm)
library(mnormt)
library(magic)
library(locfdr)
library(arm)
library(pscl)
if(colnames(X)[1] != "Intcpt") X=cbind(Intcpt=1,X)
#print(X[1:10,])
# hyperparameters
B01=0.001;B02=0.001; #Prior: P(Beta) ~ Gamma(B01,B02)
a0=0.001;b0=0.001; #Prior: P(sigma^2) ~ IVG(a0,b0) #b0 is scale;
Sigma_Gamma=matrix(0,nrow=dim(X)[2],ncol=dim(X)[2])
diag(Sigma_Gamma)=10000; #Prior: P(Gamma) ~ N(0,Sigma_Gamma)
Sigma_Alpha=matrix(0,nrow=dim(X)[2],ncol=dim(X)[2])
diag(Sigma_Alpha)=10000; #Prior: P(Alpha) ~ N(0,Sigma_Alpha)
df=4 # degrees of freedom for multivariate t proposal
# data
N=dim(X)[1]
M=dim(X)[2]
# Parameter arrays
ALPHA_array=list()
BETA_array=list()
if(theoNULL==FALSE){
SIGMA_SQ_array=list()
}
GAMMA_array=list()
Accp_Rate_array=list() #Alpha draw accept rate
Accp_Rate_array_g=list() #Gamma draw accept rate
array_ind=0
# Initialize parameters
if(is.null(inits)){
Alpha=cbind(rep(0,M));Alpha_mean=Alpha
pi0=initNULL #min(.98,locfdr(Z,nulltype=1,plot=0)$fp0[5,3]);
gamma0=log((1-pi0)/pi0) #intercept for Non-NULL gamma
Gamma=array(0,dim=c(M,1));Gamma_mean=Gamma; Gamma[1,]=gamma0
Beta=0.1;Beta_mean=Beta
Phi=1-as.numeric(abs(Z)< sort(abs(Z))[round(pi0*N)]);Phi_mean=0*Phi
Sigma_sq=1
}
if(!is.null(inits)){
last=length(inits[[1]])
Alpha=cbind(inits[[1]][[last]]);Alpha_mean=Alpha
Beta=inits[[2]][[last]];Beta_mean=Beta
Gamma=cbind(inits[[3]][[last]]);Gamma_mean=Gamma
if(theoNULL==FALSE){
Sigma_sq=inits[[4]][[last]];Sigma_sq_mean=Sigma_sq
}
if(theoNULL==TRUE){
Sigma_sq=1
}
Phi=inits[[5]];Phi_mean=0*Phi
}
PHI_match_rate=NULL
for(iter in 1:nIter){
print(iter)
Z1=abs(Z[!Phi==0])
X1=X[!Phi==0,]
## Draw ALPHA
if(det(t(X1)%*%X1) != 0){ #avoid singular
obj=Draw_Alpha_log_M_mu(Alpha,Z1,X1,Beta,Phi,df,MA,Sigma_Alpha,SSA,mu)
Alpha=obj$par;
}
print("Alpha");
print(Alpha);
## Draw BETA
Beta=rgamma(1,shape=B01+sum(exp(X1%*%Alpha)),rate=B02+sum(Z1-mu))
print(paste("Beta",Beta));
## Draw GAMMA
#Gamma draw: Multiple try MH
objg=Draw_Gamma_log_M(Gamma,Z,X,Phi,df,Sigma_Gamma,SSG,MG)
Gamma=objg$par;
print("Gamma");
print(Gamma);
if(theoNULL==FALSE){
## Draw SIGMA_SQ;
Z0=abs(Z[Phi==0])
Sigma_sq=rigamma(1,alpha=a0+length(Z0)/2,beta=b0+(Z0%*%Z0)/2);
print(paste("Sigma_sq",Sigma_sq));
}
## Draw PHI;
log_P_phi=cbind(X%*%Gamma,0)
log_P_phi[abs(Z)>mu,1]=log_P_phi[abs(Z)>mu,1]+((exp(X[abs(Z)>mu,]%*%Alpha)-1)*
log(abs(Z[abs(Z)>mu])-mu)-Beta*(abs(Z[abs(Z)>mu])-mu))+(exp(X[abs(Z)>mu,]%*%Alpha))*
log(Beta)-lgamma(exp(X[abs(Z)>mu,]%*%Alpha))
#log_P_phi[,2]=log_P_phi[,2]+log(2)-0.5*log(2*pi)-0.5*Z^2;
if(theoNULL==TRUE){
log_P_phi[,2]=log_P_phi[,2]+log(2)-0.5*log(2*pi)-0.5*Z^2;
}else{
log_P_phi[,2]=log_P_phi[,2]+log(2)-0.5*log(2*pi*Sigma_sq)-(1/(2*Sigma_sq))*Z^2;
}
P_phi=exp(log_P_phi)/apply(exp(log_P_phi),1,sum) #declare the variable P_phi;
P_phi[abs(Z)>mu,1]=1/(1+exp(log_P_phi[abs(Z)>mu,2]-log_P_phi[abs(Z)>mu,1]))
P_phi[,2]=1/(1+exp(log_P_phi[,1]-log_P_phi[,2]))
P_phi[abs(Z)<=mu,1]=0;P_phi[abs(Z)<=mu,2]=1;
Phi_new=Phi #declare variable Phi_new, create a vector;
for(i in 1:N){
Phi_new[i]=sample(c(1,0),size=1,replace=TRUE,prob=P_phi[i,])
}
Phi=Phi_new
if(simulate == TRUE) print(sum(Phi == Phi_true)/N)
## Save results after thin
if(iter%%thin==0 & iter>=burnIn){
array_ind=array_ind+1
ALPHA_array[[array_ind]]=Alpha
GAMMA_array[[array_ind]]=Gamma
BETA_array[[array_ind]]=Beta
if(theoNULL==FALSE){
SIGMA_SQ_array[[array_ind]]=Sigma_sq
}
if(det(t(X1)%*%X1) != 0){
Accp_Rate_array[[array_ind]]=obj$accp
}
else Accp_Rate_array[[array_ind]]=0
Accp_Rate_array_g[[array_ind]]=objg$accp;
print("Alpha mean:");
Alpha_mean=((array_ind-1)*Alpha_mean+ALPHA_array[[array_ind]])/array_ind
if(simulate==TRUE) print(cbind(Alpha_mean,Alpha_true))
if(simulate==FALSE) print(Alpha_mean)
print("Beta mean:");
if(simulate==TRUE) print(cbind(mean(as.numeric(BETA_array)),BETA_true))
if(simulate==FALSE) print(mean(as.numeric(BETA_array)))
if(theoNULL==FALSE){
print("Sigma_sq mean:");
if(simulate==TRUE) print(cbind(mean(as.numeric(SIGMA_SQ_array)),SIGMA_SQ_true))
if(simulate==FALSE) print(mean(as.numeric(SIGMA_SQ_array)))
}
print("Gamma mean:");
Gamma_mean=((array_ind-1)*Gamma_mean+GAMMA_array[[array_ind]])/array_ind
if(simulate==TRUE) print(cbind(Gamma_mean,Gamma_true))
if(simulate==FALSE) print(Gamma_mean)
print(paste("Multiple-try MH Accept Rate for Alpha (mean):",mean(as.numeric(Accp_Rate_array))));
print(paste("Multiple-try MH Accept Rate for Gamma (mean):",mean(as.numeric(Accp_Rate_array_g))));
if(simulate==TRUE) {
PHI_match_rate=rbind(PHI_match_rate,sum(Phi==Phi_true)/N);
print(paste("Phi matching rate (mean):",mean(PHI_match_rate)))
}
#probability of each SNP being Non-NULL, average of Phi over the iterations saved;
Phi_mean=((array_ind-1)*Phi_mean+Phi)/array_ind;
results=list()
results[[1]]=ALPHA_array
results[[2]]=BETA_array
results[[3]]=GAMMA_array
if(theoNULL==TRUE){
results[[4]]=1
}
if(theoNULL==FALSE){
results[[4]]=SIGMA_SQ_array
}
results[[5]]=Phi
save(X,Z,results,file="mcmc_intermediate_outputs.R")
}
}
#Calculate SD;
#Alpah
print("Alpha SD:");
for(i in 1:dim(X)[2]){
print(sd(as.numeric(unlist(lapply(ALPHA_array, function(x) x[i])))))
}
#beta
print(paste("Beta SD:",sd(as.numeric(BETA_array))))
if(theoNULL==FALSE){
#Sigma_sq
print(paste("Sigma SD:",sd(as.numeric(SIGMA_SQ_array))))
}
#Gamma
print("Gamma SD:");
for(i in 1:dim(X)[2]){
print(sd(as.numeric(unlist(lapply(GAMMA_array, function(x) x[i])))))
}
#return results;
#return results;
results=list()
results[[1]]=ALPHA_array
results[[2]]=BETA_array
results[[3]]=GAMMA_array
if(theoNULL==TRUE){
results[[4]]=1
}
if(theoNULL==FALSE){
results[[4]]=SIGMA_SQ_array
}
results[[5]]=Phi
return(results)
}
log_p_alpha=function(Alpha,Z,W,B,SA,MU){
gammafcn=lgamma(exp(W%*%Alpha));
#if (gammafcn == Inf || is.na (gammafcn) ) {print(paste("Gamma function",gammafcn));}
log_p=sum(exp(W%*%Alpha)*log(Z-MU)-gammafcn)+sum(exp(W%*%Alpha))*log(B)-0.5*t(Alpha)%*%solve(SA)%*%Alpha
#print(log_p)
return(log_p)
}
Draw_Alpha_log_M_mu=function(Alpha,Z,X,Beta,Phi,df,Multiple,Sigma_Alpha,SSA,mu)
{
log_p_Alpha_star=rep(0,Multiple)
log_p_Alpha_2star=rep(0,Multiple)
p=rep(0,Multiple)
den=0;num=0;
sigma=solve(t(X)%*%X);
diag(sigma)=diag(sigma)*SSA;
#if(det(sigma) == 0) {print(sigma); break}
logp=log_p_alpha(Alpha,Z,X,B=Beta,SA=Sigma_Alpha,MU=mu);
if( logp == Inf | logp == -Inf | is.na(logp)) {alpha=Alpha}
else {alpha <-optim(Alpha,Z=Z,W=X,B=Beta,SA=Sigma_Alpha,MU=mu,log_p_alpha,method="Nelder-Mead",
hessian=FALSE,control=list(maxit=10,fnscale=-1))$par}
Alpha_star=t(rmvt(n=Multiple,alpha,sigma=sigma,df=df))
for (i in 1:Multiple){
log_p_Alpha_star[i]=log_p_alpha(Alpha_star[,i],Z,X,Beta,Sigma_Alpha,mu)
}
#control overfloat, -max(log_p_Alpha_star);
p=exp(log_p_Alpha_star-max(log_p_Alpha_star))/sum(exp(log_p_Alpha_star - max(log_p_Alpha_star)))
#in case there is still overfloat;
p[is.na(p)]=(1-sum(p[!is.na(p)]))/sum(is.na(p))
j=sample(c(1:Multiple),1,prob=p);
Alpha_2star=t(rmvt(n=Multiple-1,Alpha_star[,j],sigma=sigma,df=df))
Alpha_2star <-cbind(Alpha_2star,Alpha)
for (i in 1:Multiple){
log_p_Alpha_2star[i]=log_p_alpha(Alpha_2star[,i],Z,X,Beta,Sigma_Alpha,mu)
}
#control overfloat
num=sum(exp(log_p_Alpha_star -max(log_p_Alpha_star)))
den=sum(exp(log_p_Alpha_2star -max(log_p_Alpha_star)))
rho=min(1,num/den)
#in case overfloat again
if(is.na(rho)) {rho=0.5};
accp=0;
u=runif(1)
if(u<rho){
Alpha=Alpha_star[,j]
accp=1;
}
return(list(par=Alpha, accp=accp))
}
log_p_gamma=function(Gamma,Z,X,SG,phi){
log_p=sum(phi*(X%*%Gamma)-log(1+exp(X%*%Gamma)))-0.5*t(Gamma)%*%solve(SG)%*%Gamma
return(log_p)
}
Draw_Gamma_log_M=function(Gamma,Z,X,Phi,df,Sigma_Gamma,SSG,Multiple)
{
log_p_Gamma_star=rep(0,Multiple)
log_p_Gamma_2star=rep(0,Multiple)
p=rep(0,Multiple)
#if(det(sigma) == 0) {print(sigma); break}
gamma_opt <-optim(Gamma,Z=Z,X=X,SG=Sigma_Gamma,phi=Phi,log_p_gamma,method="Nelder-Mead",
hessian=TRUE,control=list(maxit=10,fnscale=-1))
gamma=gamma_opt$par
sigma=solve(-gamma_opt$hessian)
diag(sigma)=diag(sigma)*SSG
Gamma_star=t(rmvt(n=Multiple,gamma,sigma=sigma,df=df))
for (i in 1:Multiple){
log_p_Gamma_star[i]=log_p_gamma(Gamma_star[,i],Z,X,Sigma_Gamma,Phi)
}
#control overfloat, -max(log_p_Gamma_star);
p=exp(log_p_Gamma_star-max(log_p_Gamma_star))/sum(exp(log_p_Gamma_star - max(log_p_Gamma_star)))
#in case there is still overfloat;
p[is.na(p)]=(1-sum(p[!is.na(p)]))/sum(is.na(p))
j=sample(c(1:Multiple),1,prob=p);
Gamma_2star=t(rmvt(n=Multiple-1,Gamma_star[,j],sigma=sigma,df=df))
Gamma_2star <-cbind(Gamma_2star,Gamma)
for (i in 1:Multiple){
log_p_Gamma_2star[i]=log_p_gamma(Gamma_2star[,i],Z,X,Sigma_Gamma,Phi)
}
#control overfloat
num=sum(exp(log_p_Gamma_star -max(log_p_Gamma_star)))
den=sum(exp(log_p_Gamma_2star -max(log_p_Gamma_star)))
rho=min(1,num/den)
#in case overfloat again
if(is.na(rho)) {rho=0.5};
accp=0;
u=runif(1)
if(u<rho){
Gamma=Gamma_star[,j]
accp=1;
}
return(list(par=Gamma, accp=accp))
}
M <- 5000 # No. of SNPs
L <- 5 # No. of fixed effects
K <- 5 # No. of random effects
Z.perc <- 0.1 # the proportion the entries in Z is 1
A.perc <- 0.1 # the proportion the entries in A is 1
alpha <- 0.2 # parameter in the Beta distribution
beta0 <- -2 # intercept of the logistic model
set.seed(1)
b <- rnorm(L) # fixed effects
omega <- 0.2 # proportion of relevant annotations
sigma2 <- 1 # parameter in the spike-slab prior
rep <- 10 # repeat times
bases_X=NULL;
K=2
nIter=2000;
thin=10;
burnIn=500;
SSA=1
SSG=4
MA=8
MG=5
theoNULL=FALSE
mu=.68
inits=NULL
result <- matrix(0, rep, 16)
for (i in 1:rep){
cat(i, "out of", rep, "\n")
data <- generate_data(M, L, K, alpha, Z.perc, A.perc, beta0, b, omega, sigma2)
# LSMM
fit <- LSMM(data$Pvalue, data$Z, data$A)
assoc.SNP <- assoc.SNP(fit, FDRset = 0.1, fdrControl = "global")
result[i, 1:4] <- as.numeric(performance(data$gamma, assoc.SNP$gamma, 1-fit$pi1))
result[i, 5:8] <- as.numeric(performance(data$gamma, assoc.SNP$gamma.stage1, 1-fit$pi1.stage1))
result[i, 9:12] <- as.numeric(performance(data$gamma, assoc.SNP$gamma.stage2, 1-fit$pi1.stage2))
# cmfdr
X <- cbind(rep(1, M), data$Z, data$A)
colnames(X) <- c("Intcpt", paste("Z", 1:L, sep = ""), paste("A", 1:Ks, sep = ""))
results=run_cmlocfdr(Pvalue = 1, P = data$Pvalue, X = X,bases_X = bases_X, K = K,
nIter = nIter, thin = thin, burnIn = burnIn, SSA = SSA, SSG = SSG,
MA = MA, MG = MG, theoNULL = theoNULL, mu = mu, inits = inits)
ALPHA_array=results[[1]]
BETA_array=results[[2]]
GAMMA_array=results[[3]]
SIGMA_SQ_array=results[[4]]
first=1
Alpha_vec=ALPHA_array[[first]]
Beta_vec=BETA_array[[first]]
Gamma_vec=GAMMA_array[[first]]
Alpha=ALPHA_array[[first]]
Beta=BETA_array[[first]]
Gamma=GAMMA_array[[first]]
if(theoNULL==FALSE){Sigma_sq=SIGMA_SQ_array[[first]]}
for(k in (first+1):length(ALPHA_array)){
Alpha_vec=cbind(Alpha_vec,ALPHA_array[[k]])
Beta_vec=cbind(Beta_vec,BETA_array[[k]])
Gamma_vec=cbind(Gamma_vec,GAMMA_array[[k]])
Alpha=Alpha+ALPHA_array[[k]]
Beta=Beta+BETA_array[[k]]
Gamma=Gamma+GAMMA_array[[k]]
if(theoNULL==FALSE){Sigma_sq=Sigma_sq+SIGMA_SQ_array[[k]]}
}
Alpha=cbind(Alpha/length(first:length(ALPHA_array)))
Beta=Beta/length(first:length(ALPHA_array))
Gamma=cbind(Gamma/length(first:length(ALPHA_array)))
if(theoNULL==FALSE){Sigma_sq=Sigma_sq/length(first:length(ALPHA_array))}
if(theoNULL==TRUE){Sigma_sq=1}
Z <- qnorm(data$Pvalue/2)
f0<-2*dnorm(abs(Z),mean=0,sd=Sigma_sq^.5)
f1<-f0
for (l in 1:length(Z)){
X_l=rbind(X[l,])
f1[l]<-2*dgamma(abs(Z[l])-mu,shape=exp(X_l%*%Alpha),rate=Beta)
}
p1=exp(X%*%Gamma);p0=1;
pi0=p0/(p0+p1)
pi1=1-pi0
cmfdr=pi0*f0/(pi0*f0+pi1*f1)
est <- rep(0, length(cmfdr))
cmFDR <- post2FDR(1-cmfdr)
est[which(cmFDR <= 0.1)] <- 1
result[i, 13:16] <- as.numeric(performance(data$gamma, est, cmfdr))
}
result <- as.data.frame(result)
names(result) <- c("FDR.LSMM", "power.LSMM", "AUC.LSMM", "pAUC.LSMM",
"FDR.TGM", "power.TGM", "AUC.TGM", "pAUC.TGM",
"FDR.LFM", "power.LFM", "AUC.LFM", "pAUC.LFM",
"FDR.cmfdr", "power.cmfdr", "AUC.cmfdr", "pAUC.cmfdr")