simulation_JSDM_on_different_datasets.R
In dariamed/gjamed: What the package does (short line)
rm(list=ls())
setwd("~/Documents/GitHub/gjamed")
########## Simulating the data
library(MASS)
library(repmis)
library(gjam)
library(rlist)
library(MASS)
library(truncnorm)
library(coda)
library(RcppArmadillo)
library(arm)
library(NLRoot)
library(Rcpp)
library(plyr)
library(ggplot2)
Rcpp::sourceCpp('src/cppFns.cpp')
source("R/gjamHfunctions_mod.R")
source("R/simple_gjam_0.R")
source("R/simple_gjam_1.R")
source("R/simple_gjam_2.R")
source("R/simple_gjam_3.R")
source("R/simple_gjam_4.R")
simulation_fun_paper<-function(Sp, Ntr, rval,nsamples=500, Ktrue,q=20, it=1000, burn=500,type="GJAM"){
S<-Sp
n<- nsamples
r <- rval
iterations<-it
env<-runif(-50,50,n=n)
X<-cbind(1,poly(env,2)) #nxK
idx<-sample(S)
B_0<-seq(0,100,length.out=S)[idx]
B_1<-seq(0,100,length.out=S)[idx]
B_2<-seq(0,100,length.out=S)[idx]
B<-cbind(B_0,B_1,B_2) #SxK
L<-X%*%t(B) #nxS
K=sum(S/(S+(1:S)-1)) #104, his prior number of clusters when alpha=S
if(type=="GJAM"){ cat("Prior expected number of clusters : ",K,"\n")}
else{cat("Prior expected number of clusters : ",Ktrue,"\n")}
K_t= Ktrue
cat("True number of clusters : ",K_t,"\n")
A<-matrix(NA,nrow=ceiling(K_t),ncol=q)
# sig=matrix(runif(n=q*q),ncol=q)
for(i in 1:ceiling(K_t)){
A[i,]<-mvrnorm(n = 1,rep(0,q), Sigma=3*diag(q)) #Nxq short and skinny
}
idx<-sample((1:ceiling(K_t)),S,replace=T)
Lambda<-A[idx,] #Sxr tall and skinny
Sigma<-Lambda%*%t(Lambda)+0.1*diag(S) #SxS
Sigma_true<-Sigma
Y<-mvrnorm(n = n, mu=rep(0,S), Sigma=Sigma)
xdata<-as.data.frame(X[,-1])
colnames(xdata)<-c("env1","env2")
formula<-as.formula(~env1+env2)
if(type=="GJAM"){
rl <- list(r = r, N =Ntr-1)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-gjam(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.DP<-S
pk_chains<-NULL
}
if(type=="0"){
#func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
#alpha.DP<-.bisec(func,0.01,100)
alpha.DP<-S
rl <- list(r = r, N =Ntr-1,alpha.DP=alpha.DP)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam0(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
pk_chains<- fit$chains$pk_g
}
if(type=="1"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_1(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="2"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape,V=1)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_2(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="3"){
eps=0.05
alp_sig<-as.data.frame(matrix(NA,nrow=20,ncol=3))
colnames(alp_sig)<-c("alpha","sigma","is_less_150")
alp_sig$sigma=seq(0.05,0.5,length.out = 20)
#loop to run bisecetion on a grid for sigma
for(i in 1:20){
####corrected formula : added -1
func<-function(x) {(x/alp_sig[i,"sigma"])*(prod((x+alp_sig[i,"sigma"]+c(1:S) -1)/(x+c(1:S) -1))-1) - K_t}
alp_sig[i,"alpha"]<-.bisec(func,0.01,100)
N_eps<-floor(.compute_tau_mean(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps) + 2*.compute_tau_var(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps))
ifelse(N_eps<=150,alp_sig[i,"is_less_150"]<-T,alp_sig[i,"is_less_150"]<-F)
N_eps
}
if(sum(alp_sig$is_less_150==T)==0) cat("!! no choice under N=150, need to recheck!!!")
k<-max(which(alp_sig$is_less_150==T)) #max sigma s.t. N<150
sigma_py<-alp_sig[i,"sigma"]
alpha.PY<-alp_sig[i,"alpha"]
N_eps<-floor(.compute_tau_mean(sigma_py,alpha.PY,eps) + 2*.compute_tau_var(sigma_py,alpha.PY,eps))
rl <- list(r = r, N = N_eps, sigma_py=sigma_py, alpha=alpha.PY)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_3(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
pk_chains<- fit$chains$pk_g
alpha.DP<-alpha.PY
Ntr<-N_eps+1
}
if(type=="4"){
eps=0.05
alp_sig<-as.data.frame(matrix(NA,nrow=20,ncol=3))
colnames(alp_sig)<-c("alpha","sigma","is_less_150")
alp_sig$sigma=seq(0.05,0.4,length.out = 20)
#loop to run bisecetion on a grid for sigma
for(i in 1:20){
####corrected added -1
func<-function(x) {(x/alp_sig[i,"sigma"])*(prod((x+alp_sig[i,"sigma"]+c(1:S)-1)/(x+c(1:S) -1))-1) - K_t}
alp_sig[i,"alpha"]<-.bisec(func,0.01,100)
N_eps<-floor(.compute_tau_mean(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps) + 2*.compute_tau_var(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps))
ifelse(N_eps<=150,alp_sig[i,"is_less_150"]<-T,alp_sig[i,"is_less_150"]<-F)
N_eps
}
if(sum(alp_sig$is_less_150==T)==0) cat("!! no choice under N=150, need to recheck!!!")
k<-max(which(alp_sig$is_less_150==T)) #max sigma s.t. N<150
sigma_py<-alp_sig[i,"sigma"]
alpha.PY<-alp_sig[i,"alpha"]
#fixing hyperparameters
ro.disc=1-2* sigma_py
shape=((alpha.PY)^2)/10
rate=alpha.PY/10
# 95% quantile of alpha
alpha.max=qgamma(.95, shape=shape, rate=rate)
N_eps<-floor(.compute_tau_mean(sigma_py,alpha.max,eps) + 2*.compute_tau_var(sigma_py,alpha.max,eps))
rl <- list(r = r, N = N_eps,rate=rate,shape=shape,V1=1,ro.disc=ro.disc) #here to modify N
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_4(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.PY_g
sigma.chains<-fit$chains$discount.PY_g
pk_chains<- fit$chains$pk_g
Ntr<-N_eps+1
alpha.DP<-alpha.PY
}
trace<-apply(fit$chains$kgibbs,1,function(x) length(unique(x)))
df<-as.data.frame(trace)
df$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p<-ggplot(df, aes(y=trace, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the number of groups K for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
geom_hline(yintercept = Ktrue,color = "red")
plot(p)
#####Weights plot
if(type%in%c("0","1","2","3","4")){
pk<- apply(fit$chains$pk_g[-c(1:burn),],2,mean)
last_pk<- round(pk[Ntr-1],3)
df_weights <- data.frame(matrix(NA, nrow = Ntr-1, ncol =1))
df_weights$pw<-pk
df_weights$tr<-1:(Ntr-1)
pl_weigths<- ggplot(df_weights, aes(x=tr, y=pw)) +
geom_segment( aes(x=tr,xend=tr,y=0,yend=pw)) +
geom_point( size=0.5, color="red", fill=alpha("blue", 0.3), alpha=0.4, shape=21, stroke=2)+ labs(title=paste0("Weights for the case: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr, " pN=",last_pk), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
pl_weigths
}
#####Alpha plot
if(type%in%c("1","2","4")){
df_alpha <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha$alpha<- alpha.chains[-c(1:burn)]
df_alpha$type<- "posterior"
df_alpha_prior <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
#df_alpha_prior$alpha<- rgamma(it-burn, shape, rate)
alpha_seq= seq(min(alpha.chains[-c(1:burn)]),max(alpha.chains[-c(1:burn)]),length=it-burn)
df_alpha_prior$alpha <- dgamma(alpha_seq,rate,shape)
df_alpha_prior$type<- "prior"
df_alpha_all<- rbind(df_alpha[-1,],df_alpha_prior[-1,])
###Compute mean
mu <- ddply(df_alpha_all, "type", summarise, grp.mean=mean(alpha))
mu$grp.mean[which(mu$type=="prior")]=alpha.DP
p_alpha_1<- ggplot(df_alpha_all, aes(x=alpha, color=type)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution alpha: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_alpha_1
p_alpha_2<- ggplot(df_alpha, aes(x=alpha)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density(color="red")+labs(title=paste0("Posterior distribution for alpha"), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples," S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
scale_color_manual(name = c("Legend"), values = c("prior"="#9999FF", "posterior"= "#FF6666"), labels=c("posterior mean","prior mean"))
p_alpha_2
}
#######Sigma plot
if(type%in%c("4")){
df_sigma <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_sigma$sigma<- sigma.chains[-c(1:burn)]
###Compute mean
mu <- ddply(df_sigma, "type", summarise, grp.mean=mean(sigma))
p_sigma<- ggplot(df_sigma, aes(x=sigma)) + geom_vline(data=mu, aes(xintercept=grp.mean),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution sigma: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_sigma
dfs<-as.data.frame(sigma.chains)
dfs$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p_trace_sigma<-ggplot(dfs, aes(y=sigma.chains, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the sigma for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_trace_sigma
}
pdf(paste0("plots/Plot-clusters_S",S,"r",r,"Ktr",K_t,"mod_type_",type,".pdf"))
plot(p)
if(type%in%c("1","2","4")){
plot(p_alpha_1)
plot(p_alpha_2)
}
if(type%in%c("4")){
plot(p_sigma)
plot(p_trace_sigma)
}
if(type%in%c("0","1","2","3","4")){
plot(pl_weigths)
}
dev.off()
#
# N_dim<-(it-burn)
# Z<-array(dim=c(Sp,r,N_dim))
# for(j in 1:N_dim){
# K<-fit$chains$kgibbs[j,]
# Z[,,j] <- matrix(fit$chains$sgibbs[j,],Ntr-1,r)[K,]
# #sigma[,,j] <- .expandSigma(fit$chains$sigErrGibbs[j], Sp, Z = Z, fit$chains$kgibbs[j,], REDUCT = T) #sigma
# }
# Lambda_mean<-apply(Z,c(1,2),mean)
# err<-sum((Lambda_mean-Lambda)^2)/(S*q)
# fit<-fit$rmspeAll
#fit_er<-fit$rmspeAll
N_dim<-(it-burn)
sigma<-array(dim=c(Sp,Sp,N_dim))
for(j in 1:N_dim){
K<-fit$chains$kgibbs[j,]
Z <- matrix(fit$chains$sgibbs[j,],Ntr-1,r)
sigma[,,j] <- .expandSigma(fit$chains$sigErrGibbs[j], Sp, Z = Z, fit$chains$kgibbs[j,], REDUCT = T) #sigma
}
sigma_mean<-apply(sigma,c(1,2),mean)
err<-sum((sigma_mean-Sigma_true)^2)/(Sp*Sp)
rmspe<-fit$fit$rmspeAll
#fit_er<-NULL
return(list(trace=trace, chain=fit$chains$kgibbs,
idx=idx,K=fit$chains$kgibbs[it,],
alpha=alpha.DP,alpha.chains=alpha.chains,pk_chain=pk_chains,
coeff_t=Sigma_true,coeff_f=sigma,
err=err,fit=rmspe))
}
####### Just one possible test case
#sim<-simulation_fun(Sp=50, Ntr=150, rval=3,nsamples=500, Ktrue=4,it=1000,burn=200,type=2)
# plot(as.vector(sim$coeff_t),as.vector(sim$coeff_f))
# x11()
# heatmap(sim$coeff_f)
# x11()
# heatmap(sim$coeff_t)
# plot(sim$trace)
# plot(sim$idx,sim$K)
#possible parameters to add in the loop:
# - type (T) of gjam to be fitted
# - n, the number of simulated normals
# - N, the truncation level
# - S, the number of species
# - K_t, the true number of clusters
list=list()
S_vec<-c(50,100,150,200)
r_vec<-c(3,5,10,15)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list<-list.append(list,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], rval=r_vec[j],nsamples=500, Ktrue=4,it=1000,burn=100,type="GJAM")))
names(list)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
table<-data.frame()
for(i in 1:length(list)){
str<-names(list)[[i]]
tmp<-data.frame("trace"=list[[i]]$trace,"S"=rep(substr(str,regexpr("S",str)+2 , regexpr("_r",str)-1),length(list[[i]]$trace)),
"r"=rep(substr(str,regexpr("r",str)+2, regexpr("_N",str)-1),length(list[[i]]$trace)),
"N"=rep(substr(str,regexpr("N",str)+2 , regexpr("_n",str)-1),length(list[[i]]$trace)),
"n"=rep(substr(str,regexpr("n",str)+2 , regexpr("_Kt",str)-1),length(list[[i]]$trace)),
"Kt"=rep(substr(str,regexpr("Kt_",str)+3,nchar(str)) ,length(list[[i]]$trace)),
"It"=rep(length(list[[i]]$trace),length(list[[i]]$trace)),
"x"=1:length(list[[i]]$trace),
"err"=rep(list[[i]]$err,length(list[[i]]$trace)),
"fit"=rep(list[[i]]$fit,length(list[[i]]$trace)))
table<-rbind(table,tmp)
}
table_r_3<-table[which(table$r==3),]
p_3<-ggplot(data=table_r_3,aes(x=table_r_3$x,y=table_r_3$trace,color=table_r_3$S))+geom_line()+
labs(title="r=3, K_t=4")
table_r_5<-table[which(table$r==5),]
p_5<-ggplot(data=table_r_5,aes(x=table_r_5$x,y=table_r_5$trace,color=table_r_5$S))+geom_line()+
labs(title="r=5, K_t=4")
table_r_10<-table[which(table$r==10),]
p_10<-ggplot(data=table_r_10,aes(x=table_r_10$x,y=table_r_10$trace,color=table_r_10$S))+geom_line()+
labs(title="r=10, K_t=4")
table_r_15<-table[which(table$r==15),]
p_15<-ggplot(data=table_r_15,aes(x=table_r_10$x,y=table_r_15$trace,color=table_r_15$S))+geom_line()+
labs(title="r=15, K_t=4")
grid.arrange(p_3,p_5,p_10,p_15)
###########Simulation for Continous data case :small S###################################################
####Small S, N==S, n=500
list=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list<-list.append(list,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], q=20,rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="GJAM")))
names(list)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list, file = "Sim_smallS_gjam.Rda")
list0=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list0<-list.append(list0,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], q=20,rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="0")))
names(list0)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list0, file = "Sim_smallSK4_gjam0.Rda")
#
#
# list2=list()
# S_vec<-c(20,50,80,100)
# r_vec<-c(5,10,15,20)
# k<-1
# for(i in 1:length(S_vec)){
# for(j in 1:length(r_vec)){
# list2<-list.append(list2,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=150,q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="1")))
# names(list2)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
# k=k+1
# }
# }
#
#
#
# save(list2, file = "Sim_smallSK4_type1.Rda")
#
#
#
#
#
# list3=list()
# S_vec<-c(20,50,80,100)
# r_vec<-c(5,10,15,20)
# k<-1
# for(i in 1:length(S_vec)){
# for(j in 1:length(r_vec)){
# list3<-list.append(list3,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i],q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="2")))
# names(list3)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
# k=k+1
# }
# }
#
# save(list3, file = "Sim_smallSK4_type2.Rda")
#
list4=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list4<-list.append(list4,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i],q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="3")))
names(list4)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list4, file = "Sim_smallSK4_type3.Rda")
list5=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list5<-list.append(list5,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i],q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="4")))
names(list5)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list5, file = "Sim_smallSK4_type4.Rda")
##########################
plot(density(list$S_20_r_3_N_150_n_500_Kt_4_T0$trace), col="red")
lines(density(list2$S_20_r_3_N_150_n_500_Kt_4_T0$trace), col="green")
mean(list$S_20_r_3_N_150_n_500_Kt_4_T0$trace[-c(1:100)])
table_comp<-as.data.frame(matrix(NA, nrow=2*length(S_vec), ncol=1))
table_comp$S<- rep(S_vec, each=2)
table_comp$mod<- rep(c("list","list2"), 4)
table_comp$num<- rep(1:4, each=2)
for(i in (1: nrow(table_comp))){
j<-table_comp$num[i]
if(table_comp$mod[i]=="list"){ table_comp$res[i]<- mean(list[[4*(j-1)+1]]$trace[-c(1:300)])}
if(table_comp$mod[i]=="list2"){ table_comp$res[i]<- mean(list2[[4*(j-1)+1]]$trace[-c(1:300)])}
}
p <- ggplot(table_comp, aes(S,res, colour = mod))
q<- p + geom_point( size = 2) +xlab("Species")+ylab("Mean posterior") +theme_bw()
q
#########Testing
listx=list()
S_vec<-c(20)
r_vec<-c(5)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
listx<-list.append(listx,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_1"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], q=20,rval=r_vec[j],nsamples=500, Ktrue=8,it=5000,burn=2000,type="1")))
names(listx)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
pk<- apply(fit$chains$pk_g,2,mean)
#pk<-apply()
last_pk<- round(pk[Ntr-1],3)
#plot(1:(Ntr-1),pk,type='h', ylim=c(0,max(pk)),col=gray(.5),xlab=expression(italic(i)),ylab=expression(italic(p_k)) ,lwd=3)
#points(1:(Ntr-1),pk)
#mtext(paste0("Weights p_k for N=",Ntr," ,p_N=",last_pk),side=3)
df_weights <- data.frame(matrix(NA, nrow = Ntr-1, ncol =1))
df_weights$pw<-pk
df_weights$tr<-1:(Ntr-1)
#df_weights$tr<- as.factor(df_weights$tr)
# p <- ggplot(df_weights, aes(x=tr,xend=tr,y=0,yend=pw)) +geom_segment()+ geom_point(size=0.1)
# p
pl_weigths<- ggplot(df_weights, aes(x=tr, y=pw)) +
geom_segment( aes(x=tr,xend=tr,y=0,yend=pw)) +
geom_point( size=0.5, color="red", fill=alpha("blue", 0.3), alpha=0.4, shape=21, stroke=2)+ labs(title=paste0("Weights for the case: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr, " pN=",last_pk), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
pl_weigths
df_alpha <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha$alpha<- fit$chains$alpha.DP_g[-c(1:2000)]
df_alpha$type<- "posterior"
df_alpha_prior <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha_prior$alpha<- rgamma(it-burn, shape, rate)
df_alpha_prior$type<- "prior"
df_alpha<- rbind(df_alpha[-1,],df_alpha_prior[-1,])
library(plyr)
mu <- ddply(df_alpha, "type", summarise, grp.mean=mean(alpha))
p_alpha<- ggplot(df_alpha, aes(x=alpha, color=type)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution alpha: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_alpha
dariamed/gjamed documentation built on Sept. 27, 2019, 5:31 p.m.
R Package Documentation
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rm(list=ls())
setwd("~/Documents/GitHub/gjamed")
########## Simulating the data
library(MASS)
library(repmis)
library(gjam)
library(rlist)
library(MASS)
library(truncnorm)
library(coda)
library(RcppArmadillo)
library(arm)
library(NLRoot)
library(Rcpp)
library(plyr)
library(ggplot2)
Rcpp::sourceCpp('src/cppFns.cpp')
source("R/gjamHfunctions_mod.R")
source("R/simple_gjam_0.R")
source("R/simple_gjam_1.R")
source("R/simple_gjam_2.R")
source("R/simple_gjam_3.R")
source("R/simple_gjam_4.R")
simulation_fun_paper<-function(Sp, Ntr, rval,nsamples=500, Ktrue,q=20, it=1000, burn=500,type="GJAM"){
S<-Sp
n<- nsamples
r <- rval
iterations<-it
env<-runif(-50,50,n=n)
X<-cbind(1,poly(env,2)) #nxK
idx<-sample(S)
B_0<-seq(0,100,length.out=S)[idx]
B_1<-seq(0,100,length.out=S)[idx]
B_2<-seq(0,100,length.out=S)[idx]
B<-cbind(B_0,B_1,B_2) #SxK
L<-X%*%t(B) #nxS
K=sum(S/(S+(1:S)-1)) #104, his prior number of clusters when alpha=S
if(type=="GJAM"){ cat("Prior expected number of clusters : ",K,"\n")}
else{cat("Prior expected number of clusters : ",Ktrue,"\n")}
K_t= Ktrue
cat("True number of clusters : ",K_t,"\n")
A<-matrix(NA,nrow=ceiling(K_t),ncol=q)
# sig=matrix(runif(n=q*q),ncol=q)
for(i in 1:ceiling(K_t)){
A[i,]<-mvrnorm(n = 1,rep(0,q), Sigma=3*diag(q)) #Nxq short and skinny
}
idx<-sample((1:ceiling(K_t)),S,replace=T)
Lambda<-A[idx,] #Sxr tall and skinny
Sigma<-Lambda%*%t(Lambda)+0.1*diag(S) #SxS
Sigma_true<-Sigma
Y<-mvrnorm(n = n, mu=rep(0,S), Sigma=Sigma)
xdata<-as.data.frame(X[,-1])
colnames(xdata)<-c("env1","env2")
formula<-as.formula(~env1+env2)
if(type=="GJAM"){
rl <- list(r = r, N =Ntr-1)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-gjam(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
alpha.DP<-S
pk_chains<-NULL
}
if(type=="0"){
#func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
#alpha.DP<-.bisec(func,0.01,100)
alpha.DP<-S
rl <- list(r = r, N =Ntr-1,alpha.DP=alpha.DP)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam0(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
pk_chains<- fit$chains$pk_g
}
if(type=="1"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_1(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="2"){
func<-function(x) {sum(x/(x+(1:S)-1))-K_t}
alpha.DP<-.bisec(func,0.01,100)
shape=((alpha.DP)^2)/20
rate=alpha.DP/20
rl <- list(r = r, N = Ntr-1, rate=rate,shape=shape,V=1)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_2(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.DP_g
pk_chains<- fit$chains$pk_g
}
if(type=="3"){
eps=0.05
alp_sig<-as.data.frame(matrix(NA,nrow=20,ncol=3))
colnames(alp_sig)<-c("alpha","sigma","is_less_150")
alp_sig$sigma=seq(0.05,0.5,length.out = 20)
#loop to run bisecetion on a grid for sigma
for(i in 1:20){
####corrected formula : added -1
func<-function(x) {(x/alp_sig[i,"sigma"])*(prod((x+alp_sig[i,"sigma"]+c(1:S) -1)/(x+c(1:S) -1))-1) - K_t}
alp_sig[i,"alpha"]<-.bisec(func,0.01,100)
N_eps<-floor(.compute_tau_mean(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps) + 2*.compute_tau_var(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps))
ifelse(N_eps<=150,alp_sig[i,"is_less_150"]<-T,alp_sig[i,"is_less_150"]<-F)
N_eps
}
if(sum(alp_sig$is_less_150==T)==0) cat("!! no choice under N=150, need to recheck!!!")
k<-max(which(alp_sig$is_less_150==T)) #max sigma s.t. N<150
sigma_py<-alp_sig[i,"sigma"]
alpha.PY<-alp_sig[i,"alpha"]
N_eps<-floor(.compute_tau_mean(sigma_py,alpha.PY,eps) + 2*.compute_tau_var(sigma_py,alpha.PY,eps))
rl <- list(r = r, N = N_eps, sigma_py=sigma_py, alpha=alpha.PY)
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_3(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-NULL
pk_chains<- fit$chains$pk_g
alpha.DP<-alpha.PY
Ntr<-N_eps+1
}
if(type=="4"){
eps=0.05
alp_sig<-as.data.frame(matrix(NA,nrow=20,ncol=3))
colnames(alp_sig)<-c("alpha","sigma","is_less_150")
alp_sig$sigma=seq(0.05,0.4,length.out = 20)
#loop to run bisecetion on a grid for sigma
for(i in 1:20){
####corrected added -1
func<-function(x) {(x/alp_sig[i,"sigma"])*(prod((x+alp_sig[i,"sigma"]+c(1:S)-1)/(x+c(1:S) -1))-1) - K_t}
alp_sig[i,"alpha"]<-.bisec(func,0.01,100)
N_eps<-floor(.compute_tau_mean(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps) + 2*.compute_tau_var(alp_sig[i,"sigma"], alp_sig[i,"alpha"],eps))
ifelse(N_eps<=150,alp_sig[i,"is_less_150"]<-T,alp_sig[i,"is_less_150"]<-F)
N_eps
}
if(sum(alp_sig$is_less_150==T)==0) cat("!! no choice under N=150, need to recheck!!!")
k<-max(which(alp_sig$is_less_150==T)) #max sigma s.t. N<150
sigma_py<-alp_sig[i,"sigma"]
alpha.PY<-alp_sig[i,"alpha"]
#fixing hyperparameters
ro.disc=1-2* sigma_py
shape=((alpha.PY)^2)/10
rate=alpha.PY/10
# 95% quantile of alpha
alpha.max=qgamma(.95, shape=shape, rate=rate)
N_eps<-floor(.compute_tau_mean(sigma_py,alpha.max,eps) + 2*.compute_tau_var(sigma_py,alpha.max,eps))
rl <- list(r = r, N = N_eps,rate=rate,shape=shape,V1=1,ro.disc=ro.disc) #here to modify N
ml<-list(ng=it,burnin=burn,typeNames='CA',reductList=rl)
fit<-.gjam_4(formula,xdata,ydata=as.data.frame(Y),modelList = ml)
alpha.chains<-fit$chains$alpha.PY_g
sigma.chains<-fit$chains$discount.PY_g
pk_chains<- fit$chains$pk_g
Ntr<-N_eps+1
alpha.DP<-alpha.PY
}
trace<-apply(fit$chains$kgibbs,1,function(x) length(unique(x)))
df<-as.data.frame(trace)
df$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p<-ggplot(df, aes(y=trace, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the number of groups K for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
geom_hline(yintercept = Ktrue,color = "red")
plot(p)
#####Weights plot
if(type%in%c("0","1","2","3","4")){
pk<- apply(fit$chains$pk_g[-c(1:burn),],2,mean)
last_pk<- round(pk[Ntr-1],3)
df_weights <- data.frame(matrix(NA, nrow = Ntr-1, ncol =1))
df_weights$pw<-pk
df_weights$tr<-1:(Ntr-1)
pl_weigths<- ggplot(df_weights, aes(x=tr, y=pw)) +
geom_segment( aes(x=tr,xend=tr,y=0,yend=pw)) +
geom_point( size=0.5, color="red", fill=alpha("blue", 0.3), alpha=0.4, shape=21, stroke=2)+ labs(title=paste0("Weights for the case: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr, " pN=",last_pk), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
pl_weigths
}
#####Alpha plot
if(type%in%c("1","2","4")){
df_alpha <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha$alpha<- alpha.chains[-c(1:burn)]
df_alpha$type<- "posterior"
df_alpha_prior <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
#df_alpha_prior$alpha<- rgamma(it-burn, shape, rate)
alpha_seq= seq(min(alpha.chains[-c(1:burn)]),max(alpha.chains[-c(1:burn)]),length=it-burn)
df_alpha_prior$alpha <- dgamma(alpha_seq,rate,shape)
df_alpha_prior$type<- "prior"
df_alpha_all<- rbind(df_alpha[-1,],df_alpha_prior[-1,])
###Compute mean
mu <- ddply(df_alpha_all, "type", summarise, grp.mean=mean(alpha))
mu$grp.mean[which(mu$type=="prior")]=alpha.DP
p_alpha_1<- ggplot(df_alpha_all, aes(x=alpha, color=type)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution alpha: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_alpha_1
p_alpha_2<- ggplot(df_alpha, aes(x=alpha)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density(color="red")+labs(title=paste0("Posterior distribution for alpha"), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples," S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))+
scale_color_manual(name = c("Legend"), values = c("prior"="#9999FF", "posterior"= "#FF6666"), labels=c("posterior mean","prior mean"))
p_alpha_2
}
#######Sigma plot
if(type%in%c("4")){
df_sigma <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_sigma$sigma<- sigma.chains[-c(1:burn)]
###Compute mean
mu <- ddply(df_sigma, "type", summarise, grp.mean=mean(sigma))
p_sigma<- ggplot(df_sigma, aes(x=sigma)) + geom_vline(data=mu, aes(xintercept=grp.mean),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution sigma: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_sigma
dfs<-as.data.frame(sigma.chains)
dfs$iter<-1:it
#plot(apply(fit$chains$kgibbs,1,function(x) length(unique(x))))
p_trace_sigma<-ggplot(dfs, aes(y=sigma.chains, x=iter)) + geom_point() +
labs(title=paste0("Trace plot for the sigma for S=",S," r=",r," true K=",K_t," type=",type), caption=paste0("Number of iterations: ",it," burnin: ",burn,"number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_trace_sigma
}
pdf(paste0("plots/Plot-clusters_S",S,"r",r,"Ktr",K_t,"mod_type_",type,".pdf"))
plot(p)
if(type%in%c("1","2","4")){
plot(p_alpha_1)
plot(p_alpha_2)
}
if(type%in%c("4")){
plot(p_sigma)
plot(p_trace_sigma)
}
if(type%in%c("0","1","2","3","4")){
plot(pl_weigths)
}
dev.off()
#
# N_dim<-(it-burn)
# Z<-array(dim=c(Sp,r,N_dim))
# for(j in 1:N_dim){
# K<-fit$chains$kgibbs[j,]
# Z[,,j] <- matrix(fit$chains$sgibbs[j,],Ntr-1,r)[K,]
# #sigma[,,j] <- .expandSigma(fit$chains$sigErrGibbs[j], Sp, Z = Z, fit$chains$kgibbs[j,], REDUCT = T) #sigma
# }
# Lambda_mean<-apply(Z,c(1,2),mean)
# err<-sum((Lambda_mean-Lambda)^2)/(S*q)
# fit<-fit$rmspeAll
#fit_er<-fit$rmspeAll
N_dim<-(it-burn)
sigma<-array(dim=c(Sp,Sp,N_dim))
for(j in 1:N_dim){
K<-fit$chains$kgibbs[j,]
Z <- matrix(fit$chains$sgibbs[j,],Ntr-1,r)
sigma[,,j] <- .expandSigma(fit$chains$sigErrGibbs[j], Sp, Z = Z, fit$chains$kgibbs[j,], REDUCT = T) #sigma
}
sigma_mean<-apply(sigma,c(1,2),mean)
err<-sum((sigma_mean-Sigma_true)^2)/(Sp*Sp)
rmspe<-fit$fit$rmspeAll
#fit_er<-NULL
return(list(trace=trace, chain=fit$chains$kgibbs,
idx=idx,K=fit$chains$kgibbs[it,],
alpha=alpha.DP,alpha.chains=alpha.chains,pk_chain=pk_chains,
coeff_t=Sigma_true,coeff_f=sigma,
err=err,fit=rmspe))
}
####### Just one possible test case
#sim<-simulation_fun(Sp=50, Ntr=150, rval=3,nsamples=500, Ktrue=4,it=1000,burn=200,type=2)
# plot(as.vector(sim$coeff_t),as.vector(sim$coeff_f))
# x11()
# heatmap(sim$coeff_f)
# x11()
# heatmap(sim$coeff_t)
# plot(sim$trace)
# plot(sim$idx,sim$K)
#possible parameters to add in the loop:
# - type (T) of gjam to be fitted
# - n, the number of simulated normals
# - N, the truncation level
# - S, the number of species
# - K_t, the true number of clusters
list=list()
S_vec<-c(50,100,150,200)
r_vec<-c(3,5,10,15)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list<-list.append(list,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], rval=r_vec[j],nsamples=500, Ktrue=4,it=1000,burn=100,type="GJAM")))
names(list)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
table<-data.frame()
for(i in 1:length(list)){
str<-names(list)[[i]]
tmp<-data.frame("trace"=list[[i]]$trace,"S"=rep(substr(str,regexpr("S",str)+2 , regexpr("_r",str)-1),length(list[[i]]$trace)),
"r"=rep(substr(str,regexpr("r",str)+2, regexpr("_N",str)-1),length(list[[i]]$trace)),
"N"=rep(substr(str,regexpr("N",str)+2 , regexpr("_n",str)-1),length(list[[i]]$trace)),
"n"=rep(substr(str,regexpr("n",str)+2 , regexpr("_Kt",str)-1),length(list[[i]]$trace)),
"Kt"=rep(substr(str,regexpr("Kt_",str)+3,nchar(str)) ,length(list[[i]]$trace)),
"It"=rep(length(list[[i]]$trace),length(list[[i]]$trace)),
"x"=1:length(list[[i]]$trace),
"err"=rep(list[[i]]$err,length(list[[i]]$trace)),
"fit"=rep(list[[i]]$fit,length(list[[i]]$trace)))
table<-rbind(table,tmp)
}
table_r_3<-table[which(table$r==3),]
p_3<-ggplot(data=table_r_3,aes(x=table_r_3$x,y=table_r_3$trace,color=table_r_3$S))+geom_line()+
labs(title="r=3, K_t=4")
table_r_5<-table[which(table$r==5),]
p_5<-ggplot(data=table_r_5,aes(x=table_r_5$x,y=table_r_5$trace,color=table_r_5$S))+geom_line()+
labs(title="r=5, K_t=4")
table_r_10<-table[which(table$r==10),]
p_10<-ggplot(data=table_r_10,aes(x=table_r_10$x,y=table_r_10$trace,color=table_r_10$S))+geom_line()+
labs(title="r=10, K_t=4")
table_r_15<-table[which(table$r==15),]
p_15<-ggplot(data=table_r_15,aes(x=table_r_10$x,y=table_r_15$trace,color=table_r_15$S))+geom_line()+
labs(title="r=15, K_t=4")
grid.arrange(p_3,p_5,p_10,p_15)
###########Simulation for Continous data case :small S###################################################
####Small S, N==S, n=500
list=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list<-list.append(list,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], q=20,rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="GJAM")))
names(list)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list, file = "Sim_smallS_gjam.Rda")
list0=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list0<-list.append(list0,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], q=20,rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="0")))
names(list0)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list0, file = "Sim_smallSK4_gjam0.Rda")
#
#
# list2=list()
# S_vec<-c(20,50,80,100)
# r_vec<-c(5,10,15,20)
# k<-1
# for(i in 1:length(S_vec)){
# for(j in 1:length(r_vec)){
# list2<-list.append(list2,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=150,q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="1")))
# names(list2)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
# k=k+1
# }
# }
#
#
#
# save(list2, file = "Sim_smallSK4_type1.Rda")
#
#
#
#
#
# list3=list()
# S_vec<-c(20,50,80,100)
# r_vec<-c(5,10,15,20)
# k<-1
# for(i in 1:length(S_vec)){
# for(j in 1:length(r_vec)){
# list3<-list.append(list3,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i],q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="2")))
# names(list3)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
# k=k+1
# }
# }
#
# save(list3, file = "Sim_smallSK4_type2.Rda")
#
list4=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list4<-list.append(list4,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i],q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="3")))
names(list4)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list4, file = "Sim_smallSK4_type3.Rda")
list5=list()
S_vec<-c(20,50,80,100)
r_vec<-c(5,10,15,20)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
list5<-list.append(list5,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_0"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i],q=20, rval=r_vec[j],nsamples=500, Ktrue=4,it=5000,burn=2000,type="4")))
names(list5)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
save(list5, file = "Sim_smallSK4_type4.Rda")
##########################
plot(density(list$S_20_r_3_N_150_n_500_Kt_4_T0$trace), col="red")
lines(density(list2$S_20_r_3_N_150_n_500_Kt_4_T0$trace), col="green")
mean(list$S_20_r_3_N_150_n_500_Kt_4_T0$trace[-c(1:100)])
table_comp<-as.data.frame(matrix(NA, nrow=2*length(S_vec), ncol=1))
table_comp$S<- rep(S_vec, each=2)
table_comp$mod<- rep(c("list","list2"), 4)
table_comp$num<- rep(1:4, each=2)
for(i in (1: nrow(table_comp))){
j<-table_comp$num[i]
if(table_comp$mod[i]=="list"){ table_comp$res[i]<- mean(list[[4*(j-1)+1]]$trace[-c(1:300)])}
if(table_comp$mod[i]=="list2"){ table_comp$res[i]<- mean(list2[[4*(j-1)+1]]$trace[-c(1:300)])}
}
p <- ggplot(table_comp, aes(S,res, colour = mod))
q<- p + geom_point( size = 2) +xlab("Species")+ylab("Mean posterior") +theme_bw()
q
#########Testing
listx=list()
S_vec<-c(20)
r_vec<-c(5)
k<-1
for(i in 1:length(S_vec)){
for(j in 1:length(r_vec)){
listx<-list.append(listx,assign(paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T_1"),simulation_fun_paper(Sp=S_vec[i], Ntr=S_vec[i], q=20,rval=r_vec[j],nsamples=500, Ktrue=8,it=5000,burn=2000,type="1")))
names(listx)[[k]]<-paste0("S_",S_vec[i],"_r_",r_vec[j],"_N_150_n_500_Kt_4_T0")
k=k+1
}
}
pk<- apply(fit$chains$pk_g,2,mean)
#pk<-apply()
last_pk<- round(pk[Ntr-1],3)
#plot(1:(Ntr-1),pk,type='h', ylim=c(0,max(pk)),col=gray(.5),xlab=expression(italic(i)),ylab=expression(italic(p_k)) ,lwd=3)
#points(1:(Ntr-1),pk)
#mtext(paste0("Weights p_k for N=",Ntr," ,p_N=",last_pk),side=3)
df_weights <- data.frame(matrix(NA, nrow = Ntr-1, ncol =1))
df_weights$pw<-pk
df_weights$tr<-1:(Ntr-1)
#df_weights$tr<- as.factor(df_weights$tr)
# p <- ggplot(df_weights, aes(x=tr,xend=tr,y=0,yend=pw)) +geom_segment()+ geom_point(size=0.1)
# p
pl_weigths<- ggplot(df_weights, aes(x=tr, y=pw)) +
geom_segment( aes(x=tr,xend=tr,y=0,yend=pw)) +
geom_point( size=0.5, color="red", fill=alpha("blue", 0.3), alpha=0.4, shape=21, stroke=2)+ labs(title=paste0("Weights for the case: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr, " pN=",last_pk), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
pl_weigths
df_alpha <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha$alpha<- fit$chains$alpha.DP_g[-c(1:2000)]
df_alpha$type<- "posterior"
df_alpha_prior <- data.frame(matrix(NA, nrow =it-burn, ncol =1))
df_alpha_prior$alpha<- rgamma(it-burn, shape, rate)
df_alpha_prior$type<- "prior"
df_alpha<- rbind(df_alpha[-1,],df_alpha_prior[-1,])
library(plyr)
mu <- ddply(df_alpha, "type", summarise, grp.mean=mean(alpha))
p_alpha<- ggplot(df_alpha, aes(x=alpha, color=type)) + geom_vline(data=mu, aes(xintercept=grp.mean, color=type),linetype="dashed")+
geom_density()+labs(title=paste0("Distribution alpha: S=",S," ,r=",r," true gr K=",K_t," ,type=",type, " ,N=",Ntr), caption=paste0("Number of iterations: ",it," burnin: ",burn," number of samples: ",nsamples))+
theme_bw() + theme(axis.text.x = element_text(angle = 0, hjust = 1,size = 10), strip.text = element_text(size = 15),legend.position = "top", plot.title = element_text(hjust = 0.5))
p_alpha
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