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R/LDDPdensity.R
In DPpackage: Bayesian Nonparametric Modeling in R
### LDDPdensity.R
### Fit a linear dependent DP model for conditional density estimation.
###
### Copyright: Alejandro Jara, Peter Mueller and Gary Rosner, 2008-2012.
###
### Last modification: 15-07-2012.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The authors' contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
### Peter Mueller
### Department of Mathematics
### The University of Texas at Austin
### 1, University Station, C1200
### Austin, TX 78712, USA
### Voice: (512) 471-7168 URL : http://www.ma.utexas.edu/users/pmueller/
### Fax : (512) 471-9038 Email: pmueller@math.utexas.edu
###
### Gary L. Rosner
### Division of Oncology Biostatistics/Bioinformatics
### The Sidney Kimmel Comprehensive Cancer Center
### Johns Hopkins
### 550 North Broadway, Suite 1103
### Baltimore, Maryland 21205-2013
### Voice: (410) 955-4884 URL : http://www.hopkinskimmelcancercenter.org/index.cfm/cID/1686/mpage/expertdata.cfm/expID/593
### Fax : (410) 955-0859 Email: grosner@jhmi.edu
###
"LDDPdensity"<-
function(formula,zpred,prior,mcmc,state,status,ngrid=100,grid=NULL,compute.band=FALSE,type.band="PD",data=sys.frame(sys.parent()),na.action=na.fail,work.dir=NULL)
UseMethod("LDDPdensity")
"LDDPdensity.default"<-
function(formula,
zpred,
prior,
mcmc,
state,
status,
ngrid=100,
grid=NULL,
compute.band=FALSE,
type.band="PD",
data=sys.frame(sys.parent()),
na.action=na.fail,
work.dir=NULL)
{
#########################################################################################
# call parameters
#########################################################################################
cl <- match.call()
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data","na.action"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
#########################################################################################
# data structure
#########################################################################################
y <- model.response(mf,"numeric")
nrec <- length(y)
z <- model.matrix(formula)
p <- ncol(z)
#########################################################################################
# change working directory (if requested..)
#########################################################################################
if(!is.null(work.dir))
{
cat("\n Changing working directory to ",work.dir,"\n")
old.dir <- getwd() # by default work in current working directory
setwd(work.dir)
}
#########################################################################################
# prediction
#########################################################################################
npred <- nrow(zpred)
if(is.null(grid))
{
miny <- min(y)
maxy <- max(y)
sdy <- sqrt(var(y))
grid <- seq(miny-0.01*sdy,maxy+0.01*sdy,len=ngrid)
}
else
{
grid <- as.vector(grid)
ngrid <- length(grid)
}
cband <- 0
if(compute.band)
{
cband <- 1
}
tband <- 1
if(type.band!="HPD")
{
tband <- 2
}
#########################################################################################
# Prior information
#########################################################################################
if(is.null(prior$a0))
{
a0b0 <- c(-1,-1)
alpha <- prior$alpha
}
else
{
a0b0 <- c(prior$a0,prior$b0)
alpha <- 1
}
sbeta0i <- solve(prior$S0)
m0 <- prior$m0
tau1 <- prior$tau1
taus1 <- prior$taus1
taus2 <- prior$taus2
nu <- prior$nu
psiinv <- prior$psiinv
rocc <- prior$rocc
if(is.null(rocc))rocc <- 0
nroc <- prior$nroc
if(is.null(nroc))nroc <- 100
#########################################################################################
# mcmc specification
#########################################################################################
mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay,cband,tband,rocc)
nsave <- mcmc$nsave
#########################################################################################
# Starting values
#########################################################################################
ncluster <- 1
ss <- rep(1,nrec)
fit0 <- lm(y ~ z - 1)
betas <- coefficients(fit0)
e <- residuals(fit0)
sigma2s <- sum(e*e)/fit0$df.residual
betaclus <- matrix(0,nrow=nrec+100,ncol=p)
sigmaclus <- rep(0,nrec+100)
betaclus[1,] <- betas
sigmaclus[1] <- sigma2s
sb <- vcov(fit0)
mub <- betas
tau2 <- 2.01
#########################################################################################
# output
#########################################################################################
cpo <- matrix(0,nrow=nrec,ncol=2)
cdfpm <- matrix(0,nrow=npred,ncol=ngrid)
cdfpl <- matrix(0,nrow=npred,ncol=ngrid)
cdfph <- matrix(0,nrow=npred,ncol=ngrid)
denspm <- matrix(0,nrow=npred,ncol=ngrid)
denspl <- matrix(0,nrow=npred,ncol=ngrid)
densph <- matrix(0,nrow=npred,ncol=ngrid)
meanfpm <- rep(0,npred)
meanfpl <- rep(0,npred)
meanfph <- rep(0,npred)
rocpm <- matrix(0,nrow=npred,ncol=nroc)
rocpl <- matrix(0,nrow=npred,ncol=nroc)
rocph <- matrix(0,nrow=npred,ncol=nroc)
thetasave <- matrix(0,nrow=nsave,ncol=(p+(p*(p+1)/2)+3))
randsave <- matrix(0,nrow=nsave,ncol=nrec*(p+1))
aucsave <- matrix(0,nrow=nsave,ncol=npred)
#########################################################################################
# parameters depending on status
#########################################################################################
if(status==FALSE)
{
alpha <- state$alpha
ncluster <- state$ncluster
ss <- state$ss
betaclus <- state$betaclus
sigmaclus <- state$sigmaclus
tau2 <- state$tau2
mub <- state$mub
sb <- state$sb
}
#########################################################################################
# working space
#########################################################################################
cstrt <- matrix(0,nrow=nrec,ncol=nrec)
ccluster <- rep(0,nrec)
iflagp <- rep(0,p)
betam <- rep(0,p)
betawork <- rep(0,p)
prob <- rep(0,(nrec+100))
workmh1 <- rep(0,p*(p+1)/2)
workmh2 <- rep(0,p*(p+1)/2)
workv1 <- rep(0,p)
xtx <- matrix(0,nrow=p,ncol=p)
xtx2 <- matrix(0,nrow=p,ncol=p)
xty <- rep(0,p)
xty2 <- rep(0,p)
seed <- c(sample(1:29000,1),sample(1:29000,1))
fs <- rep(0,ngrid)
fm <- rep(0,npred)
worksam <- rep(0,nsave)
workcpo <- rep(0,nrec)
rocgrid <- seq(0.01,0.99,len=nroc)
rocquan <- rep(0,nroc)
rocqgrid <- matrix(0,nrow=npred,ncol=nroc)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("lddpcdensity",
nrec = as.integer(nrec),
p = as.integer(p),
y = as.double(y),
z = as.double(z),
ngrid = as.integer(ngrid),
npred = as.integer(npred),
nroc = as.integer(nroc),
grid = as.double(grid),
rocgrid = as.double(rocgrid),
zpred = as.double(zpred),
a0b0 = as.double(a0b0),
tau1 = as.double(tau1),
taus1 = as.double(taus1),
taus2 = as.double(taus2),
m0 = as.double(m0),
sbeta0i = as.double(sbeta0i),
nu = as.integer(nu),
psiinv = as.double(psiinv),
ncluster = as.integer(ncluster),
ss = as.integer(ss),
alpha = as.double(alpha),
betaclus = as.double(betaclus),
sigmaclus = as.double(sigmaclus),
mub = as.double(mub),
sb = as.double(sb),
tau2 = as.double(tau2),
cpo = as.double(cpo),
thetasave = as.double(thetasave),
randsave = as.double(randsave),
aucsave = as.double(aucsave),
cdfpm = as.double(cdfpm),
cdfpl = as.double(cdfpl),
cdfph = as.double(cdfph),
denspm = as.double(denspm),
denspl = as.double(denspl),
densph = as.double(densph),
meanfpm = as.double(meanfpm),
meanfpl = as.double(meanfpl),
meanfph = as.double(meanfph),
rocpm = as.double(rocpm),
rocpl = as.double(rocpl),
rocph = as.double(rocph),
mcmc = as.integer(mcmcvec),
nsave = as.integer(nsave),
seed = as.integer(seed),
cstrt = as.integer(cstrt),
ccluster = as.integer(ccluster),
iflagp = as.integer(iflagp),
betam = as.double(betam),
betawork = as.double(betawork),
prob = as.double(prob),
workmh1 = as.double(workmh1),
workmh2 = as.double(workmh2),
workv1 = as.double(workv1),
xtx = as.double(xtx),
xtx2 = as.double(xtx2),
xty = as.double(xty),
xty2 = as.double(xty2),
fs = as.double(fs),
fm = as.double(fm),
worksam = as.double(worksam),
workcpo = as.double(workcpo),
rocquan = as.double(rocquan),
rocqgrid = as.double(rocqgrid),
PACKAGE="DPpackage")
#########################################################################################
# save state
#########################################################################################
if(!is.null(work.dir))
{
cat("\n\n Changing working directory back to ",old.dir,"\n")
setwd(old.dir)
}
cpom <- matrix(foo$cpo,nrow=nrec,ncol=2)
cpo <- cpom[,1]
fso <- cpom[,2]
model.name <-"Bayesian Semiparametric Conditional Density Estimation using a LDDP Mixture of Normals"
state <- list( alpha=foo$alpha,
betaclus=matrix(foo$betaclus,nrow=nrec+100,ncol=p),
sigmaclus=foo$sigmaclus,
ss=foo$ss,
ncluster=foo$ncluster,
mub=foo$mub,
sb=matrix(foo$sb,nrow=p,ncol=p),
tau2=tau2)
cdfpm <- matrix(foo$cdfpm,nrow=npred,ncol=ngrid)
cdfpl <- matrix(foo$cdfpl,nrow=npred,ncol=ngrid)
cdfph <- matrix(foo$cdfph,nrow=npred,ncol=ngrid)
denspm <- matrix(foo$denspm,nrow=npred,ncol=ngrid)
denspl <- matrix(foo$denspl,nrow=npred,ncol=ngrid)
densph <- matrix(foo$densph,nrow=npred,ncol=ngrid)
meanfpm <- foo$meanfpm
meanfpl <- foo$meanfpl
meanfph <- foo$meanfph
rocpm <- matrix(foo$rocpm,nrow=npred,ncol=nroc)
rocpl <- matrix(foo$rocpl,nrow=npred,ncol=nroc)
rocph <- matrix(foo$rocph,nrow=npred,ncol=nroc)
randsave <- matrix(foo$randsave,nrow=nsave,ncol=nrec*(p+1))
thetasave <- matrix(foo$thetasave,nrow=nsave,ncol=(p+(p*(p+1)/2)+3))
aucsave <- matrix(foo$aucsave,nrow=nsave,ncol=npred)
coeffname <- dimnames(z)[[2]]
pnames1 <- NULL
for(i in 1:p)
{
pnames1 <- c(pnames1,paste("mub",coeffname[i],sep=""))
}
pnames2 <- NULL
for(i in 1:p)
{
for(j in i:p)
{
tmp <- paste("sb",coeffname[i],sep="")
tmp <- paste(tmp,coeffname[j],sep=":")
pnames2 <- c(pnames2,tmp)
}
}
pnames <- c(pnames1,pnames2,"tau2","ncluster","alpha")
colnames(thetasave) <- pnames
coeff <- apply(thetasave, 2, mean)
renames <- NULL
for(i in 1:nrec)
{
tmp <- paste(coeffname,i,sep=":")
renames <- c(renames,tmp)
tmp <- paste("sigma2",i,sep=":")
renames <- c(renames,tmp)
}
colnames(randsave) <- renames
save.state <- list(thetasave=thetasave,
randsave=randsave,
aucsave=aucsave)
z <- list( modelname=model.name,
call=cl,
cpo=cpo,
coefficients=coeff,
fso=fso,
prior=prior,
mcmc=mcmc,
nrec=foo$nrec,
p=foo$p,
z=z,
ngrid=ngrid,
npred=npred,
zpred=zpred,
grid=grid,
rocgrid=rocgrid,
cdfp.m=cdfpm,
cdfp.l=cdfpl,
cdfp.h=cdfph,
rocp.m=rocpm,
rocp.l=rocpl,
rocp.h=rocph,
densp.m=denspm,
densp.l=denspl,
densp.h=densph,
meanfp.m=meanfpm,
meanfp.l=meanfpl,
meanfp.h=meanfph,
state=state,
save.state=save.state,
work.dir=work.dir,
compute.band=compute.band)
cat("\n\n")
class(z)<-c("LDDPdensity")
z
}
###
### Tools
###
### Copyright: Alejandro Jara, 2008
### Last modification: 02-06-2008.
###
"print.LDDPdensity" <- function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Parameters:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors:",x$p,"\n")
cat("\n\n")
invisible(x)
}
"summary.LDDPdensity"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
thetasave<-object$save.state$thetasave
ans <- c(object[c("call", "modelname")])
### CPO
ans$cpo<-object$cpo
### Baseline Information
mat<-NULL
coef.p<-NULL
dimen1 <- object$p+object$p*(object$p+1)/2+1
coef.p <- object$coefficients[1:dimen1]
mat <- thetasave[,1:dimen1]
if(dimen1>0)
{
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base<-coef.table
}
### Precision parameter
dimen1<-object$p+object$p*(object$p+1)/2+1
if(is.null(object$prior$a0))
{
dimen2<-1
coef.p<-object$coefficients[(dimen1+1)]
mat<-matrix(thetasave[,(dimen1+1)],ncol=1)
}
else
{
dimen2<-2
coef.p<-object$coefficients[(dimen1+1):(dimen1+2)]
mat<-thetasave[,(dimen1+1):(dimen1+2)]
}
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec<-coef.table
ans$nrec<-object$nrec
ans$p<-object$p
class(ans) <- "summaryLDDPdensity"
return(ans)
}
"print.summaryLDDPdensity"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(as.vector(x$cpo))), digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$base)) {
cat("\nBaseline distribution:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No baseline parameters\n")
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors:",x$p,"\n")
cat("\n\n")
invisible(x)
}
"plot.LDDPdensity"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2007
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
if(is(x, "LDDPdensity"))
{
if(is.null(param))
{
coef.p <- x$coefficients
n <- length(coef.p)
pnames <- names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:length(coef.p))
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(ts(x$save.state$thetasave[,i]),main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$save.state$thetasave[,i],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
for(i in 1:x$npred)
{
if(x$compute.band)
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.h[i,],main=title1,lty=2,type='l',lwd=2,xlab="y",ylab="density")
lines(x$grid,x$densp.l[i,],lty=2,lwd=2)
lines(x$grid,x$densp.m[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.m[i,],main=title1,lty=1,type='l',lwd=2,xlab="y",ylab="density")
}
}
}
else
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if(poss==0 && param !="predictive")
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
if(param !="predictive")
{
title1 <- paste("Trace of",pnames[poss],sep=" ")
title2 <- paste("Density of",pnames[poss],sep=" ")
plot(ts(x$save.state$thetasave[,poss]),main=title1,xlab="MCMC scan",ylab=" ")
if(param=="ncluster")
{
hist(x$save.state$thetasave[,poss],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
else
{
for(i in 1:x$npred)
{
if(x$compute.band)
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.h[i,],main=title1,lty=2,type='l',lwd=2,xlab="y",ylab="density")
lines(x$grid,x$densp.l[i,],lty=2,lwd=2)
lines(x$grid,x$densp.m[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.m[i,],main=title1,lty=1,type='l',lwd=2,xlab="y",ylab="density")
}
}
}
}
}
}
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### LDDPdensity.R
### Fit a linear dependent DP model for conditional density estimation.
###
### Copyright: Alejandro Jara, Peter Mueller and Gary Rosner, 2008-2012.
###
### Last modification: 15-07-2012.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The authors' contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
### Peter Mueller
### Department of Mathematics
### The University of Texas at Austin
### 1, University Station, C1200
### Austin, TX 78712, USA
### Voice: (512) 471-7168 URL : http://www.ma.utexas.edu/users/pmueller/
### Fax : (512) 471-9038 Email: pmueller@math.utexas.edu
###
### Gary L. Rosner
### Division of Oncology Biostatistics/Bioinformatics
### The Sidney Kimmel Comprehensive Cancer Center
### Johns Hopkins
### 550 North Broadway, Suite 1103
### Baltimore, Maryland 21205-2013
### Voice: (410) 955-4884 URL : http://www.hopkinskimmelcancercenter.org/index.cfm/cID/1686/mpage/expertdata.cfm/expID/593
### Fax : (410) 955-0859 Email: grosner@jhmi.edu
###
"LDDPdensity"<-
function(formula,zpred,prior,mcmc,state,status,ngrid=100,grid=NULL,compute.band=FALSE,type.band="PD",data=sys.frame(sys.parent()),na.action=na.fail,work.dir=NULL)
UseMethod("LDDPdensity")
"LDDPdensity.default"<-
function(formula,
zpred,
prior,
mcmc,
state,
status,
ngrid=100,
grid=NULL,
compute.band=FALSE,
type.band="PD",
data=sys.frame(sys.parent()),
na.action=na.fail,
work.dir=NULL)
{
#########################################################################################
# call parameters
#########################################################################################
cl <- match.call()
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data","na.action"), names(mf), 0)
mf <- mf[c(1, m)]
mf$drop.unused.levels <- TRUE
mf[[1]] <- as.name("model.frame")
mf <- eval(mf, parent.frame())
#########################################################################################
# data structure
#########################################################################################
y <- model.response(mf,"numeric")
nrec <- length(y)
z <- model.matrix(formula)
p <- ncol(z)
#########################################################################################
# change working directory (if requested..)
#########################################################################################
if(!is.null(work.dir))
{
cat("\n Changing working directory to ",work.dir,"\n")
old.dir <- getwd() # by default work in current working directory
setwd(work.dir)
}
#########################################################################################
# prediction
#########################################################################################
npred <- nrow(zpred)
if(is.null(grid))
{
miny <- min(y)
maxy <- max(y)
sdy <- sqrt(var(y))
grid <- seq(miny-0.01*sdy,maxy+0.01*sdy,len=ngrid)
}
else
{
grid <- as.vector(grid)
ngrid <- length(grid)
}
cband <- 0
if(compute.band)
{
cband <- 1
}
tband <- 1
if(type.band!="HPD")
{
tband <- 2
}
#########################################################################################
# Prior information
#########################################################################################
if(is.null(prior$a0))
{
a0b0 <- c(-1,-1)
alpha <- prior$alpha
}
else
{
a0b0 <- c(prior$a0,prior$b0)
alpha <- 1
}
sbeta0i <- solve(prior$S0)
m0 <- prior$m0
tau1 <- prior$tau1
taus1 <- prior$taus1
taus2 <- prior$taus2
nu <- prior$nu
psiinv <- prior$psiinv
rocc <- prior$rocc
if(is.null(rocc))rocc <- 0
nroc <- prior$nroc
if(is.null(nroc))nroc <- 100
#########################################################################################
# mcmc specification
#########################################################################################
mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay,cband,tband,rocc)
nsave <- mcmc$nsave
#########################################################################################
# Starting values
#########################################################################################
ncluster <- 1
ss <- rep(1,nrec)
fit0 <- lm(y ~ z - 1)
betas <- coefficients(fit0)
e <- residuals(fit0)
sigma2s <- sum(e*e)/fit0$df.residual
betaclus <- matrix(0,nrow=nrec+100,ncol=p)
sigmaclus <- rep(0,nrec+100)
betaclus[1,] <- betas
sigmaclus[1] <- sigma2s
sb <- vcov(fit0)
mub <- betas
tau2 <- 2.01
#########################################################################################
# output
#########################################################################################
cpo <- matrix(0,nrow=nrec,ncol=2)
cdfpm <- matrix(0,nrow=npred,ncol=ngrid)
cdfpl <- matrix(0,nrow=npred,ncol=ngrid)
cdfph <- matrix(0,nrow=npred,ncol=ngrid)
denspm <- matrix(0,nrow=npred,ncol=ngrid)
denspl <- matrix(0,nrow=npred,ncol=ngrid)
densph <- matrix(0,nrow=npred,ncol=ngrid)
meanfpm <- rep(0,npred)
meanfpl <- rep(0,npred)
meanfph <- rep(0,npred)
rocpm <- matrix(0,nrow=npred,ncol=nroc)
rocpl <- matrix(0,nrow=npred,ncol=nroc)
rocph <- matrix(0,nrow=npred,ncol=nroc)
thetasave <- matrix(0,nrow=nsave,ncol=(p+(p*(p+1)/2)+3))
randsave <- matrix(0,nrow=nsave,ncol=nrec*(p+1))
aucsave <- matrix(0,nrow=nsave,ncol=npred)
#########################################################################################
# parameters depending on status
#########################################################################################
if(status==FALSE)
{
alpha <- state$alpha
ncluster <- state$ncluster
ss <- state$ss
betaclus <- state$betaclus
sigmaclus <- state$sigmaclus
tau2 <- state$tau2
mub <- state$mub
sb <- state$sb
}
#########################################################################################
# working space
#########################################################################################
cstrt <- matrix(0,nrow=nrec,ncol=nrec)
ccluster <- rep(0,nrec)
iflagp <- rep(0,p)
betam <- rep(0,p)
betawork <- rep(0,p)
prob <- rep(0,(nrec+100))
workmh1 <- rep(0,p*(p+1)/2)
workmh2 <- rep(0,p*(p+1)/2)
workv1 <- rep(0,p)
xtx <- matrix(0,nrow=p,ncol=p)
xtx2 <- matrix(0,nrow=p,ncol=p)
xty <- rep(0,p)
xty2 <- rep(0,p)
seed <- c(sample(1:29000,1),sample(1:29000,1))
fs <- rep(0,ngrid)
fm <- rep(0,npred)
worksam <- rep(0,nsave)
workcpo <- rep(0,nrec)
rocgrid <- seq(0.01,0.99,len=nroc)
rocquan <- rep(0,nroc)
rocqgrid <- matrix(0,nrow=npred,ncol=nroc)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("lddpcdensity",
nrec = as.integer(nrec),
p = as.integer(p),
y = as.double(y),
z = as.double(z),
ngrid = as.integer(ngrid),
npred = as.integer(npred),
nroc = as.integer(nroc),
grid = as.double(grid),
rocgrid = as.double(rocgrid),
zpred = as.double(zpred),
a0b0 = as.double(a0b0),
tau1 = as.double(tau1),
taus1 = as.double(taus1),
taus2 = as.double(taus2),
m0 = as.double(m0),
sbeta0i = as.double(sbeta0i),
nu = as.integer(nu),
psiinv = as.double(psiinv),
ncluster = as.integer(ncluster),
ss = as.integer(ss),
alpha = as.double(alpha),
betaclus = as.double(betaclus),
sigmaclus = as.double(sigmaclus),
mub = as.double(mub),
sb = as.double(sb),
tau2 = as.double(tau2),
cpo = as.double(cpo),
thetasave = as.double(thetasave),
randsave = as.double(randsave),
aucsave = as.double(aucsave),
cdfpm = as.double(cdfpm),
cdfpl = as.double(cdfpl),
cdfph = as.double(cdfph),
denspm = as.double(denspm),
denspl = as.double(denspl),
densph = as.double(densph),
meanfpm = as.double(meanfpm),
meanfpl = as.double(meanfpl),
meanfph = as.double(meanfph),
rocpm = as.double(rocpm),
rocpl = as.double(rocpl),
rocph = as.double(rocph),
mcmc = as.integer(mcmcvec),
nsave = as.integer(nsave),
seed = as.integer(seed),
cstrt = as.integer(cstrt),
ccluster = as.integer(ccluster),
iflagp = as.integer(iflagp),
betam = as.double(betam),
betawork = as.double(betawork),
prob = as.double(prob),
workmh1 = as.double(workmh1),
workmh2 = as.double(workmh2),
workv1 = as.double(workv1),
xtx = as.double(xtx),
xtx2 = as.double(xtx2),
xty = as.double(xty),
xty2 = as.double(xty2),
fs = as.double(fs),
fm = as.double(fm),
worksam = as.double(worksam),
workcpo = as.double(workcpo),
rocquan = as.double(rocquan),
rocqgrid = as.double(rocqgrid),
PACKAGE="DPpackage")
#########################################################################################
# save state
#########################################################################################
if(!is.null(work.dir))
{
cat("\n\n Changing working directory back to ",old.dir,"\n")
setwd(old.dir)
}
cpom <- matrix(foo$cpo,nrow=nrec,ncol=2)
cpo <- cpom[,1]
fso <- cpom[,2]
model.name <-"Bayesian Semiparametric Conditional Density Estimation using a LDDP Mixture of Normals"
state <- list( alpha=foo$alpha,
betaclus=matrix(foo$betaclus,nrow=nrec+100,ncol=p),
sigmaclus=foo$sigmaclus,
ss=foo$ss,
ncluster=foo$ncluster,
mub=foo$mub,
sb=matrix(foo$sb,nrow=p,ncol=p),
tau2=tau2)
cdfpm <- matrix(foo$cdfpm,nrow=npred,ncol=ngrid)
cdfpl <- matrix(foo$cdfpl,nrow=npred,ncol=ngrid)
cdfph <- matrix(foo$cdfph,nrow=npred,ncol=ngrid)
denspm <- matrix(foo$denspm,nrow=npred,ncol=ngrid)
denspl <- matrix(foo$denspl,nrow=npred,ncol=ngrid)
densph <- matrix(foo$densph,nrow=npred,ncol=ngrid)
meanfpm <- foo$meanfpm
meanfpl <- foo$meanfpl
meanfph <- foo$meanfph
rocpm <- matrix(foo$rocpm,nrow=npred,ncol=nroc)
rocpl <- matrix(foo$rocpl,nrow=npred,ncol=nroc)
rocph <- matrix(foo$rocph,nrow=npred,ncol=nroc)
randsave <- matrix(foo$randsave,nrow=nsave,ncol=nrec*(p+1))
thetasave <- matrix(foo$thetasave,nrow=nsave,ncol=(p+(p*(p+1)/2)+3))
aucsave <- matrix(foo$aucsave,nrow=nsave,ncol=npred)
coeffname <- dimnames(z)[[2]]
pnames1 <- NULL
for(i in 1:p)
{
pnames1 <- c(pnames1,paste("mub",coeffname[i],sep=""))
}
pnames2 <- NULL
for(i in 1:p)
{
for(j in i:p)
{
tmp <- paste("sb",coeffname[i],sep="")
tmp <- paste(tmp,coeffname[j],sep=":")
pnames2 <- c(pnames2,tmp)
}
}
pnames <- c(pnames1,pnames2,"tau2","ncluster","alpha")
colnames(thetasave) <- pnames
coeff <- apply(thetasave, 2, mean)
renames <- NULL
for(i in 1:nrec)
{
tmp <- paste(coeffname,i,sep=":")
renames <- c(renames,tmp)
tmp <- paste("sigma2",i,sep=":")
renames <- c(renames,tmp)
}
colnames(randsave) <- renames
save.state <- list(thetasave=thetasave,
randsave=randsave,
aucsave=aucsave)
z <- list( modelname=model.name,
call=cl,
cpo=cpo,
coefficients=coeff,
fso=fso,
prior=prior,
mcmc=mcmc,
nrec=foo$nrec,
p=foo$p,
z=z,
ngrid=ngrid,
npred=npred,
zpred=zpred,
grid=grid,
rocgrid=rocgrid,
cdfp.m=cdfpm,
cdfp.l=cdfpl,
cdfp.h=cdfph,
rocp.m=rocpm,
rocp.l=rocpl,
rocp.h=rocph,
densp.m=denspm,
densp.l=denspl,
densp.h=densph,
meanfp.m=meanfpm,
meanfp.l=meanfpl,
meanfp.h=meanfph,
state=state,
save.state=save.state,
work.dir=work.dir,
compute.band=compute.band)
cat("\n\n")
class(z)<-c("LDDPdensity")
z
}
###
### Tools
###
### Copyright: Alejandro Jara, 2008
### Last modification: 02-06-2008.
###
"print.LDDPdensity" <- function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Parameters:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors:",x$p,"\n")
cat("\n\n")
invisible(x)
}
"summary.LDDPdensity"<-function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
thetasave<-object$save.state$thetasave
ans <- c(object[c("call", "modelname")])
### CPO
ans$cpo<-object$cpo
### Baseline Information
mat<-NULL
coef.p<-NULL
dimen1 <- object$p+object$p*(object$p+1)/2+1
coef.p <- object$coefficients[1:dimen1]
mat <- thetasave[,1:dimen1]
if(dimen1>0)
{
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base<-coef.table
}
### Precision parameter
dimen1<-object$p+object$p*(object$p+1)/2+1
if(is.null(object$prior$a0))
{
dimen2<-1
coef.p<-object$coefficients[(dimen1+1)]
mat<-matrix(thetasave[,(dimen1+1)],ncol=1)
}
else
{
dimen2<-2
coef.p<-object$coefficients[(dimen1+1):(dimen1+2)]
mat<-thetasave[,(dimen1+1):(dimen1+2)]
}
coef.m <-apply(mat, 2, median)
coef.sd<-apply(mat, 2, sd)
coef.se<-apply(mat, 2, stde)
if(hpd){
limm<-apply(mat, 2, hpdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
else
{
limm<-apply(mat, 2, pdf)
coef.l<-limm[1,]
coef.u<-limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec<-coef.table
ans$nrec<-object$nrec
ans$p<-object$p
class(ans) <- "summaryLDDPdensity"
return(ans)
}
"print.summaryLDDPdensity"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(as.vector(x$cpo))), digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$base)) {
cat("\nBaseline distribution:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
}
else cat("No baseline parameters\n")
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors:",x$p,"\n")
cat("\n\n")
invisible(x)
}
"plot.LDDPdensity"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2007
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
if(is(x, "LDDPdensity"))
{
if(is.null(param))
{
coef.p <- x$coefficients
n <- length(coef.p)
pnames <- names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:length(coef.p))
{
title1<-paste("Trace of",pnames[i],sep=" ")
title2<-paste("Density of",pnames[i],sep=" ")
plot(ts(x$save.state$thetasave[,i]),main=title1,xlab="MCMC scan",ylab=" ")
if(pnames[i]=="ncluster")
{
hist(x$save.state$thetasave[,i],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
for(i in 1:x$npred)
{
if(x$compute.band)
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.h[i,],main=title1,lty=2,type='l',lwd=2,xlab="y",ylab="density")
lines(x$grid,x$densp.l[i,],lty=2,lwd=2)
lines(x$grid,x$densp.m[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.m[i,],main=title1,lty=1,type='l',lwd=2,xlab="y",ylab="density")
}
}
}
else
{
coef.p<-x$coefficients
n<-length(coef.p)
pnames<-names(coef.p)
poss<-0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if(poss==0 && param !="predictive")
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
if(param !="predictive")
{
title1 <- paste("Trace of",pnames[poss],sep=" ")
title2 <- paste("Density of",pnames[poss],sep=" ")
plot(ts(x$save.state$thetasave[,poss]),main=title1,xlab="MCMC scan",ylab=" ")
if(param=="ncluster")
{
hist(x$save.state$thetasave[,poss],main=title2,xlab="values", ylab="probability",probability=TRUE)
}
else
{
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
}
else
{
for(i in 1:x$npred)
{
if(x$compute.band)
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.h[i,],main=title1,lty=2,type='l',lwd=2,xlab="y",ylab="density")
lines(x$grid,x$densp.l[i,],lty=2,lwd=2)
lines(x$grid,x$densp.m[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Density Prediction #",i,sep=" ")
plot(x$grid,x$densp.m[i,],main=title1,lty=1,type='l',lwd=2,xlab="y",ylab="density")
}
}
}
}
}
}
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