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#' Time-uncertain polynomial regression
#'
#' \code{tupolyn} performs estimation of parameters of N-th order polynomial regression of time-uncertain time series.
#'
#' @param y A vector of observations.
#' @param ti.mu A vector of estimates of timing of observations.
#' @param ti.sd A vector of standard deviations of timing.
#' @param polyorder Order of the polynomial regression.
#' @param n.sim A number of simulations.
#' @param CV TRUE/FALSE cross-validation indicator.
#' @param ... optional arguments: \cr
#' - n.chains: number of MCMC chains, the default number of chains is set to 2.\cr
#' - Thin: thinning factor, the default values is set to 4.\cr
#' - n.cores: number of cores used in cross-validation. No value or 'MAX' applies all the available cores in computation.\cr
#'
#' @examples
#' # Note: Most of models included in tuts package are computationally intensive. In the example
#' # below I set parameters to meet CRAN's testing requirement of maximum 5 sec per example.
#' # A more practical example would contain N=50 in the first line of the code and n.sim=10000.
#'
#' #1. Import or simulate the data (a simulation is chosen for illustrative purposes):
#' DATA=simtuts(N=10,Harmonics=c(4,0,0), sin.ampl=c(10,0, 0), cos.ampl=c(0,0,0),
#' trend=0,y.sd=2, ti.sd=0.2)
#' y=DATA$observed$y.obs
#' ti.mu=DATA$observed$ti.obs.tnorm
#' ti.sd= rep(0.2, length(ti.mu))
#'
#' #2. Fit the model:
#' polyorder=2
#' n.sim=1000
#' PN=tupolyn(y=y,ti.mu=ti.mu,ti.sd=ti.sd,polyorder=polyorder,n.sim=n.sim,CV=TRUE,n.cores=2)
#'
#' #3. Generate summary results (optional parameters are listed in brackets):
#' summary(PN) # Summary results (burn, CI).
#'
#' #4. Generate plots and diagnostics of the model (optional parameters are listed in brackets):
#' plot(PN,type='predTUTS',CI=0.95) # One step out of salmple predictions (CI, burn).
#' plot(PN,type='cv',burn=0.3) # 5 fold cross-validation (CI, burn).
#' plot(PN,type='GR',CI=0.95) # Gelman-Rubin diagnostic (CI).
#' plot(PN,type='mcmc') # MCMC diagnostics.
#' plot(PN,type='volatility') # Volatility realizaitons.
#' @export
tupolyn=function(y,ti.mu,ti.sd, n.sim, polyorder,CV=FALSE, ...){
# Data checking and basic operations ---------------------------------------------------------------------
if (length(y)*4!=length(ti.mu)*2+length(ti.sd)*2){stop("Vectors y, ti.mu and ti.sd should be of equal lengths.")}
if(is.numeric(y)==FALSE ){stop("y must be a vector of rational numbers.")}
if(is.numeric(ti.mu)==FALSE | sum((ti.mu)<0)>0 ){
stop("ti.mu must be a vector of positive rational numbers.")}
if(is.numeric(ti.sd)==FALSE | sum((ti.sd)<0)>0 ){
stop("ti.sd must be a vector of positive rational numbers.")}
if (sum(is.na(c(y,ti.mu,ti.sd)))>0){stop("Remove NAs.")}
if (n.sim!=abs(round(n.sim))){stop("n.sim must be a positive integer.")}
if (polyorder!=abs(round(polyorder))){stop("polyorder must be a positive integer.")}
if (!is.logical(CV)){stop("CV must be a logical value.")}
# Optional parameters
dots = list(...)
if(missing(...)){Thin=4; n.chains=2; polyorder=3 ; n.cores='MAX'}
if(!is.numeric(dots$Thin)){
Thin=4
} else{
Thin=round(abs(dots$Thin))
}
if(!is.numeric(dots$n.cores)){
n.cores='MAX'
} else{
n.cores=dots$n.cores
}
if(!is.numeric(dots$n.chains)){
n.chains=2
} else{
n.chains=round(abs(dots$n.chains))
}
y=y[order(ti.mu,decreasing = FALSE)]; ti.sd=ti.sd[order(ti.mu,decreasing = FALSE)]
ti.mu=ti.mu[order(ti.mu,decreasing = FALSE)]
# JAGS model --------------------------------------------------------------------------------------------
modelstring= "model {
for(i in 1:n) {
y[i]~dnorm(mu[i], precision )
mu[i]<- const+inprod(ti.sim.MX[i,],alpha)
}
for (i in 1:n) {
ti.sim.tmp[i]~dnorm(ti.mu[i],1/ti.sd[i])
}
ti.sim<-sort(ti.sim.tmp)
for (i in 1:n) {
for(j in 1:(polyorder)){
ti.sim.MX[i,j]<- ti.sim[i]^j
}
}
for(i in 1:polyorder){
alpha[i]~dnorm(0,0.01)
}
const~dnorm(0,0.01)
precision ~dgamma(0.01,0.01)
}"
# JAGS data ---------------------------------------------------------------------------------------------
data=list(y=y, ti.mu=ti.mu,ti.sd=ti.sd, n=length(ti.mu),polyorder=polyorder)
inits=parallel.seeds("base::BaseRNG", n.chains)
for(k in (1:n.chains)){
inits[[k]]$ti.sim.tmp=ti.mu
}
model=jags.model(textConnection(modelstring), data=data, inits=inits,n.chains=n.chains)
update(model,n.iter=n.sim,thin=Thin)
output=coda.samples(model=model, variable.names=c("const","alpha","precision","ti.sim")
,n.iter=n.sim, thin=Thin,n.chains=n.chains)
DIC = dic.samples(model=model,n.iter=n.sim,thin=Thin)
Sim.Objects=JAGS.objects(output)
Sim.Objects$JAGS=output
Sim.Objects$DIC=DIC
# Cross Validation -------------------------------------------------------------------------------------------------
if(CV==TRUE){
print(noquote('Cross-validation of the model....'))
folds = 5
fold= sample(rep(1:folds,length=length(y)))
for (i in 2:length(fold)){
if (fold[i-1]==fold[i]){
Sample=c(1:5)
Sample=Sample[Sample !=fold[i]]
fold[i]=sample(Sample,size=1)
}
}
TI.SIM=apply(Sim.Objects$ti.sim,2,'quantile',0.5)
Cores=min(c(parallel::detectCores()-1,folds))
if(n.cores=="MAX"){
Cores=Cores
} else{
if(Cores>n.cores) {
Cores=n.cores} else {
Cores=Cores
}
}
cl = parallel::makeCluster(Cores)
doParallel::registerDoParallel(cl)
BSFCV=function(i,y,ti.mu,ti.sd,modelstring,n.sim,fold){
Y=y; Y[fold==i]=NA;
data=list(y=Y, ti.mu=TI.SIM,ti.sd=ti.sd, n=length(y),polyorder=polyorder)
model=jags.model(textConnection(modelstring), data=data,n.chains=1)
update(model,n.iter=n.sim,thin=Thin)
output=coda.samples(model=model,variable.names=c("y"), n.iter=n.sim, thin=Thin)
return(output)
}
CVRES=foreach(i=1:folds,.export=c('jags.model','coda.samples')) %dopar%
BSFCV(i,fold=fold,y=y,ti.mu=TI.SIM,ti.sd=ti.sd, modelstring=modelstring, n.sim=n.sim)
stopCluster(cl)
if(is.null(dim(JAGS.objects(CVRES[[1]])$y[,fold==(1)]))){
DIM1=length(JAGS.objects(CVRES[[1]])$y[,fold==(1)])
}else{
DIM1= dim(JAGS.objects(CVRES[[1]])$y[,fold==(1)])[1]
}
pred_y = array(NA, dim=c(DIM1,length(ti.mu)))
colnames(pred_y)= paste("y[",1:length(y),"]",sep="")
for (i in 1:folds){
pred_y[,fold==(i)] = JAGS.objects(CVRES[[i]])$y[,fold==(i)]
}
Sim.Objects$CVpred=pred_y
}
Sim.Objects$y=y
Sim.Objects$ti.mu=ti.mu
Sim.Objects$polyorder=polyorder
class(Sim.Objects)='tuts_polyn'
return(Sim.Objects)
}
#' Prints summary tables of tuts_polyn objects
#'
#' \code{summary.tuts_polyn} prints summary tables of tuts_polyn objects.
#'
#' @param object A tuts_polyn object.
#'
#' @param ... A list of optional parameters: \cr
#' - burn: burn-in parameter ranging from 0 to 0.7, the default value is 0.\cr
#' - CI: confidence interval, the default value is set to 0.99.
#' @examples
#' # Note: Most of models included in tuts package are computationally intensive. In the example
#' # below I set parameters to meet CRAN’s testing requirement of maximum 5 sec per example.
#' # A more practical example would contain N=50 in the first line of the code and n.sim=10000.
#'
#' #1. Import or simulate the data (simulation is chosen for illustrative purposes):
#' DATA=simtuts(N=10,Harmonics=c(4,0,0), sin.ampl=c(10,0, 0), cos.ampl=c(0,0,0),
#' trend=0,y.sd=2, ti.sd=0.2)
#' y=DATA$observed$y.obs
#' ti.mu=DATA$observed$ti.obs.tnorm
#' ti.sd= rep(0.2, length(ti.mu))
#'
#' #2. Fit the model:
#' polyorder=2
#' n.sim=1000
#' PN=tupolyn(y=y,ti.mu=ti.mu,ti.sd=ti.sd,polyorder=polyorder,n.sim=n.sim, CV=FALSE)
#'
#' #3. Generate summary results (optional parameters are listed in brackets):
#' summary(PN) # Summary results (burn, CI).
#' @export
summary.tuts_polyn = function(object, ...) {
dots = list(...)
if(missing(...)){burn=0; CI=0.99}
if(!is.numeric(dots$CI)){
CI=0.99
} else{
if(dots$CI<=0.5 | dots$CI> 1){stop('Credible interval is bounded between 0.5 and 1')}
CI=dots$CI
}
if(!is.numeric(dots$burn)){
burn=0
} else{
burn=dots$burn
if(burn<0 | burn>0.7){stop('burn is bounded between 0 and 0.7')
}
}
n.sim=dim(object$const)[1]
if (burn==0){BURN=1}else{BURN=floor(burn*n.sim)}
# ----------------------------------------------------------------------------
cat('\n')
cat('Regression Parameters and estimates of timing:\n')
cat('----------------------------------------------\n')
const=object$const[BURN:length(object$const)]
const.lwr=quantile(const,(1-CI)/2)
const.med=quantile(const,0.5)
const.upr=quantile(const,1-(1-CI)/2)
constName="const"
lwr=med=upr=NAMES=NA
polyorder=object$polyorder
alpha=object$alpha[BURN:dim(object$alpha)[1],]
alpha.lwr=apply(alpha,2,'quantile',(1-CI)/2)
alpha.med=apply(alpha,2,'quantile',0.5)
alpha.upr=apply(alpha,2,'quantile', 1-(1-CI)/2)
alphaNames=colnames(alpha)
precision=object$precision[BURN:length(object$precision)]
precision.lwr=quantile(precision,(1-CI)/2)
precision.med=quantile(precision,0.5)
precision.upr=quantile(precision,1-(1-CI)/2)
precisionName="precision"
ti=object$ti.sim[BURN:dim(object$ti.sim)[1],]
ti.lwr=apply(ti,2,'quantile',(1-CI)/2)
ti.med=apply(ti,2,'quantile',0.5)
ti.upr=apply(ti,2,'quantile',1-(1-CI)/2)
tiNames=names(ti.med)
LWR=c(const.lwr,alpha.lwr,precision.lwr,ti.lwr)
MED=c(const.med,alpha.med,precision.med,ti.med)
UPR=c(const.upr,alpha.upr,precision.upr,ti.upr)
TABLE2=data.frame(LWR,MED,UPR)
row.names(TABLE2)=c(constName,alphaNames,precisionName,tiNames)
colnames(TABLE2)=c(paste(round((1-CI)/2,3)*100,"%",sep=""),'50%',paste(round(1-(1-CI)/2,3)*100,"%",sep=""))
print(TABLE2)
# ----------------------------------------------------------------------------
cat('\n')
cat('Deviance information criterion:\n')
cat('-------------------------------\n')
print(object$DIC)
cat('-------------------------------\n')
}
####################################################################################################
#' Plots and visual diagnostics of tuts_polyn objects
#'
#' \code{plot.tuts_polyn} generates plots and visual diagnostics of tuts_polyn objects.
#'
#' @param x A tuts_polyn object.
#' @param type plot type with the following options:\cr
#' - 'predTUTS' plots one step predictions of the model. \cr
#' - 'GR' plots Gelman-Rubin diagnostics. \cr
#' - 'cv' plots 5-fold cross validation. \cr
#' - 'mcmc' plots diagnostics of MCMC/JAGS objects. \cr
#' - 'volatility' plots volatility realizations. \cr
#' @param ... list of optional parameters:\cr
#' - burn: burn-in parameter ranging from 0 to 0.7 with default value set to 0. \cr
#' - CI: credible interval ranging from 0.3 to 1 with default value set to 0.95.
#' @examples
#' # Note: Most of models included in tuts package are computationally intensive. In the example
#' # below I set parameters to meet CRAN’s testing requirement of maximum 5 sec per example.
#' # A more practical example would contain N=50 in the first line of the code and n.sim=10000.
#'
#' #1. Import or simulate the data (simulation is chosen for illustrative purposes):
#' DATA=simtuts(N=10,Harmonics=c(4,0,0), sin.ampl=c(10,0, 0), cos.ampl=c(0,0,0),
#' trend=0,y.sd=2, ti.sd=0.2)
#' y=DATA$observed$y.obs
#' ti.mu=DATA$observed$ti.obs.tnorm
#' ti.sd= rep(0.2, length(ti.mu))
#'
#' #2. Fit the model:
#' polyorder=2
#' n.sim=1000
#' PN=tupolyn(y=y,ti.mu=ti.mu,ti.sd=ti.sd,polyorder=polyorder,n.sim=n.sim,CV=TRUE,n.cores=2)
#'
#' #3. Generate plots and diagnostics of the model (optional parameters are listed in brackets):
#' plot(PN,type='predTUTS',CI=0.95) # One step out of salmple predictions (CI, burn).
#' plot(PN,type='cv',burn=0.3) # 5 fold cross-validation (CI, burn).
#' plot(PN,type='GR',CI=0.95) # Gelman-Rubin diagnostic (CI).
#' plot(PN,type='mcmc') # MCMC diagnostics.
#' plot(PN,type='volatility') # Volatility realizaitons.
#' @export
plot.tuts_polyn = function(x, type, ...) {
if (sum(type==c('predTUTS','GR','cv','mcmc','volatility'))==0){
stop('type should be set as either predTUTS, GR, cv, mcmc or volatility')
}
dots = list(...)
if(missing(...)){burn=0; CI=0.99}
if(!is.numeric(dots$CI)){
CI=0.99
} else{
if(dots$CI<=0.5 | dots$CI> 1){stop('Credible interval is bounded between 0.5 and 1')}
CI=dots$CI
}
if(!is.numeric(dots$burn)){
burn=0
} else{
burn=dots$burn
if(burn<0 | burn>0.7){stop('burn is bounded between 0 and 0.7')
}
}
n.sim=dim(x$const)[1]
if (burn==0){BURN=1}else{BURN=floor(burn*n.sim)}
graphics::par(mfrow=c(1,1))
# ----------------------------------------------------------------------------
if(type=='cv') {
if (sum(names(x)=="CVpred")<1){stop("Object does not contain cross validation")}
PRED=apply(x$CVpred[BURN:dim(x$CVpred)[1],],2,'quantile',0.5)
MAIN="Cross-Validation: One step out of sample predictions"
graphics::plot(x=x$y,y=PRED,xlab="Actual",ylab="Predicted", main=MAIN, pch=18)
graphics::abline(0,1,col='blue')
RSQ=cor(x$y,PRED)^2* 100
LAB = bquote(italic(R)^2 == .(paste(format(RSQ, digits = 0),"%",sep="")))
graphics::text(x=(min(x$y)+0.9*(max(x$y)-min(x$y))),y=(min(PRED)+0.1*(max(PRED)-min(PRED))),LAB)
}
# ----------------------------------------------------------------------------
if(type=='predTUTS') {
if (sum(names(x)=="CVpred")<1){stop("Object does not contain cross validation")}
PRED.LWR=apply(x$CVpred[BURN:dim(x$CVpred)[1],],2,'quantile',(1-CI)/2)
PRED.MED=apply(x$CVpred[BURN:dim(x$CVpred)[1],],2,'quantile',0.5)
PRED.UPR=apply(x$CVpred[BURN:dim(x$CVpred)[1],],2,'quantile',1-(1-CI)/2)
ti.sim=apply(x$ti.sim[BURN:dim(x$ti.sim)[1],],2,'quantile',0.5)
MAIN=paste("One step out of sample predictions at CI= ", CI*100,"%",sep='')
graphics::plot(y=x$y,x=x$ti.mu,type='l',main=MAIN,ylab="Observations",xlab='time',lwd=2,
ylim=c(min(x$CVpred),1.2*max(x$CVpred)), xlim=c(min(x$ti.mu,ti.sim),max(x$ti.mu,ti.sim)))
graphics::lines(y=PRED.LWR,x=ti.sim,type='l',col='blue',lwd=1,lty=2)
graphics::lines(y=PRED.MED,x=ti.sim,type='l',col='blue',lwd=1,lty=1)
graphics::lines(y=PRED.UPR,x=ti.sim,type='l',col='blue',lwd=1,lty=2)
graphics::legend("topright",legend = c("Observed","Upper CI","Median","Lower CI"),
col=c("black","blue","blue","blue"),lwd=c(2,1,1,1),lty=c(1,2,1,2))
}
# ----------------------------------------------------------------------------
if(type=='GR') {
options(warn=-1)
if(burn>0){ABURNIN=TRUE} else{ABURNIN=FALSE}
GELMAN=gelman.diag(x$JAGS,confidence =CI,autoburnin=ABURNIN)
TIOBJ=rownames(GELMAN$psrf)%in% c(paste("ti.sim[",1:length(x$ti.mu),"]",sep=""))
REG=GELMAN$psrf[!TIOBJ,]
labels =rownames(REG)
TI=GELMAN$psrf[TIOBJ,]
graphics::par(mfrow=c(2,1))
graphics::plot(REG[,1],ylim=c(0,max(REG)+1.5),xaxt='n',ylab="Factor",
xlab='Parameters of polynomial regression and precision of the model',
main=paste("Gelman-Rubin diagnostics: Potential scale reduction factors \n with the upper confidence bounds at ",
CI*100,"%",sep="")
)
graphics::text(seq(1,length(labels),by=1), graphics::par("usr")[3]-max(REG)*0.2, srt = 00, adj= 0.5, xpd = TRUE, labels =labels, cex=0.65)
graphics::arrows(x0=1:dim(REG)[1],y0=REG[,1],x1=1:dim(REG)[1],y1=REG[,2],code=3,length=0.04,angle=90,col='darkgray')
graphics::abline(h=1);
graphics::legend("topright", c("Estimate"),lty=c(NA),pch=c(1),lwd=c(1), col=c("black"),border="white")
graphics::plot(TI[,1],ylim=c(0,(max(TI)*1.8)),ylab="Factor", xlab='Simulated timings of observations')
graphics::arrows(x0=1:dim(TI)[1],y0=TI[,1],x1=1:dim(TI)[1],y1=TI[,2],code=3,length=0.04,angle=90,col='darkgray')
graphics::abline(h=1);
graphics::legend("topright", c("Estimate"),lty=c(NA),pch=c(1),lwd=c(1), col=c("black"),border="white")
graphics::par(mfrow=c(1,1))
options(warn=0)
}
if(type=='volatility') {
graphics::plot(sqrt(sqrt(1/sqrt(x$precision[BURN:dim(x$precision)[1],]))),type='l', xlab='Sim ID',ylab='Std Deviation',main='Standard Deviaiton')
}
if(type=='mcmc') {
options(warn=-1)
mcmcplot(x$JAGS)
options(warn=0)
}
}
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