Spline ML example

library(circularEV)
plotly_installed <- requireNamespace("plotly", quietly = TRUE)
if(!plotly_installed) {
  message("Skipping plotly-based figures because the 'plotly' package is not installed.")
}

Reading Data

data(HsSP)
data(drc)
timeRange <- 54.5

idx <- order(drc)
drc <- drc[idx]
Data <- HsSP[idx]
set.seed(1234)
Data <- Data + runif(length(Data), -1e-4, 1e-4)
PlotData(Data=Data, drc=drc, thr=NULL, pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)

if(plotly_installed) {
  PolarPlotData(Data=Data, drc=drc, thr=NULL, pointSize=4, fontSize=14,
                thrWidth=4, ylim=c(0,max(Data)) )
} else {
  message("plotly not installed: skipping PolarPlotData output")
}

Threshold selection

Grid values at which the estimation is performed:

thetaVec <- 1:360
thrResultML <- ThrSelection(Data=Data, drc=drc, h=60, b=0.35, thetaGrid=thetaVec,
                         EVIestimator="ML", useKernel=TRUE, concent=10, bw=30, numCores=2)$thr
PlotData(Data=Data, drc=drc, thr=thrResultML, pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)

if(plotly_installed) {
  PolarPlotData(Data=Data, drc=drc, thr=thrResultML, pointSize=4, fontSize=12, 
                thrWidth=4, ylim=c(0,max(Data)))
} else {
  message("plotly not installed: skipping PolarPlotData output")
}

Estimation of spline ML model

The code below performs optimisation for a unique pair of lambda and kappa.

lambda <- 100
kappa <- 40

thrPerObs <- thrResultML[drc]
excess <- Data - thrPerObs
drcExcess <- drc[excess>0]
excess <- excess[excess>0]

splineFit <- SplineML(excesses = excess, drc = drcExcess, nBoot = 30, 
                      numIntKnots = 16, lambda=lambda, kappa=kappa, numCores=2)
xiBoot <- splineFit$xi
sigBoot <- splineFit$sig

PlotParamEstim(bootEstimates=xiBoot, thetaGrid=0:360, ylab=bquote(hat(xi)),
               alpha=0.05, ylim=NULL, cex.axis=15, cex.lab=2, thrWidth=2)


PlotParamEstim(bootEstimates=sigBoot, thetaGrid=0:360, ylab=bquote(hat(sigma)),
               alpha=0.05, ylim=NULL, cex.axis=15, cex.lab=2, thrWidth=2)

High Quantiles

h <- 60 # needed for calculating local probability of exceedances
RLBoot <- CalcRLsplineML(Data=Data, drc=drc, xiBoot=xiBoot, sigBoot=sigBoot, h=h,
                 TTs=c(100, 10000), thetaGrid=thetaVec,
                 timeRange=timeRange, thr=thrResultML)
# 100-year level

PlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
       TTs=c(100, 10000), whichPlot=1, alpha=0.05, ylim=NULL,
       pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)

if(plotly_installed) {
  PolarPlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
              TTs=c(100, 10000), whichPlot=1, alpha=0.05, ylim=c(0, 25),
              pointSize=4, fontSize=12, lineWidth=2)
} else {
  message("plotly not installed: skipping PolarPlotRL output")
}
# 10000-year level
PlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
       TTs=c(100, 10000), whichPlot=2, alpha=0.05, ylim=NULL,
       pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)

if(plotly_installed) {
  PolarPlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
              TTs=c(100, 10000), whichPlot=2, alpha=0.05, ylim=c(0, 25),
              pointSize=4, fontSize=12, lineWidth=2)
} else {
  message("plotly not installed: skipping PolarPlotRL output")
}