predict.spTD {spTDyn}

Spatial and temporal predictions for the spatio-temporal models.

Description

This function is used to obtain spatial predictions in the unknown locations and also to get the temporal forecasts using MCMC samples.

Usage

## S3 method for class 'spTD'
predict(object, newdata, newcoords, foreStep=NULL, type="spatial", 
        nBurn, tol.dist, Summary=TRUE, ...)

Arguments

object

Object of class inheriting from "spT".

newdata

The data set providing the covariate values for spatial prediction or temporal forecasts. This data should have the same space-time structure as the original data frame.

newcoords

The coordinates for the prediction or forecast sites. The locations are in similar format to coords, see spT.Gibbs.

foreStep

Number of K-step (time points) ahead forecast, K=1,2, ...; Only applicable if type="temporal".

type

If the value is "spatial" then only spatial prediction will be performed at the newcoords which must be different from the fitted sites provided by coords. When the "temporal" option is specified then forecasting will be performed and in this case the newcoords may also contain elements of the fitted sites in which case only temporal forecasting beyond the last fitted time point will be performed.

nBurn

Number of burn-in. Initial MCMC samples to discard before making inference.

tol.dist

Minimum tolerance distance limit between fitted and predicted locations.

Summary

To obtain summary statistics for the posterior predicted MCMC samples. Default is TRUE.

...

Other arguments.

Value

pred.samples or fore.samples

Prediction or forecast MCMC samples.

pred.coords or fore.coords

prediction or forecast coordinates.

Mean

Average of the MCMC predictions

Median

Median of the MCMC predictions

SD

Standard deviation of the MCMC predictions

Low

Lower limit for the 95 percent CI of the MCMC predictions

Up

Upper limit for the 95 percent CI of the MCMC predictions

computation.time

The computation time.

model

The model method used for prediction.

type

"spatial" or "temporal".

...

Other values "obsData", "fittedData" and "residuals" are provided only for temporal prediction.

References

Bakar, K. S., Kokic, P. and Jin, H. (2015). A spatio-dynamic model for assessing frost risk in south-eastern Australia. Journal of the Royal Statistical Society, Series C. Bakar, K. S., Kokic, P. and Jin, H. (2015). Hierarchical spatially varying coefficient and temporal dynamic process models using spTDyn. Journal of Statistical Computation and Simulation.

See Also

GibbsDyn.

Examples

##

library(spTDyn)

## Read Aus data ##
data(AUSdata)
# set a side data for validation
s<-c(1,4,10)
AUSdataFit<-spT.subset(data=AUSdata, var.name=c("s.index"), s=s, reverse=TRUE)
AUSdataFit<-subset(AUSdataFit, with(AUSdataFit, !(year == 2009)))
AUSdataPred<-spT.subset(data=AUSdata, var.name=c("s.index"), s=s)
AUSdataPred<-subset(AUSdataPred, with(AUSdataPred, !(year == 2009)))
AUSdataFore<-spT.subset(data=AUSdata, var.name=c("s.index"), s=s)
AUSdataFore<-subset(AUSdataFore, with(AUSdataFore, (year == 2009)))

## Read NY data ##
data(NYdata)
# set a side data for validation
s<-c(5,8,10,15,20,22,24,26)
fday<-c(25:31)
NYdataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
NYdataFit<-subset(NYdataFit, with(NYdataFit, !(Day %in% fday & Month == 8)))
NYdataPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=s)
NYdataPred<-subset(NYdataPred, with(NYdataPred, !(Day %in% fday & Month == 8)))
NYdataFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=s)
NYdataFore<-subset(NYdataFore, with(NYdataFore, (Day %in% fday & Month == 8)))

## Code for analysing temperature data in Section: 4 ##
## Model: Spatially varying coefficient process models ##

nItr<-13000
nBurn<-3000

# MCMC via Gibbs using defaults
# Spatially varying coefficient process model

library("spTDyn", warn.conflicts = FALSE)
set.seed(11)
post.sp <- GibbsDyn(tmax ~ soi+sp(soi)+grid+sp(grid),
           data=AUSdataFit, nItr=nItr, nBurn=nBurn, coords=~lon+lat,
           spatial.decay=decay(distribution=Gamm(2,1),tuning=0.06))
print(post.sp)

## Table: 3, Section: 4.1 ##
post.sp$PMCC

# parameter summary
summary(post.sp) # without spatially varying coefficients
summary(post.sp, coefficient="spatial")

#plot(post.sp, density=FALSE)  # without spatially varying coefficients
#plot(post.sp, coefficient="spatial", density=FALSE)

## Code for Figures: 3(a), 3(b) Section: 4.1 ##
Figure_3a<-function(){
  boxplot(t(post.sp$betasp[1:9,]),pch=".",main="SOI",
          xlab="Sites",ylab="Values")
}
Figure_3b<-function(){
  boxplot(t(post.sp$betasp[10:18,]),pch=".",main="Grid",
          xlab="Sites",ylab="Values")
}
Figure_3a()
Figure_3b()

## spatial prediction
set.seed(11)
pred.sp <- predict(post.sp,newcoords=~lon+lat,newdata=AUSdataPred)

## Table: 4, Section: 4.1, validations ##
spT.validation(AUSdataPred$tmax,c(pred.sp$Mean))
plot(AUSdataPred$tmax,c(pred.sp$Mean))

## temporal prediction
set.seed(11)
pred.sp.f <- predict(post.sp,type="temporal",foreStep=12,
                     newcoords=~lon+lat, newdata=AUSdataFore)

## Table: 4, Section: 4.1, validations ##
spT.validation(AUSdataFore$tmax,c(pred.sp.f$Mean))
plot(AUSdataFore$tmax,c(pred.sp.f$Mean))

## Code for analysing Ozone data in Section: 4 ##
## Model: spatio-temporal DLM ##

# MCMC via Gibbs using defaults
# spatio-temporal DLM

library("spTDyn", warn.conflicts = FALSE)
set.seed(11)
post.tp <- GibbsDyn(o8hrmax ~ tp(cMAXTMP)-1, data=NYdataFit,
           nItr=nItr, nBurn=nBurn, coords=~Longitude+Latitude,
           initials=initials(rhotp=0), scale.transform="SQRT",
           spatial.decay=decay(distribution=Gamm(2,1),tuning=0.05))
print(post.tp)
summary(post.tp)

## Table: 5, Section: 4.2 ##
post.tp$PMCC

## Figure: 5, Section: 4.2 ##
Figure_5<-function(){
  stat<-apply(post.tp$betatp[1:55,],1,quantile,prob=c(0.025,0.5,0.975))
  plot(stat[2,],type="p",lty=3,col=1,ylim=c(min(c(stat)),max(c(stat))),
       pch=19,ylab="",xlab="Days",axes=FALSE,main="cMAXTMP",cex=0.8)
  for(i in 1:55){
    segments(i, stat[2,i], i, stat[3,i])
    segments(i, stat[2,i], i, stat[1,i])
  }
  axis(1,1:55,labels=1:55);axis(2)
  abline(v=31.5,lty=2)
  text(15,0.32,"July");  text(45,0.32,"August");
}
Figure_5()

## spatial prediction
set.seed(11)
pred.tp <- predict(post.tp, newdata=NYdataPred, newcoords=~Longitude+Latitude)

## Table 6, Section: 4.2, validation ##
spT.validation(NYdataPred$o8hrmax,c(pred.tp$Mean))

## temporal prediction
set.seed(11)
pred.tp.f <- predict(post.tp, newdata=NYdataFore, newcoords=~Longitude+Latitude,
                     type="temporal", foreStep=7)

## Table 6, Section: 4.2, validation ##
spT.validation(NYdataFore$o8hrmax,c(pred.tp.f$Mean))

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