Description Usage Arguments Value References See Also Examples
This function is used to obtain spatial predictions in the unknown locations and also to get the temporal forecasts using MCMC samples.
1 2 3 |
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 |
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 |
nBurn |
Number of burn-in. Initial MCMC samples to discard before making inference. |
tol.dist |
Minimum tolerance distance limit between fitted and predicted locations. |
predAR |
The prediction output, if forecasts are in the prediction locations. Only applicable if type="forecast" and data fitted with the "AR" model. |
Summary |
To obtain summary statistics for the posterior predicted MCMC samples. Default is TRUE. |
... |
Other arguments. |
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. This is to analyse the codespTimer forecast output using package |
Bakar, K. S. and Sahu, S. K. (2014) spTimer: Spatio-Temporal Bayesian Modelling Using R. Technical Report, University of Southampton, UK. To appear in the Journal of Statistical Software.
Sahu, S. K. and Bakar, K. S. (2012) A comparison of Bayesian Models for Daily Ozone Concentration Levels Statistical Methodology , 9, 144-157.
Sahu, S. K. and Bakar, K. S. (2012) Hierarchical Bayesian auto-regressive models for large space time data with applications to ozone concentration modelling. Applied Stochastic Models in Business and Industry, 28, 395-415.
spT.Gibbs, as.forecast.object
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###########################
## The GP models:
###########################
##
## Spatial prediction/interpolation
##
# Read data
data(NYdata)
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
# MCMC via Gibbs using default choices
set.seed(11)
post.gp <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="GP", coords=~Longitude+Latitude,
scale.transform="SQRT")
print(post.gp)
# Define prediction coordinates
pred.coords<-as.matrix(unique(cbind(DataValPred[,2:3])))
# Spatial prediction using spT.Gibbs output
set.seed(11)
pred.gp <- predict(post.gp, newdata=DataValPred, newcoords=pred.coords)
print(pred.gp)
names(pred.gp)
# validation criteria
spT.validation(DataValPred$o8hrmax,c(pred.gp$Mean))
##
## Temporal prediction/forecast
## 1. In the unobserved locations
##
# Read data
DataValFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValFore<-subset(DataValFore, with(DataValFore, (Day %in% c(30, 31) & Month == 8)))
# define forecast coordinates
fore.coords<-as.matrix(unique(cbind(DataValFore[,2:3])))
# Two-step ahead forecast, i.e., in day 61 and 62
# in the unobserved locations using output from spT.Gibbs
set.seed(11)
fore.gp <- predict(post.gp, newdata=DataValFore, newcoords=fore.coords,
type="temporal", foreStep=2)
print(fore.gp)
names(fore.gp)
# Forecast validations
spT.validation(DataValFore$o8hrmax,c(fore.gp$Mean))
# Use of "forecast" class
#library(forecast)
#tmp<-as.forecast.object(fore.gp, site=1) # default for site 1
#plot(tmp)
#summary(tmp)
##
## Temporal prediction/forecast
## 2. In the observed/fitted locations
##
# Read data
DataFitFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28),
reverse=TRUE)
DataFitFore<-subset(DataFitFore, with(DataFitFore, (Day %in% c(30, 31) & Month == 8)))
# Define forecast coordinates
fore.coords<-as.matrix(unique(cbind(DataFitFore[,2:3])))
# Two-step ahead forecast, i.e., in day 61 and 62,
# in the fitted locations using output from spT.Gibbs
set.seed(11)
fore.gp <- predict(post.gp, newdata=DataFitFore, newcoords=fore.coords,
type="temporal", foreStep=2)
print(fore.gp)
names(fore.gp)
# Forecast validations
spT.validation(DataFitFore$o8hrmax,c(fore.gp$Mean)) #
# Use of "forecast" class
#library(forecast)
#tmp<-as.forecast.object(fore.gp, site=5) # for site 5
#plot(tmp)
##
## Fit and spatially prediction simultaneously
##
# Read data
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28),
reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
# Define the coordinates
coords<-as.matrix(unique(cbind(DataFit[,2:3])))
pred.coords<-as.matrix(unique(cbind(DataValPred[,2:3])))
# MCMC via Gibbs will provide output in *.txt format
# from C routine to avoide large data problem in R
set.seed(11)
post.gp.fitpred <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="GP", coords=coords,
newcoords=pred.coords, newdata=DataValPred,
scale.transform="SQRT")
print(post.gp.fitpred)
summary(post.gp.fitpred)
coef(post.gp.fitpred)
plot(post.gp.fitpred,residuals=TRUE)
names(post.gp.fitpred)
# validation criteria
spT.validation(DataValPred$o8hrmax,c(post.gp.fitpred$prediction[,1]))
###########################
## The AR models:
###########################
##
## Spatial prediction/interpolation
##
# Read data
data(NYdata)
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
# MCMC via Gibbs using default choices
set.seed(11)
post.ar <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="AR", coords=~Longitude+Latitude,
scale.transform="SQRT")
print(post.ar)
# Define prediction coordinates
pred.coords<-as.matrix(unique(cbind(DataValPred[,2:3])))
# Spatial prediction using spT.Gibbs output
set.seed(11)
pred.ar <- predict(post.ar, newdata=DataValPred, newcoords=pred.coords)
print(pred.ar)
names(pred.ar)
# validation criteria
spT.validation(DataValPred$o8hrmax,c(pred.ar$Mean))
##
## Temporal prediction/forecast
## 1. In the unobserved locations
##
# Read data
DataValFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValFore<-subset(DataValFore, with(DataValFore, (Day %in% c(30, 31) & Month == 8)))
# define forecast coordinates
fore.coords<-as.matrix(unique(cbind(DataValFore[,2:3])))
# Two-step ahead forecast, i.e., in day 61 and 62
# in the unobserved locations using output from spT.Gibbs
set.seed(11)
fore.ar <- predict(post.ar, newdata=DataValFore, newcoords=fore.coords,
type="temporal", foreStep=2, predAR=pred.ar)
print(fore.ar)
names(fore.ar)
# Forecast validations
spT.validation(DataValFore$o8hrmax,c(fore.ar$Mean))
# Use of "forecast" class
#tmp<-as.forecast.object(fore.ar, site=1) # default for site 1
#plot(tmp)
##
## Temporal prediction/forecast
## 2. In the observed/fitted locations
##
# Read data
DataFitFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28),
reverse=TRUE)
DataFitFore<-subset(DataFitFore, with(DataFitFore, (Day %in% c(30, 31) & Month == 8)))
# Define forecast coordinates
fore.coords<-as.matrix(unique(cbind(DataFitFore[,2:3])))
# Two-step ahead forecast, i.e., in day 61 and 62,
# in the fitted locations using output from spT.Gibbs
set.seed(11)
fore.ar <- predict(post.ar, newdata=DataFitFore, newcoords=fore.coords,
type="temporal", foreStep=2)
print(fore.ar)
names(fore.ar)
# Forecast validations
spT.validation(DataFitFore$o8hrmax,c(fore.ar$Mean)) #
# Use of "forecast" class
#tmp<-as.forecast.object(fore.ar, site=1) # default for site 1
#plot(tmp)
##
## Fit and spatially prediction simultaneously
##
# Read data
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=s)
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
# Define the coordinates
coords<-as.matrix(unique(cbind(DataFit[,2:3])))
pred.coords<-as.matrix(unique(cbind(DataValPred[,2:3])))
# MCMC via Gibbs will provide output in *.txt format
# from C routine to avoide large data problem in R
set.seed(11)
post.ar.fitpred <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="AR", coords=coords,
newcoords=pred.coords, newdata=DataValPred,
scale.transform="SQRT")
print(post.ar.fitpred)
summary(post.ar.fitpred)
names(post.ar.fitpred)
# validation criteria
spT.validation(DataValPred$o8hrmax,c(post.ar.fitpred$prediction[,1]))
#################################
## The GPP approximation models:
#################################
##
## Spatial prediction/interpolation
##
# Read data
data(NYdata)
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
# Define knots
knots<-spT.grid.coords(Longitude=c(max(coords[,1]),
min(coords[,1])),Latitude=c(max(coords[,2]),
min(coords[,2])), by=c(4,4))
# MCMC via Gibbs using default choices
set.seed(11)
post.gpp <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="GPP", coords=~Longitude+Latitude,
knots.coords=knots, scale.transform="SQRT")
print(post.gpp)
# Define prediction coordinates
pred.coords<-as.matrix(unique(cbind(DataValPred[,2:3])))
# Spatial prediction using spT.Gibbs output
set.seed(11)
pred.gpp <- predict(post.gpp, newdata=DataValPred, newcoords=pred.coords)
print(pred.gpp)
names(pred.gpp)
# validation criteria
spT.validation(DataValPred$o8hrmax,c(pred.gpp$Mean))
##
## Temporal prediction/forecast
## 1. In the unobserved locations
##
# Read data
DataValFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValFore<-subset(DataValFore, with(DataValFore, (Day %in% c(30, 31) & Month == 8)))
# define forecast coordinates
fore.coords<-as.matrix(unique(cbind(DataValFore[,2:3])))
# Two-step ahead forecast, i.e., in day 61 and 62
# in the unobserved locations using output from spT.Gibbs
set.seed(11)
fore.gpp <- predict(post.gpp, newdata=DataValFore, newcoords=fore.coords,
type="temporal", foreStep=2)
print(fore.gpp)
names(fore.gpp)
# Forecast validations
spT.validation(DataValFore$o8hrmax,c(fore.gpp$Mean))
# Use of "forecast" class
#tmp<-as.forecast.object(fore.gpp, site=1) # default for site 1
#plot(tmp)
##
## Temporal prediction/forecast
## 2. In the observed/fitted locations
##
# Read data
DataFitFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28),
reverse=TRUE)
DataFitFore<-subset(DataFitFore, with(DataFitFore, (Day %in% c(30, 31) & Month == 8)))
# Define forecast coordinates
fore.coords<-as.matrix(unique(cbind(DataFitFore[,2:3])))
# Two-step ahead forecast, i.e., in day 61 and 62,
# in the fitted locations using output from spT.Gibbs
set.seed(11)
fore.gpp <- predict(post.gpp, newdata=DataFitFore, newcoords=fore.coords,
type="temporal", foreStep=2)
print(fore.gpp)
names(fore.gpp)
# Forecast validations
spT.validation(DataFitFore$o8hrmax,c(fore.gpp$Mean)) #
# Use of "forecast" class
#tmp<-as.forecast.object(fore.gpp, site=1) # default for site 1
#plot(tmp)
##
## Fit and spatially prediction simultaneously
##
# Read data
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=s)
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
# Define the coordinates
coords<-as.matrix(unique(cbind(DataFit[,2:3])))
pred.coords<-as.matrix(unique(cbind(DataValPred[,2:3])))
knots<-spT.grid.coords(Longitude=c(max(coords[,1]),
min(coords[,1])),Latitude=c(max(coords[,2]),
min(coords[,2])), by=c(4,4))
# MCMC via Gibbs will provide output in *.txt format
# from C routine to avoide large data problem in R
set.seed(11)
post.gpp.fitpred <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="GP", coords=coords, knots.coords=knots,
newcoords=pred.coords, newdata=DataValPred,
scale.transform="SQRT")
print(post.gpp.fitpred)
summary(post.gpp.fitpred)
plot(post.gpp.fitpred)
names(post.gpp.fitpred)
# validation criteria
spT.validation(DataValPred$o8hrmax,c(post.gpp.fitpred$prediction[,1]))
##
######################################################
## The Truncated/Censored GP models:
######################################################
##
## Model fitting
##
data(NYdata)
# Truncation at 30 (say)
NYdata$o8hrmax[NYdata$o8hrmax<=30] <- 30
# Read data
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=s)
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
DataValFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValFore<-subset(DataValFore, with(DataValFore, (Day %in% c(30, 31) & Month == 8)))
DataFitFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28),
reverse=TRUE)
DataFitFore<-subset(DataFitFore, with(DataFitFore, (Day %in% c(30, 31) & Month == 8)))
#
nItr <- 5000 # number of MCMC samples for each model
nBurn <- 1000 # number of burn-in from the MCMC samples
# Truncation at 30
# fit truncated GP model
out <- spT.Gibbs(formula=o8hrmax~cMAXTMP+WDSP+RH,data=DataFit,
model="truncatedGP",coords=~Longitude+Latitude,
distance.method="geodetic:km",nItr=nItr,nBurn=nBurn,report=5,
truncation.para = list(at = 30,lambda = 4),
fitted.values="ORIGINAL")
#
summary(out)
head(fitted(out))
plot(out,density=FALSE)
#
head(cbind(DataFit$o8hrmax,fitted(out)[,1]))
plot(DataFit$o8hrmax,fitted(out)[,1])
spT.validation(DataFit$o8hrmax,fitted(out)[,1])
##
## prediction (spatial)
##
pred <- predict(out,newdata=DataValPred, newcoords=~Longitude+Latitude, tol=0.05)
names(pred)
plot(DataValPred$o8hrmax,c(pred$Mean))
spT.validation(DataValPred$o8hrmax,c(pred$Mean))
#pred$prob.below.threshold
##
## forecast (temporal)
##
# unobserved locations
fore <- predict(out,newdata=DataValFore, newcoords=~Longitude+Latitude,
type="temporal", foreStep=2, tol=0.05)
spT.validation(DataValFore$o8hrmax,c(fore$Mean))
plot(DataValFore$o8hrmax,c(fore$Mean))
#fore$prob.below.threshold
# observed locations
fore <- predict(out,newdata=DataFitFore, newcoords=~Longitude+Latitude,
type="temporal", foreStep=2, tol=0.05)
spT.validation(DataFitFore$o8hrmax,c(fore$Mean))
plot(DataFitFore$o8hrmax,c(fore$Mean))
#fore$prob.below.threshold
######################################################
## The Truncated/Censored GPP models:
######################################################
##
## Model fitting
##
data(NYdata)
# Define the coordinates
coords<-as.matrix(unique(cbind(NYdata[,2:3])))
# Define knots
knots<-spT.grid.coords(Longitude=c(max(coords[,1]),
min(coords[,1])),Latitude=c(max(coords[,2]),
min(coords[,2])), by=c(4,4))
# Truncation at 30 (say)
NYdata$o8hrmax[NYdata$o8hrmax<=30] <- 30
# Read data
s<-c(8,11,12,14,18,21,24,28)
DataFit<-spT.subset(data=NYdata, var.name=c("s.index"), s=s, reverse=TRUE)
DataFit<-subset(DataFit, with(DataFit, !(Day %in% c(30, 31) & Month == 8)))
DataValPred<-spT.subset(data=NYdata, var.name=c("s.index"), s=s)
DataValPred<-subset(DataValPred, with(DataValPred, !(Day %in% c(30, 31) & Month == 8)))
DataValFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28))
DataValFore<-subset(DataValFore, with(DataValFore, (Day %in% c(30, 31) & Month == 8)))
DataFitFore<-spT.subset(data=NYdata, var.name=c("s.index"), s=c(8,11,12,14,18,21,24,28),
reverse=TRUE)
DataFitFore<-subset(DataFitFore, with(DataFitFore, (Day %in% c(30, 31) & Month == 8)))
#
nItr <- 5000 # number of MCMC samples for each model
nBurn <- 1000 # number of burn-in from the MCMC samples
# Truncation at 30
# fit truncated GPP model
out <- spT.Gibbs(formula=o8hrmax ~cMAXTMP+WDSP+RH,
data=DataFit, model="truncatedGPP",coords=~Longitude+Latitude,
knots.coords=knots, distance.method="geodetic:km",
nItr=nItr,nBurn=nBurn,report=5,fitted="ORIGINAL",
truncation.para = list(at = 30,lambda = 4))
#
summary(out)
head(fitted(out))
plot(out,density=FALSE)
#
head(cbind(DataFit$o8hrmax,fitted(out)[,1]))
plot(DataFit$o8hrmax,fitted(out)[,1])
spT.validation(DataFit$o8hrmax,fitted(out)[,1])
##
## prediction (spatial)
##
pred <- predict(out,newdata=DataValPred, newcoords=~Longitude+Latitude, tol=0.05)
names(pred)
plot(DataValPred$o8hrmax,c(pred$Mean))
spT.validation(DataValPred$o8hrmax,c(pred$Mean))
#pred$prob.below.threshold
##
## forecast (temporal)
##
# unobserved locations
fore <- predict(out,newdata=DataValFore, newcoords=~Longitude+Latitude,
type="temporal", foreStep=2, tol=0.05)
spT.validation(DataValFore$o8hrmax,c(fore$Mean))
plot(DataValFore$o8hrmax,c(fore$Mean))
#fore$prob.below.threshold
# observed locations
fore <- predict(out,newdata=DataFitFore, newcoords=~Longitude+Latitude,
type="temporal", foreStep=2, tol=0.05)
spT.validation(DataFitFore$o8hrmax,c(fore$Mean))
plot(DataFitFore$o8hrmax,c(fore$Mean))
#fore$prob.below.threshold
######################################################
######################################################
##
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