spTimer (version 0.02)

spT.prediction: Predictions for the spatio-temporal models.

Description

This function is used to obtain predicted values using the MCMC samples.

Usage

spT.prediction(nBurn, pred.data, pred.coords, posteriors,
              tol.dist=2, Summary=TRUE)

Arguments

nBurn

Initial MCMC samples to discard before making inference.

pred.data

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

pred.coords

The coordinates for the prediction sites. The locations are in similar format to coords.

posteriors

Posterior MCMC samples obtained from function spT.Gibbs.

tol.dist

Minimum tolerance distance limit between fitted and predicted locations.

Summary

Logical, if TRUE then provide MCMC summary statistics for predictions.

Value

• predicted.samples
  Predicted MCMC samples.
• distance.method
  Name of the distance calculation method.
• .
• Distance.matrix.pred
  The distance matrix for the prediction locations.
• cov.fnc
  Name of the covariance function used in models.
• predN
  Total number of data points in the prediction.
• Mean
  Average of the MCMC predictions, if Summary=TRUE.
• Median
  Median of the MCMC predictions, if Summary=TRUE.
• SD
  Standard deviation of the MCMC predictions, if Summary=TRUE.
• Low
  Lower limit for the 95 percent CI of the MCMC predictions, if Summary=TRUE.
• Up
  Upper limit for the 95 percent CI of the MCMC predictions, if Summary=TRUE.
• computation.time
  The computation time.
• model
  The model method used for prediction.

See Also

spT.Gibbs, spT.forecast.

Examples

##

###########################
## The GP models:
###########################

##
## Prediction for GP models
##

# define prediction coordinates and variables
pred.coords<-as.matrix(val.site[,2:3])

# GP prediction
pred.gp <- spT.prediction(nBurn=100, pred.data=val.dat, 
         pred.coords, posteriors=post.gp, tol.dist=2, 
         Summary=TRUE)

names(pred.gp)

# validation criteria and plots
spT.validation(val.dat$o8hrmax,c(pred.gp$Mean)) # 
spT.pCOVER(val.dat$o8hrmax,c(pred.gp$Up),c(pred.gp$Low)) #
spT.segment.plot(val.dat$o8hrmax,c(pred.gp$Mean),
      c(pred.gp$Up),c(pred.gp$Low))
abline(a=0,b=1)


##
## Fit and Prediction simultaneously
##


pred.coords<-as.matrix(val.site[,2:3])

coords<-as.matrix(fit.site[,2:3])
time.data<-spT.time(t.series=61,segment=1)

priors<-spT.priors(model="GP",var.prior=Gam(2,1),
        beta.prior=Nor(0,10^4))
initials<-spT.initials(model="GP", sig2eps=0.01, 
            sig2eta=0.5, beta=NULL, phi=0.001)

# input for spatial decay
#spatial.decay<-spT.decay(type="FIXED", value=0.01)
spatial.decay<-spT.decay(type="MH", tuning=0.08)
#spatial.decay<-spT.decay(type="DISCRETE",limit=c(0.01,0.02),segments=5)

nItr<-5000 

# MCMC via Gibbs
post.gp.fit.pred <- spT.Gibbs(formula=o8hrmax~cMAXTMP+WDSP+RH, 
         data=fit.dat, model="GP", time.data=time.data, 
         coords=coords, pred.coords=pred.coords, pred.data=val.dat,
         priors=priors, initials=initials, 
         nItr=nItr, nBurn=1000, report=nItr, 
         tol.dist=2, distance.method="geodetic:km", 
         cov.fnc="exponential", scale.transform="SQRT", 
         spatial.decay=spatial.decay,
         annual.aggregation="NONE")

names(post.gp.fit.pred)

post.gp.fit.pred$parameter


###########################
## The AR models:
###########################


##
## Prediction for AR models
##

# define prediction coordinates and variables
pred.coords<-as.matrix(val.site[,2:3])

# AR prediction
pred.ar <- spT.prediction(nBurn=100, pred.data=val.dat, 
         pred.coords=pred.coords, 
         posteriors=post.ar, tol.dist=2, Summary=TRUE)

names(pred.ar)

# validation criteria and plots
spT.validation(val.dat$o8hrmax,c(pred.ar$Mean)) # 
spT.pCOVER(val.dat$o8hrmax,c(pred.ar$Up),c(pred.ar$Low)) # 
spT.segment.plot(val.dat$o8hrmax,c(pred.ar$Mean),
      c(pred.ar$Up),c(pred.ar$Low))
abline(a=0,b=1)


##
## fit and predict combinedly for AR models with text output
##

pred.coords<-as.matrix(val.site[,2:3])

coords<-as.matrix(fit.site[,2:3])
time.data<-spT.time(t.series=61,segment=1)

priors<-spT.priors(model="AR",var.prior=Gam(2,1),
        beta.prior=Nor(0,10^4))

initials<-spT.initials(model="AR", sig2eps=0.01, 
            sig2eta=0.5, beta=NULL, phi=0.001)

# input for spatial decay
#spatial.decay<-spT.decay(type="FIXED", value=0.01)
spatial.decay<-spT.decay(type="MH", tuning=0.08)
#spatial.decay<-spT.decay(type="DISCRETE",limit=c(0.01,0.02),segments=5)

nItr<-500
nBurn<-100

# MCMC via Gibbs
post.ar.fit.pred <- spT.Gibbs(formula=o8hrmax~cMAXTMP+WDSP+RH, 
         data=fit.dat, model="AR", time.data=time.data, 
         coords=coords, pred.coords=pred.coords, pred.data=val.dat,
         priors=priors, initials=initials, 
         nItr=nItr, nBurn=nBurn, report=nItr, 
         tol.dist=2, distance.method="geodetic:km", 
         cov.fnc="exponential", scale.transform="SQRT", 
         spatial.decay=spatial.decay,
         annual.aggregation="an4th")

names(post.ar.fit.pred)

post.ar.fit.pred$para


###########################
## Models with GPP approximations:
###########################


##
## prediction for the GPP
##

# define prediction coordinates and variables
pred.coords<-as.matrix(val.site[,2:3])

# GPP prediction
pred.gpp <- spT.prediction(nBurn=100, pred.data=val.dat, 
       pred.coords=pred.coords, posteriors=post.gpp, tol.dist=2, 
       Summary=TRUE)
 
names(pred.gpp)


# validation criteria and plots
spT.validation(val.dat$o8hrmax,c(pred.gpp$Mean)) #
spT.pCOVER(val.dat$o8hrmax,c(pred.gpp$Up),c(pred.gpp$Low)) #
spT.segment.plot(val.dat$o8hrmax,c(pred.gpp$Mean),
      c(pred.gpp$Up),c(pred.gpp$Low))#,limit=c(0,100))
abline(a=0,b=1)


##
## fit and predict together for the GPP with text output
##

pred.coords<-as.matrix(val.site[,2:3])

coords<-as.matrix(fit.site[,2:3])
knots.coords<-spT.grid.coords(Longitude=c(max(coords[,1]),
              min(coords[,1])),Latitude=c(max(coords[,2]),
              min(coords[,2])), by=c(4,4))
time.data<-spT.time(t.series=61,segment=1)

priors<-spT.priors(model="GPP",var.prior=Gam(2,1),
        beta.prior=Nor(0,10^4))
#priors<-NULL
initials<-spT.initials(model="GPP", sig2eps=0.01, 
            sig2eta=0.5, beta=NULL, phi=0.001)
#initials<-NULL

# input for spatial decay
#spatial.decay<-spT.decay(type="FIXED", value=0.01)
spatial.decay<-spT.decay(type="MH", tuning=0.0008)
#spatial.decay<-spT.decay(type="DISCRETE",limit=c(0.001,0.002),segments=5)


nItr<-500 

# MCMC via Gibbs
post.gpp.fit.pred <- spT.Gibbs(formula=o8hrmax~cMAXTMP+WDSP+RH, 
         data=fit.dat, model="GPP", time.data=time.data, 
         coords=coords, knots.coords=knots.coords,
         pred.coords=pred.coords, pred.data=val.dat,
         priors=priors, initials=initials, 
         nItr=nItr, nBurn=100, report=nItr, 
         tol.dist=2, distance.method="geodetic:km", 
         cov.fnc="exponential", scale.transform="SQRT", 
         spatial.decay=spatial.decay,
         annual.aggregation="NONE")

names(post.gpp.fit.pred)

post.gpp.fit.pred$para


##