https://github.com/cran/fields
Tip revision: f2ea916e79625f00378265f4b6112c1f1c1a5c97 authored by Douglas Nychka on 14 May 2019, 20:10:03 UTC
version 9.8-1
version 9.8-1
Tip revision: f2ea916
mKrigMLETest.R
# fields is a package for analysis of spatial data written for
# the R software environment .
# Copyright (C) 2018
# University Corporation for Atmospheric Research (UCAR)
# Contact: Douglas Nychka, nychka@ucar.edu,
# National Center for Atmospheric Research,
# PO Box 3000, Boulder, CO 80307-3000
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
suppressMessages(library( fields ))
options( echo=FALSE)
#
##### generate test data
#
data( ozone2)
# x is a two column matrix where each row is a location in lon/lat
# coordinates
x<- ozone2$lon.lat
# y is a vector of ozone measurements at day 16 a the locations.
y<- ozone2$y[16,]
#ind<- !is.na( y)
#x<- x[ind,]
#y<- y[ind]
x<-x[1:31,]
y<-y[1:31]
y[31]<-NA
################ test that optim results match the model evaluated
################ at the optimized parameters.
optim.args = list(method = "BFGS",
control = list(fnscale = -1, parscale = c(0.5, 0.5),
ndeps = c(0.05,0.05)))
MLEfit0 <- mKrigMLEJoint(x, y, lambda.start=.5,
cov.params.start= list(theta=1.2),
cov.fun="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern", smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=1),
verbose=FALSE)
test.for.zero( MLEfit0$summary["lnProfileLike.FULL"], MLEfit0$optimResults$value,
tag="Likelihood Values summary and optim")
obj0<- mKrig( x,y, cov.args = list(Covariance = "Matern",
smoothness = 1.0),
na.rm=TRUE, m=1,
lambda= MLEfit0$pars.MLE[1],
theta=MLEfit0$pars.MLE[2])
test.for.zero( MLEfit0$summary["lnProfileLike.FULL"],
obj0$lnProfileLike.FULL,
tag="Likelihood Values summary and profile")
test.for.zero( MLEfit0$summary["rhoMLE"],obj0$rho.MLE,
tag="rho MLE")
par.grid<- list( theta= c(.99, 1.0, 1.01)*MLEfit0$summary["theta"] )
MLEfit1<- mKrigMLEGrid(x, y,
cov.fun = "stationary.cov",
cov.args = list(Covariance = "Matern", smoothness = 1.0),
par.grid = par.grid,
lambda = .5,
lambda.profile = TRUE,
mKrig.args = list( m=1),
na.rm=TRUE,
verbose = FALSE)
hold<- (MLEfit1$summary[1,"lnProfileLike.FULL"] < MLEfit1$summary[2,"lnProfileLike.FULL"]) &
(MLEfit1$summary[3,"lnProfileLike.FULL"] < MLEfit1$summary[2,"lnProfileLike.FULL"])
test.for.zero(as.numeric(hold), 1, relative=FALSE,
tag="consistency of Likelihood values")
lambdaGrid<- c(.99, 1.0, 1.01)*MLEfit0$summary["lambda"]
par.grid<- list( theta= rep(MLEfit0$summary["theta"] ,3 ) )
MLEfit2 <- mKrigMLEGrid(x, y,
cov.fun = "stationary.cov",
cov.args = list(Covariance = "Matern", smoothness = 1.0),
mKrig.args = list( m=1),
par.grid = par.grid,
lambda = lambdaGrid,
lambda.profile = FALSE,
verbose = FALSE)
hold<- (MLEfit2$summary[1,"lnProfileLike.FULL"] < MLEfit2$summary[2,"lnProfileLike.FULL"]) &
(MLEfit2$summary[3,"lnProfileLike.FULL"] < MLEfit2$summary[2,"lnProfileLike.FULL"])
test.for.zero(as.numeric(hold), 1, relative=FALSE)
MLEfit3<- MLESpatialProcess( x,y,
cov.args = list(Covariance = "Matern", smoothness = 1.0),
mKrig.args = list( m=1)
)
test.for.zero(MLEfit0$summary[1:5],
(MLEfit3$MLEJoint$summary[1:5]), tol=2e-3,
tag="Testing MLESpatialProcess ")
obj<- spatialProcess( x, y, mKrig.args= list(m = 1),
theta = MLEfit0$summary[3] )
obj1<- spatialProcess( x, y, mKrig.args= list(m = 1)
)
test.for.zero(MLEfit0$summary[1],
obj$lnProfileLike.FULL,
tag="spatialProcess finding MLE " )
test.for.zero(MLEfit0$summary[1],
obj1$lnProfileLike.FULL, tol=5e-8,
tag="spatialProcess given MLE "
)
# testing Krig function
#out1<- Krig( x,y, cov.fun="stationary.cov",
# cov.args = list(Covariance = "Matern",
# smoothness=1.0, theta=.9),
# na.rm=TRUE,
# m=2)
genCovMat = function(x, theta, lambda) {
distanceMatrix<- rdist(x,x)
Sigma<- Matern( distanceMatrix/theta, smoothness=1.0 ) + diag(x=lambda, nrow=nrow(distanceMatrix))
return(Sigma)
}
#generate observation locations
set.seed( 223)
n=25
x = matrix(runif(2*n), nrow=n)
#generate observations at the locations
trueTheta = .1
trueLambda = .1
Sigma = genCovMat(x, trueTheta, trueLambda)
U = chol(Sigma)
M<- 1e4 # lots of replicated fields.
set.seed( 332)
y = t(U)%*%matrix( rnorm(n*M), n,M)
out<- mKrig( x,y, lambda=trueLambda, theta=trueTheta*.1,
cov.function ="stationary.cov",cov.args = list(Covariance = "Matern",
smoothness=1.0)
)
optim.args = list(method = "BFGS",
control = list(fnscale = -1, parscale = c(0.5, 0.5),
ndeps = c(0.05,0.05)))
MLEfitA <- mKrigMLEJoint(x, y, lambda.start=.5,
cov.params.start= list(theta=.12),
cov.fun="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=0),
verbose=FALSE)
cat("Testing mKrigMLEJoint against true values",
fill=TRUE)
test.for.zero( MLEfitA$summary["lambda"],.1, tol=.02)
test.for.zero( MLEfitA$summary["theta"],.1, tol=.02)
test.for.zero( MLEfitA$summary["rhoMLE"], 1.0, tol=.002)
### now test REML fitting
MLEfitB <- mKrigMLEJoint(x, y, lambda.start=.5,
cov.params.start= list(theta=.12),
cov.fun="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=0),
REML=TRUE,
verbose=FALSE)
cat("Testing mKrigMLEJoint with REML against true values",
fill=TRUE)
test.for.zero( MLEfitB$summary["lambda"],.1, tol=.02)
test.for.zero( MLEfitB$summary["theta"],.1, tol=.02)
test.for.zero( MLEfitB$summary["rhoMLE"], 1.0, tol=.002)
cat("Testing mKrigMLEJoint with REML FALSE against true values",
fill=TRUE)
MLEfitC <- mKrigMLEJoint(x, y, lambda.start=.5,
cov.params.start= list(theta=.12),
cov.fun="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=2),
REML=FALSE,
verbose=FALSE
)
test.for.zero( MLEfitC$summary["lambda"], .1, tol=.02)
test.for.zero( MLEfitC$summary[ "theta"], .1, tol=.02)
test.for.zero( MLEfitC$summary["rhoMLE"], 1.0, tol=.002)
MLEfitA$summary
MLEfitB$summary
MLEfitC$summary
# simple Monte Carlo test
NS<- 2
n<-75
M<- 1000
set.seed(123)
x = matrix(runif(2*n), nrow=n)
trueTheta = .1
trueLambda = .04
Sigma = genCovMat(x, trueTheta, trueLambda)
U = chol(Sigma)
set.seed( 332)
hold<- matrix(NA, nrow=NS, ncol=7 )
for( k in 1:NS){
cat(k, " ")
#generate observations at the locations
y = t(U)%*%matrix( rnorm(n*M), n,M)
MLEfitC <- mKrigMLEJoint(x, y, lambda.start=.5,
cov.params.start= list(theta=.12),
cov.fun="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=2),
REML=FALSE,
verbose=FALSE)
hold[k,]<- MLEfitC$summary
}
cat(" ", fill=TRUE)
test.for.zero( trueTheta, mean(hold[,3]), tol=5e-3,
tag="Monte Carlo theta")
test.for.zero( trueLambda, mean(hold[,2]), tol=5e-2,
tag="Monte Carlo lambda")
cat("all done with mKrigMLEGrid tests", fill=TRUE)
options( echo=TRUE)