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# 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.
############################################################################
# Begin tests of Matern covaraince parameter estimate
# Note that in all tests the smoothness (nu) is fixed
# and only theta (range), sill ( rho) and nugget (sigma2) are considered.
##########################################################################
suppressMessages(library(fields))
options( echo=FALSE)
test.for.zero.flag<-1
# ozone data as a test case
data( ozone2)
x<- ozone2$lon.lat
y<- ozone2$y[16,]
is.good <- !is.na( y)
x<- x[is.good,]
y<- y[is.good]
nu<- 1.5
# reduce data set to speed calculations
x<-x[1:75,]
y<- y[1:75]
# testing REML formula as used in gcv.Krig
loglmvn <- function(pars, nu, x, y) {
N <- length(y)
Tmatrix <- fields.mkpoly(x, 2)
qr.T <- qr(Tmatrix)
Q2 <- qr.yq2(qr.T, diag(1, N))
ys <- t(Q2) %*% y
N2 <- length(ys)
lrho = pars[1]
ltheta = pars[2]
lsig2 = pars[3]
d <- rdist(x, x)
A <- exp(lrho)*(Matern(d, range = exp(ltheta),
smoothness = nu) + exp(lsig2)/exp(lrho) * diag(N))
A <- t(Q2) %*% A %*% Q2
A <- chol(A)
w = backsolve(A, ys, transpose = TRUE)
ycept <- (N2/2) * log(2 * pi) + sum(log(diag(A))) + (1/2) *
t(w) %*% w
return( ycept)
}
logProfilemvn <- function(lambda, theta, nu, x, y) {
N <- length(y)
Tmatrix <- fields.mkpoly(x, 2)
qr.T <- qr(Tmatrix)
Q2 <- qr.yq2(qr.T, diag(1, N))
ys <- t(Q2) %*% y
N2 <- length(ys)
d <- rdist(x, x)
print( dim ( d))
print( dim (diag( 1, N) ))
A <- (Matern(d, range = theta,
smoothness = nu) + diag( 1, N)*lambda )
A <- t(Q2) %*% A %*% Q2
A <- chol(A)
lnDetCov<- sum( log(diag(A)))*2
w = backsolve(A, ys, transpose = TRUE)
rho.MLE<- sum( w^2)/N2
REMLLike<- -1 * (-N2/2 - log(2 * pi) * (N2/2) - (N2/2) * log(rho.MLE) -
(1/2) * lnDetCov)
return( REMLLike)
}
out<- Krig( x,y, Covariance="Matern", smoothness= nu, theta= 2.0, method="REML" )
pars<- c(log( out$rho.MLE), log( 2.0), log( out$shat.MLE^2) )
REML0<- out$lambda.est[6,5]
REML1<- loglmvn( pars,nu, x,y)
REML2<- logProfilemvn( out$lambda, 2.0, nu, x,y)
test.for.zero( REML0, REML1, tol=2e-4, tag="sanity check 1 for REML from Krig")
test.for.zero( REML0, REML2, tag= "sanity check 2 for REML from Krig")
##D hold1<- MaternGLS.test( x,y, nu)
##D hold2<- MaternGLSProfile.test( x,y,nu)
##D test.for.zero( hold1$pars[1], hold2$pars[1], tol=2e-5, tag="check REML rho")
##D test.for.zero( hold1$pars[2], hold2$pars[2], tol=2e-5, tag="check REML theta")
##D test.for.zero( hold1$pars[3], hold2$pars[3], tol=5e-6, tag=" check REML sigma2")
hold3<- MaternQR.test( x,y,nu)
hold4<- MaternQRProfile.test( x,y,nu)
test.for.zero( hold3$pars[1], hold4$pars[1], tol=1e-3, tag="check REML rho")
test.for.zero( hold3$pars[2], hold4$pars[2], tol=1e-3, tag="check REML theta")
test.for.zero( hold3$pars[3], hold4$pars[3], tol=.0002, tag=" check REML sigma2")
nu<- hold3$smoothness
out1<- Krig( x,y, Covariance="Matern", theta= hold3$pars[2],
smoothness=nu, method="REML")
# evaluate Profile at full REML MLE
lam<- hold3$pars[3]/hold3$pars[1]
l1<-Krig.flplike( lam, out1)
# evaluate Profile at full REML MLE
out2<- Krig( x,y, Covariance="Matern", theta= hold4$pars[2],
smoothness=nu, method="REML")
lam<- hold4$pars[3]/hold4$pars[1]
l2<-Krig.flplike( lam, out2)
test.for.zero( l1,l2, tag="Profile likelihoods from Krig and optim")
hold5<- MLE.Matern( x,y,nu)
test.for.zero( hold5$llike,l2, tag="Profile likelihoods from Krig and golden search")
#hold6<- spatialProcess( x,y, smoothness=nu, theta= hold5$theta.MLE, REML=TRUE)
cat("done with Matern REML estimator tests where smoothness is fixed", fill=TRUE)
options( echo=TRUE)
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