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#
# fields is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2022 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka, douglasnychka@gmail.edu,
#
# 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.
#
# You should have received a copy of the GNU General Public License
# along with the R software environment if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
# or see http://www.r-project.org/Licenses/GPL-2
##END HEADER
##END HEADER
# tests of SEs from the Omega matrix
# using Monte Carlo
suppressMessages(library(fields))
options( echo=FALSE)
test.for.zero.flag<- TRUE
X<- ChicagoO3$x
n<- nrow( X)
tau2<- .1
sigma<- 2.0
processCov<- sigma*Exp.cov( X,X,aRange=50)
cholCov<- chol( processCov + diag( tau2 , n ) )
nreps<- 1e5
set.seed( 111)
# extra random covariate
Z<- matrix( rnorm(n),n)
# the stochastic part
E<- matrix( rnorm(n*nreps),n,nreps)
# NOTE: all fixed effects set to zero
Y<- t( cholCov)%*%E
out<- mKrig( X,Y, aRange=50, Z=Z,
collapseFixedEffect = FALSE,
lambda=.1/2.0)
testCov<- var( t(out$beta) )
test.for.zero(testCov, sigma*out$Omega, tol=.05 )
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