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test.R
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test.R
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#####
#####
#####
#####
#####
# testing functions for the covariance of mixture data set
# tests the fitLKINLAStandard function using data simulated from the LK model
# buffer: buffer distance between domain edge of basis lattice and domain edge of data.
# n: number of observations
# xRange: range of x coordinates
# yRange: range of y coordinates
# nx: number of basis function lattice points in x directions
# NOTE: ny is determined automatically to match scale of x lattice points
# Xmat: design matrix
# ys: observations
# first.time: is first time evaluating function. User should always set to FALSE
# thetas: originally was c(.1, 3), but 3 is too large
testLKINLAModelMixture = function(seed=1, nLayer=3, nx=20, ny=nx, assumeMeanZero=TRUE, nu=1,
nBuffer=5, normalize=TRUE, fastNormalize=TRUE, NC=14, testCovs=FALSE,
printVerboseTimings=FALSE, latInfo=NULL, n=900, thetas=NULL,
testfrac=1/9, plotNameRoot="", sigma2=.1^2, useKenya=FALSE,
effRangeRange=NULL, urbanOverSamplefrac=0, nHyperSamples=1000,
intStrategy="ccd", strategy="gaussian", separateRanges=FALSE,
leaveOutRegion=TRUE, gscratch=FALSE,
savePrecomputationResults=FALSE, loadPrecomputationResults=FALSE,
precomputationFileNameRoot="precomputationResults") {
set.seed(seed)
clusterEffect=TRUE
if(useKenya)
distanceBreaks = seq(0, 300, l=20)
else
distanceBreaks = seq(0, 0.5, l=20)
# set plotNameRoot
if(length(NC) == 1) {
if(separateRanges)
NC = c(14, 126) # by default, use two layers with the finest layer having resolution equal to 10km
}
if(separateRanges)
nLayer = length(NC)
# set plotNameRoot
# > 2/.08 * 5
# [1] 125
# > 2/.8 * 5
# [1] 12.5
ncText = ""
if(length(NC) == 1) {
if(separateRanges)
ncText = "_NC14_126"
else {
ncText = paste0("_NC", NC)
}
} else {
tempText = do.call("paste0", as.list(c(NC[1], paste0("_", NC[-1]))))
ncText = paste0("_NC", tempText)
}
plotNameRoot = paste0(plotNameRoot, "_L", nLayer, ncText, "_sepRange", separateRanges, "_n", n, "_nu", nu, "_nugV",
round(sigma2, 2), "_Kenya", useKenya, "_noInt", assumeMeanZero, "_urbOversamp", round(urbanOverSamplefrac, 4))
# set true parameter values
if(useKenya) {
if(is.null(thetas))
thetas=c(.08, .8) * (1000/2) / sqrt(8)
} else {
if(is.null(thetas))
thetas=c(.08, .8) / sqrt(8)
}
rho = 1
effectiveRange = thetas * sqrt(8)
# load data set if necessary
if(is.null(n)) {
out = load("mixtureDataSet.RData")
} else {
spatialCorFun = function(x) {0.5 * stationary.cov(x, theta=thetas[1], Covariance="Matern", smoothness=nu) +
0.5 * stationary.cov(x, theta=thetas[2], Covariance="Matern", smoothness=nu)}
mixtureCorFun = function(x) {0.5 * stationary.cov(x, theta=thetas[1], Covariance="Matern", smoothness=nu) +
0.5 * stationary.cov(x, theta=thetas[2], Covariance="Matern", smoothness=nu)}
nTest = round(testfrac * n)
if(leaveOutRegion) {
simulationData = getSimulationDataSetsGivenCovarianceTest(mixtureCorFun, nTotal=n, nTest=nTest, marginalVar=rho, errorVar=sigma2,
nDataSets=2, plotNameRoot=paste0("(0.5*Matern(", thetas[1], ") + 0.5*Matern(", thetas[2], "))"), fileNameRoot="mix",
saveDataSetPlot=FALSE, doPredGrid=TRUE)
} else {
simulationData = getSimulationDataSetsGivenCovariance(mixtureCorFun, nTotal=n, nTest=nTest, marginalVar=rho, errorVar=sigma2,
nDataSets=2, plotNameRoot=paste0("(0.5*Matern(", thetas[1], ") + 0.5*Matern(", thetas[2], "))"), fileNameRoot="mix",
saveDataSetPlot=FALSE, useKenyaLocations=useKenya, urbanOverSamplefrac=urbanOverSamplefrac)
}
}
coords = cbind(simulationData$xTrain[,1], simulationData$yTrain[,1])
ys = simulationData$zTrain[,1]
# generate lattice and simulate observations
# coords = matrix(runif(2*n), ncol=2)
if(useKenya) {
xRangeDat = simulationData$xRange
yRangeDat = simulationData$yRange
# if(is.null(effRangeRange))
# effRangeRange=exp(c(-6, 7))
} else {
xRangeDat = c(-1, 1)
yRangeDat = c(-1, 1)
}
if(is.null(latInfo))
latInfo = makeLatGrids(xRangeDat, yRangeDat, NC, nBuffer, nLayer)
AObs = makeA(coords, latInfo)
# Q = makeQ(kappa=kappa, rho=rho, latInfo, alphas=alphas, normalized=normalize, fastNormalize=fastNormalize)
# L = as.matrix(t(chol(solve(Q))))
# zsims = matrix(rnorm(nrow(Q)), ncol=1)
# fieldSims = L %*% zsims
# ys = as.numeric(AObs %*% fieldSims) + 1 # add a constant unit mean term to be estimated by INLA
# # ys = 1 + as.numeric(AObs %*% fieldSims) + coords[,1] # x-valued mean term to be estimated by INLA
# errs = rnorm(n, sd=sqrt(sigma2))
# ys = ys + errs
# plot the observations
pdf(file=paste0("Figures/mixtureLKINLAObservations", plotNameRoot, ".pdf"), width=5, height=5)
par(mfrow=c(1,1))
quilt.plot(coords, ys)
dev.off()
# make prediction coordinates on a grid, and add testing points
mx = 100
my = 100
predPts = make.surface.grid(list(x=seq(xRangeDat[1], xRangeDat[2], l=mx), y=seq(yRangeDat[1], yRangeDat[2], l=my)))
if(useKenya) {
# remove grid points outside of Kenya national boundaries
load("../U5MR/adminMapData.RData")
polys = adm0@polygons
kenyaPoly = polys[[1]]@Polygons[[77]]@coords
kenyaPolyProj = projKenya(kenyaPoly)
inKenya = in.poly(predPts, kenyaPolyProj)
predPts = predPts[inKenya,]
# add other testing locations to matrix of prediction locations and remember which
predPts = rbind(predPts, cbind(simulationData$xTest[,1], simulationData$yTest[,1]))
predPts = rbind(predPts, cbind(simulationData$xTestRural[,1], simulationData$yTestRural[,1]))
predPts = rbind(predPts, cbind(simulationData$xTestUrban[,1], simulationData$yTestUrban[,1]))
plotGridI = 1:sum(inKenya)
overallTestI = simulationData$overallTestI
ruralTestI = simulationData$ruralTestI
urbanTestI = simulationData$urbanTestI
gridTestI = (max(urbanTestI) + 1):(max(urbanTestI) + length(simulationData$xGrid))
} else {
predPts = rbind(predPts, cbind(simulationData$xTest[,1], simulationData$yTest[,1]))
}
predPts = rbind(predPts, cbind(simulationData$xGrid, simulationData$yGrid))
ysTest = c(simulationData$zTest[,1], simulationData$zTestRural[,1], simulationData$zTestUrban[,1], simulationData$zGrid[,1])
# generate hyperparameters based on median and quantiles of inverse exponential and inverse gamma
# priorPar = getPrior(.1, .1, 10)
# generate hyperparameters for pc priors
# median effective range is .4 or 200 for kenya data (a fifth of the spatial domain diameter), median spatial variance is 1
if(!useKenya)
priorPar = getPCPrior(.4, .5, 1, nLayer=nLayer, separateRanges=separateRanges, latticeInfo=latInfo)
else
priorPar = getPCPrior(200, .5, 1, nLayer=nLayer, separateRanges=separateRanges, latticeInfo=latInfo)
X = matrix(rep(1, nrow(coords)), ncol=1)
# X = matrix(coords[,1], ncol=1)
XPred = matrix(rep(1, nrow(predPts)), ncol=1)
# add linear terms in lat/lon to covariate matrices if requested
if(testCovs) {
X = cbind(X, coords)
XPred = cbind(XPred, predPts)
}
if(assumeMeanZero) {
X = NULL
XPred = NULL
}
# show priors on effective correlation, marginal variance, and error variance:
if(!useKenya)
xs1 = seq(.01, 2, l=500)
else
xs1 = seq(.01, 1000, l=500)
if(!separateRanges) {
pdf(file=paste0("Figures/mixtureLKINLAPriorEffRange", plotNameRoot, ".pdf"), width=5, height=5)
plot(xs1, dinvexp(xs1, rate=priorPar$corScalePar), type="l", col="blue",
xlab="Effective Correlation Range", main="Effective Correlation Prior",
ylab="Prior Density")
abline(v=qinvexp(.5, rate=priorPar$corScalePar), col="red")
dev.off()
} else {
for(i in 1:nLayer) {
if(!useKenya)
xs1 = seq(.01, 2, l=500)
else
xs1 = seq(.01, 1000, l=500)
if(i == nLayer && useKenya)
xs1 = seq(1, 200, l=500)
else if(!useKenya)
xs1 = seq(.001, .4, l=500)
pdf(file=paste0("Figures/mixtureLKINLAPriorEff", i, "Range", plotNameRoot, ".pdf"), width=5, height=5)
plot(xs1, dinvexp(xs1, rate=priorPar$corScalePar[i]), type="l", col="blue",
xlab="Effective Correlation Range", main="Effective Correlation Prior",
ylab="Prior Density")
abline(v=qinvexp(.5, rate=priorPar$corScalePar[i]), col="red")
dev.off()
}
}
if(priorPar$priorType == "orig") {
xs2 = seq(.01, 10.5, l=500)
pdf(file=paste0("Figures/mixtureLKINLAPriorMargVar", plotNameRoot, ".pdf"), width=5, height=5)
plot(xs2, invgamma::dinvgamma(xs2, shape=priorPar$varPar1, rate=priorPar$varPar2), type="l", col="blue",
xlab="Marginal Variance", main="Marginal Variance Prior",
ylab="Prior Density")
abline(v=qinvgamma(.1, shape=priorPar$varPar1, rate=priorPar$varPar2), col="red")
abline(v=qinvgamma(.9, shape=priorPar$varPar1, rate=priorPar$varPar2), col="red")
dev.off()
} else if(priorPar$priorType == "pc") {
xs2 = seq(.01, 11.5, l=500)
pdf(file=paste0("Figures/mixtureLKINLAPriorMargVar", plotNameRoot, ".pdf"), width=5, height=5)
plot(xs2, dpcvar(xs2, alpha=priorPar$alpha, u=priorPar$u), type="l", col="blue",
xlab="Marginal Variance", main="Marginal Variance Prior",
ylab="Prior Density")
abline(v=qpcvar(.1, alpha=priorPar$alpha, u=priorPar$u), col="red")
abline(v=qpcvar(.9, alpha=priorPar$alpha, u=priorPar$u), col="red")
abline(v=1, col="green")
dev.off()
}
# xs2 = seq(.001, invgamma::qinvgamma(.905, shape=0.1, rate=0.1), l=500)
# pdf(file="Figures/mixtureLKINLAPriorErrorVar.pdf", width=5, height=5)
# plot(xs2, invgamma::dinvgamma(xs2, shape=0.1, rate=0.1), type="l", col="blue",
# xlab="Error Variance", main="Error Variance Prior",
# ylab="Prior Density")
# abline(v=invgamma::qinvgamma(.1, shape=0.1, rate=0.1), col="red")
# abline(v=invgamma::qinvgamma(.9, shape=0.1, rate=0.1), col="red")
# dev.off()
xs2 = seq(.01, 1, l=500)
pdf(file=paste0("Figures/mixtureLKINLAPriorErrorVar", plotNameRoot, ".pdf"), width=5, height=5)
plot(xs2, dpcvar(xs2, alpha=.05, u=1), type="l", col="blue",
xlab="Error Variance", main="Error Variance Prior",
ylab="Prior Density")
abline(v=qpcvar(.1, alpha=.05, u=1), col="red")
abline(v=qpcvar(.9, alpha=.05, u=1), col="red")
abline(v=sqrt(.1), col="green")
dev.off()
# browser()
for(l in 1:nLayer) {
pdf(file=paste0("Figures/mixtureLKINLAPriorAlpha", l, plotNameRoot, ".pdf"), width=5, height=5)
xs = seq(0, 1, l=500)
tempYs = dbeta(xs, priorPar$alphaPar[l], sum(priorPar$alphaPar[-l]))
plot(xs, tempYs, type="l", xlab=TeX(paste0("$\\alpha_", l, "$")), ylab="Density",
main=TeX(paste0("Marginal for $\\alpha_", l, "$")), xlim=c(0,1), ylim=c(0, max(tempYs[is.finite(tempYs)])))
abline(v=qbeta(c(0.025, 0.975), priorPar$alphaPar[l], sum(priorPar$alphaPar[-l])), col="purple", lty=2)
dev.off()
}
# prior on covariogram
alphaVals = t(rdirichlet(100, alpha=priorPar$alphaPar))
rhoVals = rpcvar(100, alpha=priorPar$alpha, u=priorPar$u)
if(!separateRanges) {
kappaVals = sqrt(8)/rinvexp(100, rate=priorPar$corScalePar) * latInfo[[1]]$latWidth
} else {
kappaVals = matrix(sqrt(8)/rinvexp(100*3, rate=priorPar$corScalePar) * sapply(latInfo, function(x) {x$latWidth}), nrow=nLayer)
}
nuggetVarVals = rpcvar(100, alpha=.05, u=1)
if(loadPrecomputationResults)
loadFilename = precomputationFileNameRoot
else
loadFilename = ""
out = covarianceDistributionLKINLA(latInfo, kappaVals, rhoVals, nuggetVarVals, alphaVals,
normalize=normalize, fastNormalize=fastNormalize, precomputationsFileNameRoot=loadFilename)
d = out$d
sortI = sort(d, index.return=TRUE)$ix
d = d[sortI]
covMean = out$cov[sortI]
upperCov=out$upperCov[sortI]
lowerCov=out$lowerCov[sortI]
covMat=out$covMat[sortI]
corMean = out$cor[sortI]
upperCor=out$upperCor[sortI]
lowerCor=out$lowerCor[sortI]
corMat=out$corMat[sortI]
# true correlation and covariance functions
spatialCorFun = function(x) {0.5 * stationary.cov(x, theta=thetas[1], Covariance="Matern", distMat=x, smoothness=nu) +
0.5 * stationary.cov(x, theta=thetas[2], Covariance="Matern", distMat=x, smoothness=nu)}
spatialCovFun = spatialCorFun
mixtureCovFun = function(x) {
out = spatialCorFun(x)
out[x == 0] = 1 + sigma2
out
}
mixtureCorFun = function(x) { mixtureCovFun(x) * (1 / (1 + sigma2)) }
# plot the covariance an correlation priors
yRange = range(c(covMean, lowerCov, upperCov, mixtureCovFun(d)))
pdf(file=paste0("Figures/mixtureLKINLAPriorCov", plotNameRoot, ".pdf"), width=5, height=5)
plot(d, covMean, type="l", main="Posterior of covariance function", xlab="Distance", ylab="Covariance",
ylim=yRange)
lines(d, lowerCov, lty=2)
lines(d, upperCov, lty=2)
lines(d, mixtureCovFun(d), col="green")
legend("topright", c("Truth", "Estimate", "80% CI"), lty=c(1, 1, 2), col=c("green", "black", "black"))
dev.off()
pdf(file=paste0("Figures/mixtureLKINLAPriorCor", plotNameRoot, ".pdf"), width=5, height=5)
yRange = range(c(corMean, lowerCor, upperCor, mixtureCorFun(d)))
plot(d, corMean, type="l", main="Posterior of correlation function", xlab="Distance", ylab="Covariance",
ylim=c(0,1))
lines(d, lowerCor, lty=2)
lines(d, upperCor, lty=2)
lines(d, mixtureCorFun(d), col="green")
legend("topright", c("Truth", "Estimate", "80% CI"), lty=c(1, 1, 2), col=c("green", "black", "black"))
dev.off()
# fit the model
time = system.time(fit <- fitLKINLAStandard2(coords, ys, predCoords=predPts, seed=seed, nLayer=nLayer, NC=NC,
nBuffer=nBuffer, priorPar=priorPar, xObs=X, xPred=XPred, normalize=normalize,
intStrategy=intStrategy, strategy=strategy, fastNormalize=fastNormalize,
printVerboseTimings=printVerboseTimings, latInfo=latInfo, effRangeRange=effRangeRange,
separateRanges=separateRanges, clusterEffect=clusterEffect,
savePrecomputationResults=savePrecomputationResults,
loadPrecomputationResults=loadPrecomputationResults,
precomputationFileNameRoot=precomputationFileNameRoot))
mod = fit$mod
preds=fit$preds
predSDs=fit$sigmas
latInfo=fit$latInfo
latWidth=fit$latWidth
obsPreds=fit$obsPreds
obsSDs=fit$obsSDs
coefPreds = fit$coefPreds
coefSDs = fit$coefSDs
# print out the total time
print(paste0("Total time: ", time[3]))
# show a model summary
print(summary(mod))
# function for determining if points are in correct range
if(!useKenya) {
inRange = function(pts, rangeShrink=0) {
inX = (rangeShrink < pts[,1]) & (pts[,1] < 1-rangeShrink)
inY = (rangeShrink < pts[,2]) & (pts[,2] < 1-rangeShrink)
inX & inY
}
} else {
inRange = function(pts, rangeShrink=0) {
rep(TRUE, nrow(pts))
}
}
# show predictive surface, SD, and data
if(nLayer==1) {
pdf(file=paste0("Figures/mixtureLKINLAPreds", plotNameRoot, ".pdf"), width=9, height=6)
par(mfrow=c(2,3))
# obsInds = 1:n
# predInds = (n+1):(n+mx*my)
# coefInds = (n+mx*my+1):(n+mx*my+nx*ny)
colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeSD = range(c(range(predSDs[inRange(predPts)]), coefSDs[[1]][inRange(gridPtsL1)],
coefSDs[[2]][inRange(gridPtsL2)], coefSDs[[3]][inRange(gridPtsL3)]))
gridPtsL1 = latInfo[[1]]$latCoords
quilt.plot(coords, ys, main="True Process", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefPreds[[1]], main="Basis Coefficient Mean (Layer 1)", xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefSDs[[1]], main="Basis Coefficient SD (Layer 1)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
# quilt.plot(coords, obsPreds, main="Prediction mean", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat,
# zlim=range(predSDs[inRange(predPts)]))
plot.new()
quilt.plot(predPts[,1], predPts[,2], preds, main="Prediction Mean", zlim=colRangeDat,
xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], predSDs, main="Prediction SD",
xlim=xRangeDat, ylim=yRangeDat)
}
else if(nLayer==2) {
pdf(file=paste0("Figures/mixtureLKINLAPreds", plotNameRoot, ".pdf"), width=12, height=6)
par(mfrow=c(2,4))
# obsInds = 1:n
# predInds = (n+1):(n+mx*my)
# coefInds = (n+mx*my+1):(n+mx*my+nx*ny)
colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeCoef = range(c(coefPreds))
colRangeSD = range(c(predSDs, obsSDs, coefSDs))
gridPtsL1 = latInfo[[1]]$latCoords
gridPtsL2 = latInfo[[2]]$latCoords
quilt.plot(coords, ys, main="True Process", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], preds, main="Prediction Mean", zlim=colRangeDat,
xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefPreds[[1]], main="Basis Coefficient Mean (Layer 1)", xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefPreds[[2]], main="Basis Coefficient Mean (Layer 2)", xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(coords, obsPreds, main="Observation Mean", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], predSDs, main="Prediction SD",
xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefSDs[[1]], main="Basis Coefficient SD (Layer 1)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefSDs[[2]], main="Basis Coefficient SD (Layer 2)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
}
else if(nLayer==3) {
pdf(file=paste0("Figures/mixtureLKINLAPreds", plotNameRoot, ".pdf"), width=15, height=6)
par(mfrow=c(2,5), mar=c(5.1, 4.1, 4.1, 6))
# obsInds = 1:n
# predInds = (n+1):(n+mx*my)
# coefInds = (n+mx*my+1):(n+mx*my+nx*ny)
# colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeCoef = range(c(coefPreds))
colRangeSD = range(c(predSDs, obsSDs, coefSDs))
gridPtsL1 = latInfo[[1]]$latCoords
gridPtsL2 = latInfo[[2]]$latCoords
gridPtsL3 = latInfo[[3]]$latCoords
quilt.plot(coords, ys, main="True Process", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], preds, main="Prediction Mean", zlim=colRangeDat,
xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefPreds[[1]], main="Basis Coefficient Mean (Layer 1)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefPreds[[2]], main="Basis Coefficient Mean (Layer 2)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL3[,1], gridPtsL3[,2], coefPreds[[3]], main="Basis Coefficient Mean (Layer 3)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
# quilt.plot(coords, obsPreds, main="Observation Mean", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
# plot.new()
quilt.plot(coords, ys, main="Observations", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], predSDs, main="Prediction SD",
xlim=xRangeDat, ylim=yRangeDat, zlim=range(predSDs[inRange(predPts, rangeShrink=.03)]))
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefSDs[[1]], main="Basis Coefficient SD (Layer 1)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefSDs[[2]], main="Basis Coefficient SD (Layer 2)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL3[,1], gridPtsL3[,2], coefSDs[[3]], main="Basis Coefficient SD (Layer 3)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
}
else if(nLayer==4) {
pdf(file=paste0("Figures/mixtureLKINLAPreds", plotNameRoot, ".pdf"), width=18, height=6)
par(mfrow=c(2,6), mar=c(5.1, 4.1, 4.1, 6))
# obsInds = 1:n
# predInds = (n+1):(n+mx*my)
# coefInds = (n+mx*my+1):(n+mx*my+nx*ny)
# colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeCoef = range(c(coefPreds))
colRangeSD = range(c(predSDs, obsSDs, coefSDs))
gridPtsL1 = latInfo[[1]]$latCoords
gridPtsL2 = latInfo[[2]]$latCoords
gridPtsL3 = latInfo[[3]]$latCoords
gridPtsL4 = latInfo[[4]]$latCoords
quilt.plot(coords, ys, main="True Process", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], preds, main="Prediction Mean", zlim=colRangeDat,
xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefPreds[[1]], main="Basis Coefficient Mean (Layer 1)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefPreds[[2]], main="Basis Coefficient Mean (Layer 2)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL3[,1], gridPtsL3[,2], coefPreds[[3]], main="Basis Coefficient Mean (Layer 3)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL4[,1], gridPtsL4[,2], coefPreds[[4]], main="Basis Coefficient Mean (Layer 4)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
# quilt.plot(coords, obsPreds, main="Observation Mean", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
# plot.new()
quilt.plot(coords, ys, main="Observations", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], predSDs, main="Prediction SD",
xlim=xRangeDat, ylim=yRangeDat, zlim=range(predSDs[inRange(predPts, rangeShrink=.03)]))
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefSDs[[1]], main="Basis Coefficient SD (Layer 1)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefSDs[[2]], main="Basis Coefficient SD (Layer 2)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL3[,1], gridPtsL3[,2], coefSDs[[3]], main="Basis Coefficient SD (Layer 3)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL4[,1], gridPtsL4[,2], coefSDs[[4]], main="Basis Coefficient SD (Layer 4)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
}
else if(nLayer==5) {
pdf(file=paste0("Figures/mixtureLKINLAPreds", plotNameRoot, ".pdf"), width=21, height=6)
par(mfrow=c(2,7), mar=c(5.1, 4.1, 4.1, 6))
# obsInds = 1:n
# predInds = (n+1):(n+mx*my)
# coefInds = (n+mx*my+1):(n+mx*my+nx*ny)
# colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeDat = range(c(ys, obsPreds, preds, coefPreds))
colRangeCoef = range(c(coefPreds))
colRangeSD = range(c(predSDs, obsSDs, coefSDs))
gridPtsL1 = latInfo[[1]]$latCoords
gridPtsL2 = latInfo[[2]]$latCoords
gridPtsL3 = latInfo[[3]]$latCoords
gridPtsL4 = latInfo[[4]]$latCoords
gridPtsL5 = latInfo[[5]]$latCoords
quilt.plot(coords, ys, main="True Process", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], preds, main="Prediction Mean", zlim=colRangeDat,
xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefPreds[[1]], main="Basis Coefficient Mean (Layer 1)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefPreds[[2]], main="Basis Coefficient Mean (Layer 2)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL3[,1], gridPtsL3[,2], coefPreds[[3]], main="Basis Coefficient Mean (Layer 3)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL4[,1], gridPtsL4[,2], coefPreds[[4]], main="Basis Coefficient Mean (Layer 4)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
quilt.plot(gridPtsL5[,1], gridPtsL5[,2], coefPreds[[5]], main="Basis Coefficient Mean (Layer 5)",
xlim=xRangeDat, ylim=yRangeDat, zlim=colRangeCoef)
# quilt.plot(coords, obsPreds, main="Observation Mean", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
# plot.new()
quilt.plot(coords, ys, main="Observations", zlim=colRangeDat, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(predPts[,1], predPts[,2], predSDs, main="Prediction SD",
xlim=xRangeDat, ylim=yRangeDat, zlim=range(predSDs[inRange(predPts, rangeShrink=.03)]))
quilt.plot(gridPtsL1[,1], gridPtsL1[,2], coefSDs[[1]], main="Basis Coefficient SD (Layer 1)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL2[,1], gridPtsL2[,2], coefSDs[[2]], main="Basis Coefficient SD (Layer 2)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL3[,1], gridPtsL3[,2], coefSDs[[3]], main="Basis Coefficient SD (Layer 3)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL4[,1], gridPtsL4[,2], coefSDs[[4]], main="Basis Coefficient SD (Layer 4)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
quilt.plot(gridPtsL5[,1], gridPtsL5[,2], coefSDs[[5]], main="Basis Coefficient SD (Layer 5)", zlim=colRangeSD, xlim=xRangeDat, ylim=yRangeDat)
}
dev.off()
pdf(file=paste0("Figures/mixtureLKINLALeftOutResiduals", plotNameRoot, ".pdf"), width=5, height=5)
testIndices = (length(preds) - length(ysTest) + 1):length(preds)
plot(preds[testIndices], ysTest-preds[testIndices], pch=19, cex=.5, col="blue", main="Residuals versus fitted",
ylab="Residuals", xlab="Fitted")
abline(h=0, lty=2)
dev.off()
if(useKenya) {
pdf(file=paste0("Figures/mixtureLKINLALeftOutResidualsLabeled", plotNameRoot, ".pdf"), width=5, height=5)
testIndices = (length(preds) - length(ysTest) + 1):length(preds)
gridIndices =
ylim = range(ysTest-preds[testIndices])
xlim = range(preds[testIndices])
plot(preds[testIndices][overallTestI], ysTest[overallTestI]-preds[testIndices][overallTestI], pch=19, cex=.1, col="black", main="Residuals versus fitted",
ylab="Residuals", xlab="Fitted", xlim=xlim, ylim=ylim)
points(preds[testIndices][ruralTestI], ysTest[ruralTestI]-preds[testIndices][ruralTestI], pch=19, cex=.1, col="green")
points(preds[testIndices][urbanTestI], ysTest[urbanTestI]-preds[testIndices][urbanTestI], pch=19, cex=.1, col="blue")
points(preds[testIndices][gridTestI], ysTest[gridTestI]-preds[testIndices][gridTestI], pch=19, cex=.1, col="red")
abline(h=0, lty=2)
legend("topright", c("Overall", "Rural", "Urban", "Grid"), col=c("black", "green", "blue", "red"), pch=19)
dev.off()
}
# calculate true effective range and marginal variance:
latticeWidth = latInfo[[1]]$latWidth
if(separateRanges)
latticeWidth = sapply(latInfo, function(x) {x$latWidth})#
# marginalVar = rho/(4*pi * kappa^2)
# marginalVar = getMultiMargVar(kappa, rho, nLayer=nLayer, nu=nu, xRange=xRangeBasis,
# yRange=yRangeBasis, nx=nx, ny=ny)[1]
marginalVar = rho
# # plot marginals on interpretable scale (effective range, marginal variance)
# effRangeMarg = inla.tmarginal(exp, mod$marginals.hyperpar$`Theta1 for field`)
# varMarg = inla.tmarginal(exp, mod$marginals.hyperpar$`Theta2 for field`)
# sigma2Marg = inla.tmarginal(function(x) {1/x}, mod$marginals.hyperpar$`Precision for the Gaussian observations`)
# covNames = names(mod$marginals.fixed)
# if(!assumeMeanZero) {
# XMarginals = list()
# for(i in 1:length(covNames)) {
# XMarginal = inla.tmarginal(function(x) {x}, mod$marginals.fixed[[covNames[i]]])
# XMarginals = c(XMarginals, list(XMarginal))
# }
# }
#
# par(mfrow=c(1,1))
# if(!separateRanges) {
# pdf(file=paste0("Figures/mixtureLKINLAEffRange", plotNameRoot, ".pdf"), width=5, height=5)
# plot(effRangeMarg, type="l", main="Marginal for effective range")
# abline(v=effectiveRange, col="green")
# abline(v=inla.qmarginal(c(.025, .975), effRangeMarg), col="purple", lty=2)
# dev.off()
# } else {
# for(l in 1:nLayer) {
# pdf(file=paste0("Figures/mixtureLKINLAEffRange", "Layer", l, plotNameRoot, ".pdf"), width=5, height=5)
# plot(effRangeMarg, type="l", main=paste0("Marginal for effective range (Layer ", l, ")"))
# abline(v=effectiveRange, col="green")
# abline(v=inla.qmarginal(c(.025, .975), effRangeMarg), col="purple", lty=2)
# dev.off()
# }
# }
# plot marginals on interpretable scale (effective range, marginal variance)
if(!separateRanges) {
effRangeMarg = inla.tmarginal(exp, mod$marginals.hyperpar$`Theta1 for field`)
varMarg = inla.tmarginal(exp, mod$marginals.hyperpar$`Theta2 for field`)
} else {
numberThetas = nLayer + 1 + nLayer - 1
allNames = paste0("Theta", 1:numberThetas, " for field")
effRangeMargs = list()
for(i in 1:nLayer) {
effRangeMargs = c(effRangeMargs, list(inla.tmarginal(exp, mod$marginals.hyperpar[[allNames[i]]])))
}
varMarg = inla.tmarginal(exp, mod$marginals.hyperpar[[allNames[nLayer+1]]])
}
sigma2Marg = inla.tmarginal(function(x) {1/x}, mod$marginals.hyperpar[[1]])
covNames = names(mod$marginals.fixed)
XMarginals = list()
if(length(covNames) != 0) {
for(i in 1:length(covNames)) {
XMarginal = inla.tmarginal(function(x) {x}, mod$marginals.fixed[[covNames[i]]])
XMarginals = c(XMarginals, list(XMarginal))
}
}
par(mfrow=c(1,1))
if(!separateRanges) {
pdf(file=paste0("Figures/mixtureLKINLAEffRange", plotNameRoot, ".pdf"), width=5, height=5)
plot(effRangeMarg, type="l", main="Marginal for effective range")
abline(v=inla.qmarginal(c(.025, .975), effRangeMarg), col="purple", lty=2)
dev.off()
} else {
for(i in 1:nLayer) {
pdf(file=paste0("Figures/mixtureLKINLAEffRange", i, plotNameRoot, ".pdf"), width=5, height=5)
plot(effRangeMargs[[i]], type="l", main="Marginal for effective range")
abline(v=inla.qmarginal(c(.025, .975), effRangeMargs[[i]]), col="purple", lty=2)
dev.off()
}
}
# plot(mod$marginals.hyperpar$`Theta1 for field`, type="l", main="Marginal for log range")
pdf(file=paste0("Figures/mixtureLKINLAVar", plotNameRoot, ".pdf"), width=5, height=5)
plot(varMarg, type="l", main="Marginal for spatial variance")
abline(v=marginalVar, col="green")
abline(v=inla.qmarginal(c(.025, .975), varMarg), col="purple", lty=2)
dev.off()
# plot(mod$marginals.hyperpar$`Theta2 for field`, type="l", main="Marginal for log variance")
pdf(file=paste0("Figures/mixtureLKINLASigma2", plotNameRoot, ".pdf"), width=5, height=5)
plot(sigma2Marg, type="l", main="Marginal for error variance")
abline(v=sigma2, col="green")
abline(v=inla.qmarginal(c(.025, .975), sigma2Marg), col="purple", lty=2)
dev.off()
if(!assumeMeanZero) {
for(i in 1:length(covNames)) {
XMarginal = XMarginals[[i]]
pdf(file=paste0("Figures/mixtureLKINLA", covNames[i], plotNameRoot, ".pdf"), width=5, height=5)
plot(XMarginal, type="l", main="Marginal for fixed effect")
abline(v=0, col="green")
abline(v=inla.qmarginal(c(.025, .975), XMarginal), col="purple", lty=2)
dev.off()
}
}
# pdf(file="Figures/mixtureLKINLARho.pdf", width=5, height=5)
# plot(sigma2Marg, type="l", main=TeX("Marginal for $\\rho$"), xlab=TeX("$\\rho$"))
# abline(v=rho, col="green")
# dev.off()
# do the same for kappa, rho
# in order to get distribution for rho, must sample from joint hyperparameters
kappaMarg = inla.tmarginal(function(x) {sqrt(8)/exp(x) * latticeWidth}, mod$marginals.hyperpar$`Theta1 for field`)
# thetasToRho = function(xs) {
# logCor = xs[2]
# logVar = xs[3]
# kappa = sqrt(8)/exp(logCor) * latticeWidth
# sigma2 = exp(logVar)
# sigma2 * 4*pi * kappa^2
# }
# samples = inla.hyperpar.sample(50000, mod, TRUE)
# rhos = apply(samples, 1, thetasToRho)
# pdf(file=paste0("Figures/mixtureLKINLAKappa", plotNameRoot, ".pdf"), width=5, height=5)
# plot(kappaMarg, type="l", xlab="kappa", main="Marginal for kappa")
# abline(v=inla.qmarginal(c(.025, .975), kappaMarg), col="purple", lty=2)
# dev.off()
# pdf(file="Figures/mixtureLKINLARho.pdf", width=5, height=5)
# hist(rhos, xlab="rho", main="Marginal for Rho", breaks=1000, freq=F, xlim=c(0, quantile(probs=.95, rhos)))
# abline(v=rho, col="green")
# dev.off()
## Now generate marginals for the alpha parameters. In order to do this, we must generate draws from
## the posterior, and transform them back to the probability scale
out = inla.hyperpar.sample(nHyperSamples, mod, improve.marginals=TRUE)
if(separateRanges)
alphaI = (1 + nLayer+1 + 1):(1 + nLayer+1 + nLayer-1)
else
alphaI = 4:(3+nLayer-1)
zSamples = matrix(out[,alphaI], ncol=length(alphaI))
xSamples = t(matrix(apply(zSamples, 1, multivariateExpit), ncol=length(alphaI)))
xSamples = rbind(xSamples, 1-colSums(xSamples))
for(l in 1:nLayer) {
pdf(file=paste0("Figures/mixtureLKINLAAlpha", l, plotNameRoot, ".pdf"), width=5, height=5)
hist(xSamples[l,], xlab=TeX(paste0("$\\alpha_", l, "$")), main=TeX(paste0("Marginal for $\\alpha_", l, "$")), breaks=100, freq=F, xlim=c(0,1))
abline(v=mean(xSamples[l,]), col="purple", lty=1)
abline(v=quantile(probs=c(.025, .975), xSamples[l,]), col="purple", lty=2)
dev.off()
}
## plot covariance and correlation functions
# first get the true covariance an correlation functions
# spatialCovFun = function(x) {0.4 * Exp.cov(x, theta=0.1) + 0.6 * Exp.cov(x, theta=3)}
# mixtureCovFun = function(x) {
# out = spatialCovFun(x)[1,]
# out[x == 0] = 1 + sqrt(.1)
# out
# }
# mixtureCorFun = function(x) { mixtureCovFun(x) * (1 / (1 + sqrt(.1))) }
# spatialCorFun = function(x) {0.4 * Exp.cov(x, theta=thetas[1]) + 0.6 * Exp.cov(x, theta=thetas[2])}
spatialCorFun = function(x) {0.5 * stationary.cov(x, theta=thetas[1], Covariance="Matern", distMat=x, smoothness=nu) +
0.5 * stationary.cov(x, theta=thetas[2], Covariance="Matern", distMat=x, smoothness=nu)}
spatialCovFun = spatialCorFun
mixtureCovFun = function(x) {
out = spatialCorFun(x)
out[x == 0] = 1 + sigma2
out
}
mixtureCorFun = function(x) { mixtureCovFun(x) * (1 / (1 + sigma2)) }
# first to transform all the hyperparameter samples to their relevant values
# 1: error precision
# 2: log effective range
# 3: log spatial variance
# 4-(3 + nLayer - 1): multivariateLogit alpha
# nuggetVarVals = 1 / out[,1]
nuggetVarVals = rep(0, ncol(xSamples))
if(separateRanges) {
kappaVals = t(sweep(sqrt(8)/exp(out[,2:(nLayer+1)]), 2, sapply(latInfo, function(x) {x$latWidth}), "*"))
rhoVals = exp(out[,nLayer+2])
} else {
kappaVals = sqrt(8)/exp(out[,2]) * latticeWidth
rhoVals = exp(out[,3])
}
alphaMat = xSamples
# compute the covariance function for many different hyperparameter samples
out = covarianceDistributionLKINLA(latInfo, kappaVals, rhoVals, nuggetVarVals, alphaMat, precomputationsFileNameRoot=loadFilename)
d = out$d
sortI = sort(d, index.return=TRUE)$ix
d = d[sortI]
covMean = out$cov[sortI]
upperCov=out$upperCov[sortI]
lowerCov=out$lowerCov[sortI]
covMat=out$covMat[sortI,]
corMean = out$cor[sortI]
upperCor=out$upperCor[sortI]
lowerCor=out$lowerCor[sortI]
corMat=out$corMat[sortI,]
covInfo = list(d=d, covMean=covMean, upperCov=upperCov, lowerCov=lowerCov, covMat=covMat,
corMean=corMean, upperCor=upperCor, lowerCor=lowerCor, corMat=corMat)
# plot the covariance function
pdf(file=paste0("Figures/mixtureLKINLACov", plotNameRoot, ".pdf"), width=5, height=5)
plot(d, covMean, type="l", main="Posterior of covariance function", xlab="Distance", ylab="Covariance")
lines(d, lowerCov, lty=2)
lines(d, upperCov, lty=2)
lines(d, mixtureCovFun(d), col="green")
dev.off()
pdf(file=paste0("Figures/mixtureLKINLACor", plotNameRoot, ".pdf"), width=5, height=5)
plot(d, corMean, type="l", main="Posterior of correlation function", xlab="Distance", ylab="Correlation")
lines(d, lowerCor, lty=2)
lines(d, upperCor, lty=2)
lines(d, mixtureCorFun(d), col="green")
dev.off()
yRange = range(c(covMean, lowerCov, upperCov, mixtureCovFun(d)))
pdf(file=paste0("Figures/mixtureLKINLACov", plotNameRoot, ".pdf"), width=5, height=5)
plot(d, covMean, type="l", main="Posterior of covariance function", xlab="Distance", ylab="Covariance",
ylim=yRange)
lines(d, lowerCov, lty=2)
lines(d, upperCov, lty=2)
lines(d, mixtureCovFun(d), col="green")
legend("topright", c("Truth", "Estimate", "80% CI"), lty=c(1, 1, 2), col=c("green", "black", "black"))
dev.off()
pdf(file=paste0("Figures/mixtureLKINLACor", plotNameRoot, ".pdf"), width=5, height=5)
yRange = range(c(corMean, lowerCor, upperCor, mixtureCorFun(d)))
plot(d, corMean, type="l", main="Posterior of correlation function", xlab="Distance", ylab="Correlation",
ylim=c(0,1))
lines(d, lowerCor, lty=2)
lines(d, upperCor, lty=2)
lines(d, mixtureCorFun(d), col="green")
legend("topright", c("Truth", "Estimate", "80% CI"), lty=c(1, 1, 2), col=c("green", "black", "black"))
dev.off()
# get scoring rules
testIndices = (length(preds) - length(ysTest) + 1):length(preds)
leftOutIndices = (length(preds) - length(ysTest) + 1):(length(preds) - length(ysTest) + length(simulationData$zTest[,1]))
gridIndices = (length(preds) - length(ysTest) + length(simulationData$zTest[,1]) + 1):length(preds)
leftOutIndicesTest = match(leftOutIndices, testIndices)
gridIndicesTest = match(gridIndices, testIndices)
# first calculate scoring rules at grid points
truth = ysTest[gridIndicesTest]
est = preds[gridIndices]
vars = predSDs[gridIndices]^2
lower = fit$lower[gridIndices]
upper = fit$upper[gridIndices]
# compute nearest neighbor distances and scores as a function of them
gridPts = predPts[gridIndices,]
distMat = rdist(coords, gridPts)
nndists = apply(distMat, 2, function(x) {min(x[x != 0])})
print("Binned grid scores:")
gridScoringRules = getScores(truth, est, vars, lower, upper, distances=nndists, breaks=distanceBreaks)
print(gridScoringRules$pooledResults)
print(gridScoringRules$binnedResults)
# now calculate square rules at left out points
truth = ysTest[leftOutIndicesTest]
est = preds[leftOutIndices]
vars = predSDs[leftOutIndices]^2
lower = fit$lower[leftOutIndices]
upper = fit$upper[leftOutIndices]
leftOutScoringRules = getScores(truth, est, vars, lower, upper)
leftOutScoringRules = data.frame(c(leftOutScoringRules, Time=time[3]))
print("Binned left out scores:")
print(leftOutScoringRules)
scoringRules = list(gridScoringRules=gridScoringRules, leftOutScoringRules=leftOutScoringRules)
#
# # get scoring rules
# truth = ysTest
# est = preds[testIndices]
# vars = predSDs[testIndices]^2
# lower = fit$lower[testIndices]
# upper = fit$upper[testIndices]
#
# # compute nearest neighbor distances and scores as a function of them
# testPts = predPts[testIndices,]
# distMat = rdist(coords, testPts)
# nndists = apply(distMat, 2, function(x) {min(x[x != 0])})
# print("Binned scores:")
# scoringRules = getScores(truth, est, vars, lower, upper, distances=nndists, breaks=distanceBreaks)
# scoringRules$pooledResults = data.frame(c(scoringRules$pooledResults, Time=time[3]))
# print(scoringRules$binnedResults)
# print("Grid scores:")
# print(getScores(truth[gridTestI], est[gridTestI], vars[gridTestI], lower[gridTestI], upper[gridTestI],
# distances=nndists[gridTestI], breaks=distanceBreaks)$binnedResults)
#
# # plot scores as a function of distance
# distanceScores = getScores(truth[gridTestI], est[gridTestI], vars[gridTestI], lower[gridTestI], upper[gridTestI],
# distances=nndists[gridTestI], breaks=distanceBreaks)$binnedResults
# pdf(file=paste0("Figures/mixtureSPDEScoreBias", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$Bias, pch=19, col="blue", main="Bias", ylab="Bias", xlab="Nearest neighbor distance (km)")
# abline(h=0, lty=2)
# dev.off()
#
# pdf(file=paste0("Figures/mixtureSPDEScoreVar", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$Var, pch=19, col="blue", main="Variance", ylab="Variance", xlab="Nearest neighbor distance (km)",
# ylim=c(0, max(distanceScores$Var)))
# abline(h=0, lty=2)
# dev.off()
#
# pdf(file=paste0("Figures/mixtureSPDEScoreMSE", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$MSE, pch=19, col="blue", main="MSE", ylab="MSE", xlab="Nearest neighbor distance (km)",
# ylim=c(0, max(distanceScores$MSE)))
# abline(h=0, lty=2)
# dev.off()
#
# pdf(file=paste0("Figures/mixtureSPDEScoreRMSE", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$RMSE, pch=19, col="blue", main="RMSE", ylab="RMSE", xlab="Nearest neighbor distance (km)",
# ylim=c(0, max(distanceScores$RMSE)))
# abline(h=0, lty=2)
# dev.off()
#
# pdf(file=paste0("Figures/mixtureSPDEScoreCRPS", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$CRPS, pch=19, col="blue", main="CRPS", ylab="CRPS", xlab="Nearest neighbor distance (km)",
# ylim=c(0, max(distanceScores$CRPS)))
# abline(h=0, lty=2)
# dev.off()
#
# pdf(file=paste0("Figures/mixtureSPDEScoreCvg", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$Coverage, pch=19, col="blue", main="80% Coverage", ylab="80% Coverage", xlab="Nearest neighbor distance (km)",
# ylim=c(0, max(distanceScores$Coverage)))
# abline(h=0, lty=2)
# dev.off()
#
# pdf(file=paste0("Figures/mixtureSPDEScoreWidth", plotNameRoot, ".pdf"), width=5, height=5)
# plot(distanceScores$NNDist, distanceScores$Width, pch=19, col="blue", main="Width", ylab="Width", xlab="Nearest neighbor distance (km)",
# ylim=c(0, max(distanceScores$Width)))
# abline(h=0, lty=2)
# dev.off()
if(!useKenya) {
# print("Pooled scores:")
# print(data.frame(c(getScores(truth, est, vars, lower, upper), Time=time[3])))
} else {
print("Pooled scores:")
print(data.frame(c(getScores(truth, est, vars, lower, upper), Time=time[3])))
print("Overall scores:")
print(data.frame(c(getScores(truth[overallTestI], est[overallTestI], vars[overallTestI], lower[overallTestI], upper[overallTestI]), Time=time[3])))
print("Rural scores:")
print(data.frame(c(getScores(truth[ruralTestI], est[ruralTestI], vars[ruralTestI], lower[ruralTestI], upper[ruralTestI]), Time=time[3])))
print("Urban scores:")
print(data.frame(c(getScores(truth[urbanTestI], est[urbanTestI], vars[urbanTestI], lower[urbanTestI], upper[urbanTestI]), Time=time[3])))
# print("Grid scores:")
# print(data.frame(c(getScores(truth[gridTestI], est[gridTestI], vars[gridTestI], lower[gridTestI], upper[gridTestI]), Time=time[3])))
}
# get aggregated predictions
# A = t(sapply(1:(mx*my), getARow))
# A = sweep(A, 1, rowSums(A), "/")
# mx = 100
# my = 100
# predPts = make.surface.grid(list(x=seq(xRangeDat[1], xRangeDat[2], l=mx), y=seq(yRangeDat[1], yRangeDat[2], l=my)))
gridCoords = cbind(simulationData$xGrid, simulationData$yGrid)
# testIndices = (length(preds) - length(ysTest) + 1):length(preds)
# gridIndices = (length(preds) - length(simulationData$xGrid) + 1):length(preds)
# gridIndicesEst = (length(est) - length(simulationData$xGrid) + 1):length(est)
A = makeNumericalIntegralMat(gridCoords, mx=3, my=3)
aggregatedPreds = A %*% preds[gridIndices]
truth = A %*% ysTest[gridIndicesTest]
est = A %*% preds[gridIndices]
aggregatedPredMat = A %*% fit$predMat[gridIndices,]
vars = apply(aggregatedPredMat, 1, var)
sds = apply(aggregatedPredMat, 1, sd)
lower = apply(aggregatedPredMat, 1, function(x) {quantile(x, probs=.1)})
upper = apply(aggregatedPredMat, 1, function(x) {quantile(x, probs=.9)})
predictionMatrix = data.frame(Truth=truth, Est=est, SDs=sds, Lower=lower, Upper=upper)
print("Aggregated prediction summary statistics:")
print(predictionMatrix)
print("Pooled aggregated scores:")
pooledAggregatedScores = getScores(truth, est, vars, lower, upper)
print(pooledAggregatedScores)
print("Left out region aggregated scores:")
leftOutAggregatedScores = getScores(truth[5], est[5], vars[5], lower[5], upper[5])
leftOutAggregatedScores$Var = sds[5]
names(leftOutAggregatedScores)[2] = "Predictive.SD"
print(leftOutAggregatedScores)
print("Included regions aggregated scores:")
includedAggregatedScores = getScores(truth[-5], est[-5], vars[-5], lower[-5], upper[-5])
print(includedAggregatedScores)
aggregatedScoringRules = list(pooledAggregatedScores=pooledAggregatedScores, leftOutAggregatedScores=leftOutAggregatedScores,
includedAggregatedScores=includedAggregatedScores)
fit$mod = NULL
if(!gscratch)
save(scoringRules, fit, covInfo, predictionMatrix, aggregatedScoringRules, file=paste0("savedOutput/simulations/mixtureLKINLA", plotNameRoot, ".RData"))
else
save(scoringRules, fit, covInfo, predictionMatrix, aggregatedScoringRules, file=paste0("/work/johnpai/mixtureLKINLA", plotNameRoot, ".RData"))
invisible(list(scoringRules, fit, covInfo, predictionMatrix, aggregatedScoringRules))
}
# tests the fitLKINLAStandard function using data simulated from the LK model
# buffer: buffer distance between domain edge of basis lattice and domain edge of data.
# n: number of observations
# xRange: range of x coordinates
# yRange: range of y coordinates
# nx: number of basis function lattice points in x directions
# NOTE: ny is determined automatically to match scale of x lattice points
# Xmat: design matrix
# ys: observations
# first.time: is first time evaluating function. User should always set to FALSE
# thetas: originally was c(.1, 3), but 3 is too large
# testLKINLAModelMixtureMultiple = function(seed=1, nSamples=10, nLayer=3, nx=20, ny=nx, assumeMeanZero=TRUE, nu=1,
# nBuffer=5, normalize=TRUE, fastNormalize=TRUE, NC=14, testCovs=FALSE,
# printVerboseTimings=FALSE, latInfo=NULL, n=900, thetas=NULL,
# testfrac=.1, plotNameRoot="", sigma2=.1^2, useKenya=FALSE,
# effRangeRange=NULL, urbanOverSamplefrac=0,
# intStrategy="ccd", strategy="gaussian", separateRanges=FALSE,
# leaveOutRegion=TRUE) {
testLKINLAModelMixtureMultiple = function(seed=1, nSamples=100, NC=14, nLayer=3, separateRanges=FALSE, n=900, nu=1, sigma2=0.1^2,
useKenya=FALSE, assumeMeanZero=TRUE, urbanOverSamplefrac=0, gscratch=TRUE, ...) {
# set random seeds for each simulation
set.seed(seed)
allSeeds = sample(1:1000000, nSamples, replace = FALSE)
# load in the results
print("Loading in simulation results")
# set plotNameRoot
if(length(NC) == 1) {
if(separateRanges)
NC = c(14, 126) # by default, use two layers with the finest layer having resolution equal to 10km
}
if(separateRanges)
nLayer = length(NC)
# set plotNameRoot
# > 2/.08 * 5
# [1] 125
# > 2/.8 * 5
# [1] 12.5
ncText = ""
if(length(NC) == 1) {
if(separateRanges)
ncText = "_NC14_126"
else {
ncText = paste0("_NC", NC)
}
} else {
tempText = do.call("paste0", as.list(c(NC[1], paste0("_", NC[-1]))))
ncText = paste0("_NC", tempText)
}
plotNameRoot = paste0("_L", nLayer, ncText, "_sepRange", separateRanges, "_n", n, "_nu", nu, "_nugV",
round(sigma2, 2), "_Kenya", useKenya, "_noInt", assumeMeanZero, "_urbOversamp", round(urbanOverSamplefrac, 4))