A Random subsample of data(exp2d)
, or
Latin Hypercube sampled data evaluated with exp2d.Z
1  exp2d.rand(n1 = 50, n2 = 30, lh = NULL, dopt = 1)

n1 
Number of samples from the first, interesting, quadrant 
n2 
Number of samples from the other three, uninteresting, quadrants 
lh 
If 
dopt 
If 
When is.null(lh)
, data is subsampled without replacement from
data(exp2d)
. Of the n1 + n2 <= 441
input/response pairs X,Z
, there are n1
are taken from the
first quadrant, i.e., where the response is interesting,
and the remaining n2
are taken from the other three
quadrants. The remaining 441  (n1 + n2)
are treated as
predictive locations
Otherwise, when !is.null(lh)
, Latin Hypercube Sampling
(lhs
) is used
If dopt >= 2
then n1*dopt
LH candidates are used
for to get a Doptimal subsample of size n1
from the
first (interesting) quadrant. Similarly n2*dopt
in the
rest of the uninteresting region.
A total of lh*dopt
candidates will be used for sequential Doptimal
subsampling for predictive locations XX
in all four
quadrants assuming the alreadysampled X
locations will
be in the design.
In all three cases, the response is evaluated as
Z(X) = X1 * exp(X1^2X2^2),
thus creating the outputs Ztrue
and ZZtrue
.
Zeromean normal noise with sd=0.001
is added to the
responses Z
and ZZ
Output is a list
with entries:
X 
2d 
Z 
Numeric vector describing the responses (with noise) at the

Ztrue 
Numeric vector describing the true responses (without
noise) at the 
XX 
2d 
ZZ 
Numeric vector describing the responses (with noise) at
the 
ZZtrue 
Numeric vector describing the responses (without
noise) at the 
Robert B. Gramacy, rbgramacy@chicagobooth.edu, and Matt Taddy, taddy@chicagobooth.edu
Gramacy, R. B. (2007). tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models. Journal of Statistical Software, 19(9). http://www.jstatsoft.org/v19/i09
Gramacy, R. B., Lee, H. K. H. (2007). Bayesian treed Gaussian process models with an application to computer modeling Journal of the American Statistical Association, to appear. Also available as ArXiv article 0710.4536 http://arxiv.org/abs/0710.4536
http://bobby.gramacy.com/r_packages/tgp
lhs
, exp2d
, exp2d.Z
,
btgp
, and other b*
functions
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  ## randomly subsampled data
## 
eds < exp2d.rand()
# higher span = 0.5 required because the data is sparse
# and was generated randomly
eds.g < interp.loess(eds$X[,1], eds$X[,2], eds$Z, span=0.5)
# perspective plot, and plot of the input (X & XX) locations
par(mfrow=c(1,2), bty="n")
persp(eds.g, main="loess surface", theta=30, phi=20,
xlab="X[,1]", ylab="X[,2]", zlab="Z")
plot(eds$X, main="Randomly Subsampled Inputs")
points(eds$XX, pch=19, cex=0.5)
## Latin Hypercube sampled data
## 
edlh < exp2d.rand(lh=c(20, 15, 10, 5))
# higher span = 0.5 required because the data is sparse
# and was generated randomly
edlh.g < interp.loess(edlh$X[,1], edlh$X[,2], edlh$Z, span=0.5)
# perspective plot, and plot of the input (X & XX) locations
par(mfrow=c(1,2), bty="n")
persp(edlh.g, main="loess surface", theta=30, phi=20,
xlab="X[,1]", ylab="X[,2]", zlab="Z")
plot(edlh$X, main="Latin Hypercube Sampled Inputs")
points(edlh$XX, pch=19, cex=0.5)
# show the quadrants
abline(h=2, col=2, lty=2, lwd=2)
abline(v=2, col=2, lty=2, lwd=2)
## Not run:
## Doptimal subsample with a factor of 10 (more) candidates
## 
edlhd < exp2d.rand(lh=c(20, 15, 10, 5), dopt=10)
# higher span = 0.5 required because the data is sparse
# and was generated randomly
edlhd.g < interp.loess(edlhd$X[,1], edlhd$X[,2], edlhd$Z, span=0.5)
# perspective plot, and plot of the input (X & XX) locations
par(mfrow=c(1,2), bty="n")
persp(edlhd.g, main="loess surface", theta=30, phi=20,
xlab="X[,1]", ylab="X[,2]", zlab="Z")
plot(edlhd$X, main="Doptimally Sampled Inputs")
points(edlhd$XX, pch=19, cex=0.5)
# show the quadrants
abline(h=2, col=2, lty=2, lwd=2)
abline(v=2, col=2, lty=2, lwd=2)
## End(Not run)

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