A Random subsample of data(exp2d), or
Latin Hypercube sampled data evaluated with exp2d.Z
Usage
exp2d.rand(n1 = 50, n2 = 30, lh = NULL, dopt = 1)
Arguments
n1
Number of samples from the first, interesting, quadrant
n2
Number of samples from the other three, uninteresting, quadrants
lh
If !is.null(lh) then Latin Hypercube (LH) sampling
(lhs) is used instead of subsampling from
data(exp2d); lh should be a single nonnegative
integer specifying the desired number of predictive locations,
XX; or, it should be a vector of length 4, specifying the
number of predictive locations desired from each of the four
quadrants (interesting quadrant first, then counter-clockwise)
dopt
If dopt >= 2 then d-optimal subsampling from LH
candidates of the multiple indicated by the value of
dopt will be used. This argument only
makes sense when !is.null(lh)
Details
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 D-optimal subsample of size n1 from the
first (interesting) quadrant. Similarly n2*dopt in the
rest of the un-interesting region.
A total of lh*dopt candidates will be used for sequential D-optimal
subsampling for predictive locations XX in all four
quadrants assuming the already-sampled X locations will
be in the design.
In all three cases, the response is evaluated as
Z(X) = X1 * exp(-X1^2-X2^2),
thus creating the outputs Ztrue and ZZtrue.
Zero-mean normal noise with sd=0.001 is added to the
responses Z and ZZ
Value
Output is a list with entries:
X
2-d data.frame with n1 + n2 input locations
Z
Numeric vector describing the responses (with noise) at the
X input locations
Ztrue
Numeric vector describing the true responses (without
noise) at the X input locations
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