s.chi {emulator} | R Documentation |
Returns estimator for a priori sigma^2
s.chi(H, Ainv, d, s0 = 0, fast.but.opaque = TRUE)
H |
Regression basis function (eg that returned by regressor.multi() ) |
Ainv |
inv(A) where A is a correlation matrix (eg that
returned by corr.matrix() ) |
d |
Vector of data points |
s0 |
Optional offset |
fast.but.opaque |
Boolean, with default TRUE meaning to
use quad.form() , and FALSE meaning to use straightforward
%*% . The first form should be faster, but the code is less
intelligible than the second form. Comparing the returned value
with this argument on or off should indicate the likely accuracy attained. |
See O'Hagan's paper (ref below), equation 12 for details and context.
Robin K. S. Hankin
A. O'Hagan 1992. “Some Bayesian Numerical Analysis”, pp345-363 of Bayesian Statistics 4 (ed J. M. Bernardo et al), Oxford University Press
# example has 10 observations on 6 dimensions. # function is just sum( (1:6)*x) where x=c(x_1, ... , x_2) data(toy) val <- toy colnames(val) <- letters[1:6] H <- regressor.multi(val) d <- apply(H,1,function(x){sum((0:6)*x)}) # create A matrix and its inverse: A <- corr.matrix(val,scales=rep(1,ncol(val)), power=1.5) Ainv <- solve(A) # add some suitably correlated noise: d <- as.vector(rmvnorm(n=1, mean=d, 0.1*A)) # now evaluate s.chi(): s.chi(H, Ainv, d) # assess accuracy: s.chi(H, Ainv, d, fast=TRUE) - s.chi(H, Ainv, d, fast=FALSE)