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 |
Ainv |
inv(A) where A is a correlation matrix (eg that
returned by |
d |
Vector of data points |
s0 |
Optional offset |
fast.but.opaque |
Boolean, with default |
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))) 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)