| sigmahatsquared {emulator} | R Documentation |
Returns maximum likelihood estimate for sigma squared. The
“.A” form does not need Ainv, thus removing the need to
invert A. Note that this form is slower than
the other if Ainv is known in advance, as solve(.,.) is slow.
sigmahatsquared(H, Ainv, d) sigmahatsquared.A(H, A, d)
H |
Regressor matrix (eg as returned by regressor.multi()) |
A |
Correlation matrix (eg corr.matrix(val)) |
Ainv |
Inverse of the correlation matrix (eg solve(corr.matrix(val))) |
d |
Vector of observations |
The formula is
ommitted; see pdf
where y is the data vector, H the matrix whose rows are the regressor functions of the design matrix, A the correlation matrix, n the number of observations and q the number of elements in the basis function.
Robin K. S. Hankin
## First, set sigmasquared to a value that we will try to estimate at the end:
REAL.SIGMASQ <- 0.3
## First, some data:
val <- latin.hypercube(100,6)
H <- regressor.multi(val,func=regressor.basis)
## now some scales:
fish <- c(1,1,1,1,1,4)
## A and Ainv
A <- corr.matrix(as.matrix(val),scales=fish,power=2)
Ainv <- solve(A)
## a real relation; as used in helppage for interpolant:
real.relation <- function(x){sum( (1:6)*x )}
## use the real relation:
d <- apply(val,1,real.relation)
## now add some Gaussian process noise:
d.noisy <- as.vector(rmvnorm(n=1,mean=d, REAL.SIGMASQ*A))
## now estimate REAL.SIGMASQ:
sigmahatsquared(H,Ainv,d.noisy)
## That shouldn't be too far from the real value specified above.
## Finally, a sanity check:
sigmahatsquared(H,Ainv,d.noisy) - sigmahatsquared.A(H,A=A,d.noisy)