STK_PREDICT performs a kriging prediction from data
CALL: ZP = stk_predict (MODEL, XI, ZI, XP)
performs a kriging prediction at the points XP, given the observations
(XI, ZI) and the prior MODEL. The input arguments XI, ZI, and XP can be
either numerical matrices or dataframes. More precisely, on a factor space
of dimension DIM,
* XI must have size NI x DIM,
* ZI must have size NI x 1,
* XP must have size NP x DIM,
where NI is the number of observations and NP the number of prediction
points. The output ZP is a dataframe of size NP x 2, with:
* the kriging predictor in the first column (ZP.mean), and
* the kriging variance in the second column (ZP.var).
From a Bayesian point of view, ZP.mean and ZP.var are respectively the
posterior mean and variance of the Gaussian process prior MODEL given the
data (XI, ZI). Note that, in the case of noisy data, ZP.var is the
(posterior) variance of the latent Gaussian process, not the variance of a
future noisy observation at location XP.
CALL: [ZP, LAMBDA, MU] = stk_predict (MODEL, XI, ZI, XP)
also returns the matrix of kriging weights LAMBDA and the matrix of
Lagrange multipliers MU.
CALL: [ZP, LAMBDA, MU, K] = stk_predict (MODEL, XI, ZI, XP)
also returns the posterior covariance matrix K at the locations XP (this is
an NP x NP covariance matrix). From a frequentist point of view, K can be
seen as the covariance matrix of the prediction errors.
SPECIAL CASE
If ZI is empty, everything but ZP.mean is computed. Indeed, neither the
kriging variance ZP.var nor the matrices LAMBDA and MU actually depend on
the observed values.