STK_PREDICT performs a kriging prediction CALL: ZP = stk_predict (MODEL, XP) CALL: ZP = stk_predict (MODEL, XI, ZI, XP) performs a kriging prediction at the points XP, given the MODEL and, if available, the data (XI, ZI). The MODEL argument can be either a prior model structure (as provided by stk_model) or a model object (for instance, a posterior model represented by an stk_model_gpposterior object). If MODEL is already a posterior object and some additional data (XI, ZI) is provided, the model is first updated with the data before the prediction is actually carried out. The input arguments XI, ZI, and XP can be either numerical matrices or dataframes. More precisely, on an input 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 prediction mean in the first column (ZP.mean), and * the prediction 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, ...) also returns the matrix of kriging weights LAMBDA and the matrix of Lagrange multipliers MU. CALL: [ZP, LAMBDA, MU, K] = stk_predict (MODEL, ...) 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.
Package: stk