LOO_preds {hetGP}

Leave one out predictions

Description

Provide leave one out predictions, e.g., for model testing and diagnostics. This is used in the method plot available on GP and TP models.

Usage

LOO_preds(model, ids = NULL)

Arguments

model

homGP or hetGP model, TP version is not considered at this point

ids

vector of indices of the unique design point considered (default to all)

Value

list with mean and variance predictions at x_i assuming this point has not been evaluated

Note

For TP models, psi is considered fixed.

References

O. Dubrule (1983), Cross validation of Kriging in a unique neighborhood, Mathematical Geology 15, 687–699.

F. Bachoc (2013), Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification, Computational Statistics & Data Analysis, 55–69.

Examples

set.seed(32)
## motorcycle data
library(MASS)
X <- matrix(mcycle$times, ncol = 1)
Z <- mcycle$accel
nvar <- 1

## Model fitting
model <- mleHomGP(X = X, Z = Z, lower = rep(0.1, nvar), upper = rep(10, nvar),
                  covtype = "Matern5_2", known = list(beta0 = 0))
LOO_p <- LOO_preds(model)
 
# model minus observation(s) at x_i
d_mot <- find_reps(X, Z)

LOO_ref <- matrix(NA, nrow(d_mot$X0), 2)
for(i in 1:nrow(d_mot$X0)){
 model_i <- mleHomGP(X = list(X0 = d_mot$X0[-i,, drop = FALSE], Z0 = d_mot$Z0[-i],
                     mult = d_mot$mult[-i]), Z = unlist(d_mot$Zlist[-i]),
                     lower = rep(0.1, nvar), upper = rep(50, nvar), covtype = "Matern5_2",
                     known = list(theta = model$theta, k_theta_g = model$k_theta_g, g = model$g,
                                  beta0 = 0))
 model_i$nu_hat <- model$nu_hat
 p_i <- predict(model_i, d_mot$X0[i,,drop = FALSE])
 LOO_ref[i,] <- c(p_i$mean, p_i$sd2)
}

# Compare results

range(LOO_ref[,1] - LOO_p$mean)
range(LOO_ref[,2] - LOO_p$sd2)

# Use of LOO for diagnostics
plot(model)