The function computes the closed-form posterior mean and variance for the DNAmf model both at the fidelity levels used in model fitting and at any user-specified target fidelity level, using the chosen nonseparable kernel.
closed_form_DNA(
fit1,
fit2,
targett,
kernel,
nn,
tt,
nlevel,
x,
XX = NULL,
pseudo_yy = NULL
)A list of predictive posterior mean and variance for each level containing:
mu_1, sig2_1, ..., mu_L, sig2_L: A vector of predictive posterior mean and variance at each level.
mu: A vector of predictive posterior mean at target tuning parameter.
sig2: A vector of predictive posterior variance at target tuning parameter.
A fitted GP object for \(f_1\).
A fitted GP object for \(f\).
A numeric value of target tuning parameter to predict.
A character specifying the kernel type to be used. Choices are "sqex"(nonseparable squared exponential kernel), "matern1.5"(nonseparable Matern kernel with \(\nu=1.5\)), or "matern2.5"(nonseparable Matern kernel with \(\nu=2.5\)). Default is "sqex".
A vector specifying the number of design points at each fidelity level.
A vector of tuning parameters for each fidelity level.
The number of fidelity levels \(L\).
A vector or matrix of new input locations to predict.
A list containing a pseudo-complete inputs X_star(\(\left\{\mathcal{X}^*_l\right\}_{l=1}^{L}\)), an original inputs X_list(\(\left\{\mathcal{X}_l\right\}_{l=1}^{L}\)), and a pseudo inputs X_tilde(\(\left\{\widetilde{\mathcal{X}}_l\right\}_{l=1}^{L}\)) for non-nested design.
A list containing a pseudo-complete outputs y_star(\(\left\{\mathbf{y}^*_l\right\}_{l=1}^{L}\)), an original outputs y_list(\(\left\{\mathbf{y}_l\right\}_{l=1}^{L}\)), and a pseudo outputs y_tilde(\(\left\{\widetilde{\mathbf{y}}_l\right\}_{l=1}^{L}\)) imputed by imputer_DNA.