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DNAmf (version 0.1.1)

closed_form_DNA: Closed-form prediction for DNAmf model

Description

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.

Usage

closed_form_DNA(
  fit1,
  fit2,
  targett,
  kernel,
  nn,
  tt,
  nlevel,
  x,
  XX = NULL,
  pseudo_yy = NULL
)

Value

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.

Arguments

fit1

A fitted GP object for \(f_1\).

fit2

A fitted GP object for \(f\).

targett

A numeric value of target tuning parameter to predict.

kernel

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".

nn

A vector specifying the number of design points at each fidelity level.

tt

A vector of tuning parameters for each fidelity level.

nlevel

The number of fidelity levels \(L\).

x

A vector or matrix of new input locations to predict.

XX

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.

pseudo_yy

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.