closed_form {DNAmf}R Documentation

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

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.

Value

A list of predictive posterior mean and variance for each level containing:


[Package DNAmf version 0.1.0 Index]