closed_form: Closed-form prediction for DNAmf model

In DNAmf: Diffusion Non-Additive Model with Tunable Precision

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:

• 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.

DNAmf documentation built on June 23, 2025, 5:08 p.m.