imputer: Imputation step in stochastic EM for the non-nested DNA Model

In DNAmf: Diffusion Non-Additive Model with Tunable Precision

Imputation step in stochastic EM for the non-nested DNA Model

Description

The function performs the imputation step of the stochastic EM algorithm for the DNA model when the design is not nested. The function generates pseudo outputs \widetilde{\mathbf{y}}_l at pseudo inputs \widetilde{\mathcal{X}}_l.

Usage

imputer(XX, yy, kernel=kernel, t, pred1, fit2)

Arguments

XX	A list of design sets for all fidelity levels, containing X_star, X_list, and X_tilde.
yy	A list of current observed and pseudo-responses, containing y_star, y_list, and y_tilde.
kernel	A character specifying the kernel type to be used. Choices are "sqex"(squared exponential), "matern1.5", or "matern2.5".
t	A vector of tuning parameters for each fidelity level.
pred1	Predictive results for the lowest fidelity level f_1. It should include cov obtained by setting cov.out=TRUE.
fit2	A fitted model object for higher fidelity levels f from (t_{-1}, X_{-1}, y_{-1}).

Details

For non-nested designs, pseudo-input locations \widetilde{\mathcal{X}}_l are constructed using the internal makenested function. The imputer function then imputes the corresponding pseudo outputs \widetilde{\mathbf{y}}_l = f_l(\widetilde{\mathcal{X}}_l) by drawing samples from the conditional normal distribution, given fixed parameter estimates and previous-level outputs Y_{-L}^{*(m-1)}, at the m-th iteration of the EM algorithm.

For further details, see Heo, Boutelet, and Sung (2025+, <arXiv:2506.08328>).

Value

An updated yy list containing:

• y_star: An updated pseudo-complete outputs \mathbf{y}^*_l.

• y_list: An original outputs \mathbf{y}_l.

• y_tilde: A newly imputed pseudo outputs \widetilde{\mathbf{y}}_l.

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