The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions. Ic. IMSPE-optimal designs with circular-disk prediction domains

TL;DR

This paper develops a method to compute IMSPE for computer experiment designs within circular disks, extending previous work on Nu-class functions, and demonstrates optimal designs including twin-point configurations.

Contribution

It introduces a new method for calculating IMSPE in circular domains and identifies novel optimal designs, including twin-point arrangements, expanding the scope of prior research.

Findings

Method for IMSPE computation in circular disks

Optimal designs include twin-point configurations

Designs are extendable to multiple factors and domains

Abstract

This paper is an extension of Part I of a series about Nu-class multifunctions. A method is presented for computing the integrated mean-squared prediction error (IMSPE) in the design of computer experiments, when the prediction domain is a circular disk. The method is extensible to more than two factors, to prediction domains other than squares or disks, and to a variety of assumed covariance functions. Three example optimal designs, under Gaussian covariance with known hyperparameters, are found using the method: an n=1 design centered on the disk; an n=2 continuously rotatable design with assumed inversion symmetry about the center of the disk; and an n=4 twin-point design similar to the n=4 twin-point design observed previously for a square prediction domain [1]. The four-point design on the disk demonstrates that non-round boundaries are not a prerequisite for the occurrence of twin-point optimal designs.