The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions. Ia. MINOS for IMSPE Evaluation and Optimal-IMSPE-Design Search

TL;DR

This paper introduces simplified algebraic expressions for complex integrals related to low-degree-truncated rational functions and uses MINOS optimization to identify IMSPE-optimal designs for various correlation functions, aiding design software development.

Contribution

It provides compact algebraic formulas to replace complex integrals and applies MINOS to find optimal experimental designs for specific correlation models.

Findings

Simplified algebraic expressions for integrals I6 and I8.

Tabulated IMSPE-optimal designs for exponential, Matérn, and Gaussian correlations.

Results serve as standards for optimal design software.

Abstract

We provide compact algebraic expressions that replace the lengthy symbolic-algebra-generated integrals I6 and I8 in Part I of this series of papers [1]. The MRSE entries of Part I, Table 4.3 are thus updated to simpler algebraic expressions. We use MINOS [2-4] to tabulate several IMSPE-optimal designs with one factor and one or two design points, for the exponential-, two of the Mat\'ern-, and the Gaussian-correlation functions, i.e. for the class of problems considered in Part I. The tabulated results can be used as standards for optimal-design-software developers and users.