Corpus ID: 88522782

The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters

@article{Crary2017TheNC,
  title={The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters},
  author={Selden B. Crary and Richard Diehl Martinez and Michael A. Saunders},
  journal={arXiv: Methodology},
  year={2017}
}
This paper is an extension of Parts I and Ia of a series about Nu-class multifunctions. We provide hand-generated algebraic expressions for integrals of single Matern-covariance functions, as well as for products of two Matern-covariance functions, for all odd-half-integer class parameters. These are useful both for IMSPE-optimal design software and for testing universality of Nu-class-multifunction properties, across covariance classes. 

References

SHOWING 1-6 OF 6 REFERENCES
The Nu Class of Low-Degree-Truncated Rational Functions. I. IMSPE in Design of Computer Experiments: Integrals and Very-Low-N, Single-Factor, Free-Ranging Designs
We provide detailed algebra for determining the integrated mean-squared prediction error (IMSPE) of designs of computer experiments, with one factor and one or two points, under the exponential,
Approximation of IMSE-optimal Designs via Quadrature Rules and Spectral Decomposition
TLDR
It is shown that the IMSE and its approximation by spectral truncation can be easily evaluated, which makes their global minimization affordable.
Combinatorial proofs of inverse relations and log-concavity for Bessel numbers
TLDR
Bessel numbers satisfy two properties of Stirling numbers: the two kinds of Bessel numbers are related by inverse formulas, and both BesselNumbers of the first kind and those of the second kind form log-concave sequences.
Four-Point, 2D, Free-Ranging, IMSPE-Optimal, Twin-Point Designs
We report the discovery of a set of four-point, two-factor, free-ranging, putatively IMSPE-optimal designs with a pair of twin points, in the statistical design of computer experiments, under
The Fubini Principle
TLDR
The number of permutations leaving j unchanged is (n − 1)!, so that the sum of the ones, counted by columns, equals S = n · ( n − 1)! = n!.
Using derivative information in the statistical analysis of computer models
TLDR
A Gaussian process emulator is proposed which, as long as the model is suitable for emulation, can be used to estimate derivatives even without any derivative information known a priori, to reduce the demand for writing and running adjoint models.