IMM

INFORMATICS AND STATISTICAL MODELLING

Technological University of Denmark

DK-2800 Kgs. Lyngby – Denmark

DACE

A M ATLAB Kriging Tool kit

Version 2 . 0, August 1, 2002

Søren N. Lophaven

Hans Bruun Nielsen

Jacob Søndergaard

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Technical Report IMM-TR-2002-12

Please immediate communication to Hans Bruun Nielsen ([email protected] dtu. dk)

Contents

1 . Introduction

you

2 . Modeling and Prediction

1

2 . 1 . The Kriging Predictor..........................

2

2 . 2 . Regression Models............................

5

2 . several. Correlation Designs............................

6

several. Generalized Least Squares Suit

9

3. 1 . Computational Aspects.......................... 10 4. Experimental Design

doze

4. 1 ) Rectangular Grid............................. 12 four. 2 . Latina Hypercube Sampling........................ 12 a few. Reference Manual

13

your five. 1 . Style Construction............................ 18 5. 2 . Evaluate the Version............................ 15 five. 3. Regression Models............................ 16 5. 4. Correlation Designs............................ 17 your five. 5. Experimental Design........................... 18 5. six. Auxiliary Functions............................ 19 five. 7. Data Files................................. 20 six. Examples of Usage

21

six. 1 . Work-through Example.......................... 21 years old 6. installment payments on your Adding a Regression Function...................... 24 7. Notation

24

1 .

Intro

This record describes the backdrop for and use of the software program package DACE (Design and Analysis of Computer Experiments), which is a Matlab toolbox intended for working with kriging approximations to computer designs.

The typical make use of this applications are to construct a kriging approximation model based on data from a computer experiment, and to use this approximation unit as a surrogate for the pc model. In this article, a computer try things out is a variety of pairs of input and responses from runs of the computer style. Both the suggestions and the response from the computer system model will tend to be high dimensional. The computer types we address are deterministic, and thus an answer from a model lacks random error, i. e., repeated runs for the same input parameters gives the same response through the model.

Often the approximation types are needed as a part of a design difficulty, in which the greatest set of parameters for working the computer version is determined. To example challenges where a laptop model is definitely fitted to physical info. This design and style problem is associated with the more basic problem of predicting output from a computer model at untried inputs.

In Section 2 all of us consider designs for laptop experiments and efficient predictors, Section several discusses generalized least potager and rendering aspects, in addition to Section four we consider experimental design for the predictors. Section 5 is actually a reference manual for the toolbox, and finally examples of usage and list of explication are given in Sections six and several.

2 .

Modelling and Conjecture

Given a set of m design and style sites S i9000 = [s1 · · · sm ] with si ∈ I d and reactions R

Sumado a = [y1 · · · ym ] with yi ∈ I q. The data is assumed to satisfy the normalization R

conditions1

µ[S:, j ] = 0,

V S:, m, S:, l = one particular, j = 1,..., in,

(2. 1)

V Con:, j, Y:, j = 1, l = you,..., q,

µ[Y:, l ] = zero,

where X:, j is definitely the vector provided by the jth column in matrix Times, and µ[ · ] and Versus ·, · denote respectively the imply and the covariance.

Following [9] we adopt a model con that expresses the deterministic response y(x) ∈ My spouse and i q, ˆ

R...

References: [1] G. Golub, C. Van Financial loan, Matrix Computations. Johns Hopkins University Press,

Baltimore, UNITED STATES, 3rd release, 1996.

[2] E. H. Isaaks, Ur. M. Srivastava, An Introduction to Applied Geostatistics. Oxford

School Press, New York, USA, 1989.

Elsevier, Nyc, USA, late 1960s.

DTU. (2002), 44 web pages. Available since

http://www.imm.dtu.dk/∼hbn/publ/TR0213.ps

Randomly Fields. Physica-Verlag, Heidelberg, Australia, 2001.

[7] J. Nocedal, S. M. Wright, Statistical Optimization, Springer, New York, UNITED STATES,

1999.

a few, pp. 479-488, 1998.

[9] J. Sacks, W. J. Welch, T. J. Mitchell, H. L. Wynn, Style and Evaluation of Laptop Experiments, Statistical Science, vol. 4, no . 4, pp. 409-435, 1989.

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