Validation of the Twin-Point-Design Concept in the Design of Computer Experiments

• Activity Number: 511
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Selden Crary*+ and Rachel Johnson
• Companies: Crary Group, Inc. and Naval Postgraduate School
• Keywords: design of computer experiments ; IMSE ; gaussian processes ; twin-points ; essential discontinuity ; rational function

Abstract

We use symbolic analysis to circumvent the notorious ill-conditioning of the covariance matrix V used for computing the integrated mean squared error (IMSE) in gaussian-processes design of experiments. The steps are as follows: (1) expand V in powers of the Cartesian components deltai, i=1 to D, of the separation between the pair of proximal design points x1 and x2; (2) invert the key matrix in hybrid-numeric-symbolic form and expand the inverse in powers of the deltai; (3) compute IMSE as a rational function of power laws in the deltai; and (4) take the limit as the deltai go to zero. The potentially problematic terms of the inverse cancel identically. This method allows the computation of IMSE for designs with a pair of proximal points, without requiring extended-precision arithmetic. The method validated twin-point designs described in the engineering literature using extended-precisi