On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

DUI client characteristics - an interim analysis of the random assignment process. Interim report.

National Highway Traffic Safety Administration, Office of Driver and Pedestrian Programs, Washington, D.C.

Passenger response to random vibration in transportation vehicles - literature review. Research report.

Transportation Department of Office of University Research, Washington, D.C.

Analysis of a random-assignment short term rehabilitation program. Analytic study 5 and 6.

National Highway Traffic Safety Administration, Office of Driver and Pedestrian Programs, Washington, D.C.

The expectation of parts into which a magnitude is divided at random, investigated mainly by algebraical methods,

A chapter supplementary to the author's Choice and Chance.

Analog computation with random pulse sequences.

Vita.

Random number generation on the I.B.M. 360.

"Errata" ([3] p.) inserted.

On random 3-2 trees /

"UIUCDCS-R-74-679"

RASER: random to serial converter.

"COO 1469-0209."

A display for demonstrating analog computations with random pulse sequences,

"Supported in part by the Office of Naval Research under Contract N000 14-67-A-0305-0007."

Generating pseudo-random numbers in the ILLIAC /

"This work has been supported by Contract N6ori-71 Task XXX United States Navy ONR NR 044 001"

Random generation of sentences from context free and context sensitive phrase structure grammars.

Bibliography: p. 67.