Séminaire LJK-Statistique

 

Le Jeudi 11 Février 2010 à 14h00 en Salle 1 - Tour IRMA

 

Séminaire de Olivier ROUSTANT (École des Mines de Saint-Etienne)

 

A new statistical and graphical tool for selecting space-filling designs in computer experiments

 

Résumé:

 

Computer experiments is a research field devoted to the analysis of costly simulators that are modelling complex phenomenon (as crash-test, nuclear accident, ...). When no simulations have been run, one often tries to follow the two requirements. First, filling space as uniformly as possible. Space-filling designs (SFD) were introduced in that respect. Furthermore, most of the time, the codes depend only a few influential variables, which may be linear combinations of the given variables. Hence, it is desirable that the space-filling property should be also satisfied in the (orthogonal) projection onto subspaces.
Some designs are conceived in this sense as Latin hypercubes or orthogonal arrays, but they consider only the projections onto the axes or the coordinate planes. We introduce a statistic which allows studying the good distribution of points according to all 1-dimensional projections. By angularly scanning the domain, we obtain a useful graphical representation. The advantages of this new tool are demonstrated on usual SFDs. In particular, we show how to select good 8D-designs of size 80.

Keywords: computer experiments, space-filling designs, dimension reduction.