** Xavier
Bay's Homepage **

**Ecole
des Mines de Saint-Etienne (ENSM-SE), LSTI/Crocus, 3MI
158, cours Fauriel
**

tel: (33) 4.77.42.00.23

e-mail: bay@emse.fr

___________________________________

**Current research papers
(2010):**

**Abstract: **The
orthogonal projection associated to optimal interpolation in a reproducing
kernel Hilbert space is characterized by the spectral decomposition of an
integral operator. This operator is built from the reproducing kernel and a
measure on the interpolation set. As an application, we illustrate how boundary
value constraints can be enforced in Gaussian process models.

**Keywords:**
Reproducing kernel Hilbert space, Optimal interpolation, Integral Operator,
Kriging, Boundary value constraints

X. Bay, B. Gauthier, *Extended
Formula For Kriging Interpolation*, submitted July 2^{nd}, 2010

**Abstract: **In
many fields, Kriging interpolation techniques are used within a finite discrete
set of known values of a real function (no evaluation or measurement error). In
this paper, we extend the simple Kriging formula to the case the function is
known on a general (infinite) subset of points. This extension is based on the
spectral decomposition of a certain nuclear Hilbert-Schmidt operator. As a step
by step application, we revisit the problem of prediction for the Brownian
sheet knowing its values on a separation line.

**Keywords: **Kriging,
Gaussian process regression, Gaussian processes, Gaussian measure, regular
conditional probability, Gaussian Hilbert spaces, Hilbert-Schmidt operator,
reproducing kernel Hilbert space (RKHS), Karhunen-Loève expansion, Brownian
sheet, separation line

**Abstract:
**The orthogonal
projection associated to optimal interpolation in a Hilbert subspace is characterized
by the spectral decomposition of

problem
adapted integral operators. We then propose a methodology to construct
interpolators that take into account an infinite number of information.

As
an application, we illustrate how boundary constraints can be enforced in
Gaussian process models.

**Keywords:
**Hilbert Subspaces,
Optimal interpolation, Integral Operators, Spectral Decomposition, Infinite
data set