Additivity and Ortho-Additivity in Gaussian Random Fields

Nicolas Lenz (1)

1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]

This master thesis presents a decomposition of squared-integrable covariance kernels into so-called additive, ortho-additive, and cross-covariance parts. This decomposition governs to some extent the additivity of associated Gaussian random field paths, and can be used to assess the degree of additivity of functions approximated by Gaussian process modelling. The decomposition is explicitely calculated for tensor product kernels, and numerical experiments illustrate the potential of the approach.

Mots clés: Covariance kernels; additivity; Hilbert space decompositions

Domaines: Modélisation et simulation; Méthodologie [stat.ME]; Machine Learning [stat.ML]; Statistiques [math.ST]; Théorie [stat.TH]

Nicolas Lenz. Additivity and Ortho-Additivity in Gaussian Random Fields. 2013. ⟨hal-01063741⟩