Finite-dimensional approximation of Gaussian processes with inequality constraints and errors measurements

Hassan Maatouk (1, 2, 3)

1 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 ASPI - Applications of interacting particle systems to statistics

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all inputs. We develop a finite-dimensional approximation of GPs capable of incorporating inequality constraints and noisy observations for computer model emulators. It is based on a linear combination between Gaussian random coefficients and deterministic basis functions. By this methodology , the inequality constraints are respected in the entire domain. The mean and the maximum of the posterior distribution are well defined. A simulation study to show the efficiency and the performance of the proposed model in term of predictive accuracy and uncertainty quantification is included.

Mots clés: Finite-dimensional approximation; Shape constraint; Truncated Gaussian vector; inequality constraints; Noisy data; Gaussian processes; uncertainty quantification

Domaines: Méthodologie [stat.ME]; Probabilités [math.PR]

Hassan Maatouk. Finite-dimensional approximation of Gaussian processes with inequality constraints and errors measurements. 2017. ⟨hal-01533356v2⟩