Xavier Bay

• Mines Saint-Étienne

In this paper, we revisit the problem of Bayesian shape-restricted function estimation. The finite-dimensional Gaussian process (GP) approximation proposed by Maatouk and Bay (Math Geosci 49(5): 557–582, 2017) is considered, which admits an equivalent formulation of the shape constraints in terms of basis coefficients. This approximation satisfies...

In this paper, we extend the correspondence between Bayesian estimation and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) by adding convex constraints to the problem. Through a sequence of approximating Hilbertian subspaces and a discretized model, we prove that the Maximum a posteriori (MAP) of the posterior distribution is exactl...

Due to their flexibility Gaussian processes are a well-known Bayesian framework for nonparametric function estimation. Integrating inequality constraints, such as monotonicity, convexity, and boundedness, into Gaussian process models significantly improves prediction accuracy and yields more realistic credible inter- vals in various real-world data...

Gaussian processes have become essential for nonparametric function estimation and are widely used in many fields, like machine learning. In this paper, large scale Gaussian process regression (GPR) is investigated. This problem is related to the simulation of high-dimensional Gaussian vectors truncated on the intersection of a set of hyperplanes....

Generating multivariate normal distributions is widely used in various fields, including engineering, statistics, finance and machine learning. In this paper, simulating large multivariate normal distributions truncated on the intersection of a set of hyperplanes is investigated. Specifically, the proposed methodology focuses on cases where the pri...

Statistical researchers have shown increasing interest in generating conditional multivariate normal distributions. In this paper, we discuss several existing methods for the simulation of multivariate normal distribution truncated on the intersection of a set of hyperplanes. We also propose an approach based Contrarily to the standard approaches,...

In this paper, we extend the correspondence between Bayesian estimation and optimal smoothing in a Reproducing Kernel Hilbert Space (RKHS) adding a convexe constraints on the solution. Through a sequence of approximating Hilbertian spaces and a discretized model, we prove that the Maximum A Posteriori (MAP) of the posterior distribution is exactly...

The need for globally optimizing expensive-to-evaluate functions frequently occurs in many real-world applications. Among the methods developed for solving such problems, the Efficient Global Optimization (EGO) is regarded as one of the state-of-the-art unconstrained continuous optimization algorithms. The surrogate model used in EGO is a Gaussian...

The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectral theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of Gaussian measures on Hilbert spaces, the so-called Karhunen-Lo{\`e}ve expansion. In this paper, we extend this resu...

The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectral theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of Gaussian measures on Hilbert spaces, the so-called Karhunen-L{\`o} eve expansion. In this paper, we extend this res...

Physical phenomena are observed in many fields (science and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input va...

Statistical researchers have shown increasing interest in generating truncated multivariate normal distributions. In this paper, we only assume that the acceptance region is convex and we focus on rejection sampling. We propose a new algorithm that outperforms crude rejection method for the simulation of truncated multivariate Gaussian random varia...

In this paper, we extend the correspondence between Bayes’ estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of convex constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given data interpola...

Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input v...

In this paper, we extend the correspondence between Bayes' estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of linear inequality constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given dat...

Gaussian Processes (GPs) are often used to predict the output of a parameterized deterministic experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of experiments and global optimization. Nearly all of the applications of GPs to Computer Experiments require the...

Statistical researchers have shown increasing interest in generating truncated multivariate normal distributions. In this paper, we only assume that the acceptance region is convex and we focus on rejection sampling. We propose a new algorithm that outperforms crude rejection method for the simulation of truncated multivariate Gaussian random varia...

We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Tw...

http://afst.cedram.org/afst-bin/fitem?id=AFST_2012_6_21_3_439_0

http://www.iste.co.uk/index.php?f=a&ACTION=View&id=261

https://www.eccm-2010.org/abstract_pdf/abstract_936.pdf

Résumé — La conception d'un treillis en présence d'incertitudes gaussiennes est formulé au moyen des critères du quantile de son volume et de son taux de fiabilité. Les estimations de ces critères sont réalisées par simulation de Monte Carlo sur des méta-modèles de krigeage. Cet article discute en particulier le choix des entrées et sorties des mét...

http://editions.lavoisier.fr/not.asp?id=3LKSX3C3R6XOUN

In the computer experiments setting, Space-Filling Designs (SFDs) are widely used to explore the complex relationship between inputs and outputs. In this paper, a new SFD is initially defined with the help of the Strauss process. Through Markov chain Monte-Carlo (McMC) methods, more general Gibbs processes can be used to perform different goals. We...

http://www.lynxial.fr/clients/IA/sitebfa.nsf/596bcf8a875bf7b2c125787b003e73fe/f33b614605a915eac125787b002c6880?OpenDocument&Highlight=0,Roustant

http://typhoon.jaea.go.jp/icnc2003/Proceeding/paper/5.25_063.pdf

Temperature modelling is a major issue for valuation of weather derivatives. Goodness of fit is usually assessed from historical data. However, estimation errors can result in large price uncertainty that may be problematic for practical applications. In this paper, we consider a temperature ARMA model and quantify the price uncertainties for weath...

http://www.actuaries.org/ASTIN/Colloquia/Bergen/Roustant_Laurent_Bay_Carraro.pdf

Rapport d'avancement, contrat ARMINES/IPSN n° 40700B048750/SH

http://www.affi.asso.fr/uploads/Externe/ba/CTR_FICHIER_386_1226353438.doc

Rapport d'avancement, contrat ARMINES/IPSN n° 40700B048750/SH

Rapport d'avancement, contrat ARMINES/IPSN n° 40700B048750/SH

Rapport d'avancement, contrat ARMINES/IPSN n° 40700B048750/SH

The accurate determination of confidence intervals is one of the outstanding problems of the standard Monte Carlo algorithm used for solving the homogeneous neutrons transport equation. If we denote k i the k-effective estimate corresponding to generation i, the best estimate of the eigenvalue after N generations is the average of k i within the N...