Research

I work on uncertainty quantification for expensive experiments and numerical simulations. The main topics are function approximation using Gaussian processes, sequential methods for choosing new simulations efficiently, Bayesian optimization, reliability analysis, set inversion and predictive calibration.

Function approximation using Gaussian processes

Gaussian processes provide a probabilistic framework for approximating an unknown function from a limited number of evaluations. My work addresses the choice of covariance functions and parameter selection, regularized regression, numerical robustness and diagnostics, as well as conditional simulation and the assessment of predictive distributions.

Current directions include calibration, multi-fidelity experiments, high-dimensional problems and large numbers of observations. The aim is to understand not only pointwise accuracy, but also whether the predictive distribution is appropriate for the quantity or decision of interest.

Sequential design and Stepwise Uncertainty Reduction

In sequential design, each new evaluation point is chosen using the observations already available. Such problems can be formulated within Bayesian decision theory: the next point is selected to minimize the expected remaining uncertainty about a quantity or decision of interest.

Applications of Stepwise Uncertainty Reduction include excursion-set estimation, failure-probability estimation, reliable set inversion and quantile-set inversion. The articles on failure-probability estimation (2012) and parallel SUR for excursion sets (2014) develop sequential and batch-sequential strategies. Bayesian subset simulation (2017) combines Gaussian-process-based sequential design with subset simulation for estimating small failure probabilities. The same principle extends to multi-fidelity computer experiments, where the information expected from an evaluation must be balanced against its cost.

Bayesian optimization

Bayesian optimization addresses the optimization of expensive-to-evaluate functions. The work covers an informational criterion for global optimization (2009), convergence properties of expected improvement (2010), a fully Bayesian expected improvement criterion (2011), and constrained single- and multi-objective optimization (2017). More recent results establish simple-regret rates and minimax optimality for fixed-prior expected improvement in Matérn and squared-exponential RKHSs.

Recent work studies the calibration of the lower tail of Gaussian-process predictive distributions for expected improvement. In minimization, this part of the distribution directly drives the exploration-exploitation trade-off, so calibration must be considered in relation to the optimization objective.

Calibration of predictive distributions

Predictive distributions obtained from a Gaussian process can be miscalibrated, in particular when covariance parameters are selected from the data. I study Bayesian and conformal approaches to improve coverage and probabilistic calibration while retaining predictive distributions that can be used in sequential algorithms.

Current themes include design-marginal calibration, goal-oriented calibration and cross-validation-based diagnostics. They connect the statistical assessment of predictive distributions with the decisions made from them.

Scientific software

My methodological work is accompanied by open-source software development. GPmp provides tools for function approximation using Gaussian processes, including interpolation and regression, parameter selection, diagnostics, fast leave-one-out cross-validation, conditional simulation and posterior exploration. gpmp-contrib provides higher-level methods for Bayesian optimization, excursion-set estimation and set inversion. I previously contributed to STK, a MATLAB/Octave toolbox for kriging.

PhD students

PhD students supervised or co-supervised, in chronological order:

• Miguel Piera-Martinez
• Julien Villemonteix
• Aimad El Habachi
• Sándor Bilicz
• Ling Li
• Romain Benassi
• Paul Féliot
• Rémi Stroh
• Bruno Tebbal Barracosa
• Sébastien Petit
• Subhasish Basak
• Romain Ait Abdelmalek-Lomenech
• Boris Kratz
• Enikő Bartók
• Aurélien Pion
• Mohamed Badi

Selected publications

• 2026 — A. Pion and E. Vazquez, Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization, ICML 2026.
• 2026 — E. Vazquez and S. Petit, Simple-regret rates and minimax optimality of fixed-prior expected improvement in Matérn and squared-exponential RKHSs, preprint.
• 2025 — A. Pion and E. Vazquez, Design-Marginal Calibration of Gaussian Process Predictive Distributions: Bayesian and Conformal Approaches, preprint.
• 2025 — S. J. Petit, J. Bect and E. Vazquez, Relaxed Gaussian Process Interpolation: a Goal-Oriented Approach to Bayesian Optimization, Journal of Machine Learning Research, 26(195), 1–70.
• 2025 — R. Ait Abdelmalek-Lomenech, J. Bect, V. Chabridon and E. Vazquez, Bayesian Sequential Design of Computer Experiments for Quantile Set Inversion, Technometrics, 67(1), 112–121.
• 2023 — S. J. Petit, J. Bect, P. Feliot and E. Vazquez, Parameter Selection in Gaussian Process Interpolation: An Empirical Study of Selection Criteria, SIAM/ASA Journal on Uncertainty Quantification, 11(4), 1308–1328.
• 2022 — R. Stroh, J. Bect, S. Demeyer, N. Fischer, D. Marquis and E. Vazquez, Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction, Technometrics, 64(2), 199–209.
• 2017 — P. Feliot, J. Bect and E. Vazquez, A Bayesian Approach to Constrained Single- and Multi-Objective Optimization, Journal of Global Optimization, 67(1), 97–133.
• 2017 — J. Bect, L. Li and E. Vazquez, Bayesian Subset Simulation, SIAM/ASA Journal on Uncertainty Quantification, 5(1), 762–786.
• 2014 — C. Chevalier, J. Bect, D. Ginsbourger, E. Vazquez, V. Picheny and Y. Richet, Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set, Technometrics, 56(4), 455–465.
• 2012 — J. Bect, D. Ginsbourger, L. Li, V. Picheny and E. Vazquez, Sequential Design of Computer Experiments for the Estimation of a Probability of Failure, Statistics and Computing, 22, 773–793.
• 2011 — R. Benassi, J. Bect and E. Vazquez, Robust Gaussian process-based global optimization using a fully Bayesian expected improvement criterion, Learning and Intelligent Optimization, Lecture Notes in Computer Science 6683, 176–190.
• 2010 — E. Vazquez and J. Bect, Convergence properties of the expected improvement algorithm with fixed mean and covariance functions, Journal of Statistical Planning and Inference, 140(11), 3088–3095.
• 2009 — J. Villemonteix, E. Vazquez and E. Walter, An Informational Approach to the Global Optimization of Expensive-to-Evaluate Functions, Journal of Global Optimization, 44(4), 509–534.

See the Publications tab for the complete list.

Last updated: September 2026.