Preprints

1. J. Demange-Chryst, F. Bachoc and J. Morio
   "Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling"
   [arXiv]
2. J. Bona-Pellissier, F. Bachoc and F. Malgouyres
   "Parameter identifiability of a deep feedforward ReLU neural network"
   [arXiv]
3. F. Bachoc and A. Lagnoux
   "Posterior contraction rates for constrained deep Gaussian processes in density estimation and classication"
   [arXiv]
4. F. Bachoc and M. Fathi
   "Bounds in L1 Wasserstein distance on the normal approximation of general M-estimators"
   [arXiv]
5. C. Muehlmann, F. Bachoc, K. Nordhausen and M. Yi
   "Test of the latent dimension of a spatial blind source separation model"
   [arXiv]
6. J. Bétancourt, F. Bachoc and T. Klein
   "Gaussian process regression for scalar and functional inputs with funGp - the in-depth tour"
   [hal]
7. F. Bachoc, F. Gamboa, M. Halford, J-M. Loubes and L. Risser
   "Entropic variable projection for explainability and intepretability"
   [arXiv]

Refereed journal articles

1. F. Bachoc, A. F. López-Lopera and O. Roustant
   "Sequential construction and dimension reduction of Gaussian processes under inequality constraints"
   SIAM Journal on Mathematics of Data Science, forthcoming
   [arXiv]
2. F. Bachoc, A. P. Peron and E. Porcu
   "Multivariate Gaussian random fields over generalized product spaces involving the hypertorus"
   Theory of Probability and Mathematical Statistics, special issue Theory and Applications of Random Fields, forthcoming
   [hal]
3. M.T. Vu, F. Bachoc and E. Pauwels
   "Rate of convergence for geometric inference based on the empirical Christoffel function"
   ESAIM: probability and statistics, forthcoming
   [arXiv]
4. C. Muehlmann, F. Bachoc and K. Nordhausen
   "Blind source separation for non-stationary random fields"
   Spatial Statistics, forthcoming
   [arXiv]
5. B. Broto, F. Bachoc, L. Clouvel and J-M Martinez
   "Block-diagonal covariance estimation and application to the Shapley effects in sensitivity analysis"
   SIAM/ASA Journal on uncertainty quantification, forthcoming
   [arXiv]
6. F. Bachoc, N. Durrande, D. Rullière and C. Chevalier
   "Properties and comparison of some Kriging sub-model aggregation methods"
   Mathematical geosciences, forthcoming
   [pdf] [hal] [arXiv]
7. D. Idier, A. Aurouet, F. Bachoc, A. Baills, J. Betancourt, F. Gamboa, T. Klein, A. F. López-Lopera, R. Pedreros, J. Rohmer and A. Thibault
   "A user-oriented local coastal flooding early warning system using metamodelling techniques"
   Journal of marine science and engineering, 9(11) (2021)
   [journal]
8. A. F. López-Lopera, D. Idier, J. Rohmer and F. Bachoc
   "Multi-output Gaussian processes with functional data: a study on coastal flood hazard assessment"
   Reliability engineering and system safety, forthcoming
   [arXiv]
9. F. Bachoc, E. Porcu, M. Bevilacqua, R. Furrer and T. Faouzi
   "Asymptotically equivalent prediction in multivariate geostatistics"
   Bernoulli, forthcoming
   [arXiv]
10. B. Broto, F. Bachoc, M. Depecker and J.M. Martinez
    "Gaussian linear approximation for the estimation of the Shapley effects"
    SIAM/ASA Journal on uncertainty quantification, forthcoming
    [hal]
11. F. Bachoc, T. Barthe, T. Santner and Y. Richet
    "Sequential design of mixture experiments with an empirically determined input domain and an application to burn-up credit penalization of nuclear fuel rods"
    Nuclear engineering and design, 374 (2021) 111034
    [arXiv]
12. A. Fradi, C. Samir and F. Bachoc
    "A scalable approximate Bayesian inference for high-dimensional Gaussian processes"
    Communications in statistics - theory and methods, (2020)
    [journal]
13. A. Fradi, Y. Feunteunp, C. Samir, M. Baklouti, F. Bachoc and J-M. Loubes
    "Bayesian regression and classification using Gaussian process priors indexed by probability density functions"
    Information sciences, 548(16) (2021) 56-68
    [journal]
14. J-M. Azais, F. Bachoc, A. Lagnoux and T.M.N. Nguyen
    "Semi-parametric estimation of the variogram of a Gaussian process with stationary increments"
    ESAIM: probability and statistics, 24 (2020) 842-882
    [arXiv]
15. F. Bachoc, A. Suvorikova, D. Ginsbourger, J-M. Loubes and V. Spokoiny
    "Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding"
    Electronic journal of statistics, 14(2) (2020) 2742-2772
    [arXiv]
16. F. Bachoc, J. Bétancourt, R. Furrer and T. Klein
    "Asymptotic properties of the maximum likelihood and cross validation estimators for transformed Gaussian processes"
    Electronic journal of statistics, 14(1) (2020) 1962-2008
    [arXiv]
17. B. Broto, F. Bachoc and M. Depecker
    "Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution"
    SIAM/ASA Journal on uncertainty quantification, 8(2) (2020) 693-716
    [arXiv]
18. F. Bachoc and A. Lagnoux
    "Fixed-domain asymptotic properties of composite likelihood estimators for Gaussian processes"
    Journal of statistical planning and inference, 209 (2020) 62-75
    [hal]
19. F. Bachoc, C. Helbert and V. Picheny
    "Gaussian process optimization with failures: classification and convergence proof"
    Journal of global optimization, 78 (2020) 483-506
    [pdf] [hal]
20. J. Betancourt, F. Bachoc, T. Klein, D. Idier, R. Pedreros and J. Rohmer
    "Gaussian process metamodeling of functional-input code for coastal flood hazard assessment"
    Reliability engineering and system safety, 198 (2020) 106870
    [hal]
21. F. Bachoc, M. G. Genton, K. Nordhausen, A. Ruiz-Gazen and J. Virta
    "Spatial blind source separation"
    Biometrika, 107(3) (2020) 627-646
    [arXiv]
22. F. Bachoc, B. Broto, F. Gamboa and J-M. Loubes
    "Gaussian processes indexed on the symmetric group: prediction and learning"
    Electronic journal of statistics, 14 (2020) 503-546
    [arXiv]
23. F. Bachoc, D. Preinerstorfer and L. Steinberger
    "Uniformly valid confidence intervals post-model-selection"
    Annals of statistics, 48(1) (2020) 440-463.
    [arXiv]
24. F. Bachoc, A. Lagnoux and A. F. López-Lopera
    "Maximum likelihood estimation for Gaussian processes under inequality constraints"
    Electronic journal of statistics, 13(2) (2019) 2921-2969
    [arXiv]
25. F. Bachoc, M. Bevilacqua and D. Velandia
    "Composite likelihood estimation for a Gaussian process under fixed domain asymptotics"
    Journal of multivariate analysis, 174 (2019)
    [arXiv]
26. M. Ben Salem, F. Bachoc, O. Roustant, F. Gamboa and L. Tomaso
    "Gaussian process based dimension reduction for goal-oriented sequential design"
    SIAM/ASA Journal on uncertainty quantification, 7(4) (2019) 1369-1397
    [hal]
27. B. Broto, F. Bachoc, M. Depecker and J.M. Martinez
    "Sensitivity indices for independent groups of variables"
    Mathematics and computers in simulation, 163 (2019) 19-31
    [arXiv]
28. J. Bect, F. Bachoc and D. Ginsbourger
    "A supermartingale approach to Gaussian process based sequential design of experiments"
    Bernoulli, 25(4A) (2019) 2883-2919
    [hal] [arXiv]
29. F. Bachoc, H. Leeb and B. Pötscher
    "Valid confidence intervals for post-model-selection predictors"
    Annals of statistics, 47(3) (2019) 1475-1504
    [arXiv]
30. F. Bachoc, G. Blanchard and P. Neuvial
    "On the Post Selection Inference constant under Restricted Isometry Properties"
    Electronic journal of statistics, 12(2) (2018) 3736-3757
    [arXiv]
31. A. F. López-Lopera, F. Bachoc, N. Durrande and O. Roustant
    "Finite-dimensional Gaussian approximation with linear inequality constraints"
    SIAM/ASA Journal on uncertainty quantification, 6(3) (2018) 1224-1255.
    [pdf] [arXiv]
32. F. Bachoc, F. Gamboa, J-M. Loubes and N. Venet
    "Gaussian process regression model for distribution inputs"
    IEEE transactions on information theory, 64(10) (2018) 6620-6637
    [pdf] [arXiv]
33. F. Bachoc
    "Asymptotic analysis of covariance parameter estimation for Gaussian processes in the misspecified case"
    Bernoulli 24(2) (2018) 1531-1575
    [pdf] [arXiv] [supplementary material]
34. D. Rullière, N. Durrande, F. Bachoc and C. Chevalier,
    "Nested Kriging predictions for datasets with large number of observations",
    Statistics and computing 28(4) (2018) 849-867
    [pdf], [hal] [arXiv]
35. F. Bachoc, A. Lagnoux and T.M.N. Nguyen,
    "Cross-validation estimation of covariance parameters under fixed-domain asymptotics",
    Journal of multivariate analysis 160 (2017) 42-67
    [pdf] [hal] [arXiv]
36. D. Velandia, F. Bachoc, M. Bevilacqua, X. Gendre, J-M. Loubes
    "Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics",
    Electronic journal of statistics 11(2) (2017) 2978-3007
    [pdf] [arXiv]
37. F. Bachoc, M. Ehler and M.Gräf
    "Optimal configurations of lines and a statistical application"
    Advances in computational mathematics 43(1) (2017) 113-126
    [pdf] [arXiv]
38. R. Furrer, F. Bachoc and J. Du
    "Asymptotic properties of multivariate tapering for estimation and prediction"
    Journal of multivariate analysis 149 (2016) 177-191
    [pdf] [arXiv]
39. F. Bachoc and Reinhard Furrer
    "On the smallest eigenvalues of covariance matrices of multivariate spatial processes"
    Stat 5 (2016) 102–107
    [pdf] [arXiv]
40. F. Bachoc, K. Ammar and J.M. Martinez
    "Improvement of code behaviour in a design of experiments by metamodeling"
    Nuclear science and engineering 183(3) (2016) 387-406
    [pdf] [arXiv]
41. F. Bachoc
    "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes"
    Journal of multivariate analysis 125 (2014) 1–35
    [pdf] [arXiv] [supplementary material]
42. F. Bachoc, G. Bois, J. Garnier and J.M. Martinez
    "Calibration and improved prediction of computer models by universal Kriging"
    Nuclear science and engineering 176(1) (2014) 81-97
    [pdf] [arXiv]
43. F. Bachoc
    "Cross Validation and Maximum Likelihood estimation of hyper-parameters of Gaussian processes with model misspecification"
    Computational statistics and data analysis 66 (2013) 55–69
    [pdf] [arXiv]

Refereed international conference proceedings

1. F. Bachoc, T. Cesari and S. Gerchinovitz
   "Instance-dependent bounds for zeroth-order Lipschitz optimization with error certificates"
   NeurIPS, Conference on Neural Information Processing Systems, 2021
   [arXiv]
2. F. Bachoc, T. Cesari and S. Gerchinovitz
   "The sample complexity of level set approximation"
   AISTATS - oral presentation, International Conference on Artificial Intelligence and Statistics, 2021
   [arXiv]
3. D. Idier, A. Aurouet, F. Bachoc, A. Baills, J. Betancourt, J. Durand, R. Mouche, J. Rohmer, F. Gamboa, T. Klein, J. Lambert, G. Le Cozannet, S. Le Roy, J. Louisor, R. Pedreros and A-L Véron
   "Toward a user-based, robust and fast running method for coastal flooding forecast, early warning, and risk prevention"
   Journal of coastal research, special issue 95, p. 11-15, proceedings from the International Coastal Symposium (ICS) 2020, forthcoming
   
4. C. Samir, J-M. Loubes, A.-F. Yao and F. Bachoc
   "Learning a Gaussian process model on the Riemannian manifold of non-decreasing distribution functions"
   PRICAI, Pacific Rim International Conference on Artificial Intelligence, Trends in Artificial Intelligence pp 107-120, 2019
   [hal]
5. A. F. López-Lopera, F. Bachoc, N. Durrande, J. Rohmer, D. Idier and O. Roustant
   "Approximating Gaussian process emulators with linear inequality constraints and noisy observations via MC and MCMC"
   MCQMC, Monte Carlo and Quasi-Monte Carlo Methods (2018)
   [arXiv]

Refereed book chapters

1. F. Bachoc
   "Asymptotic analysis of maximum likelihood estimation of covariance parameters for Gaussian processes: an introduction with proofs"
   Advances in Contemporary Statistics and Econometrics (2021) pp 283-303, Festschrift in honor of Christine Thomas Agnan
   [arXiv]
2. F. Bachoc, E. Contal, H. Maatouk and D. Rullière
   "Gaussian processes for computer experiments"
   ESAIM: Proceedings and Surveys 60 (2017) 163 - 179
   [pdf]
3. F. Bachoc, A. Bachouch and L. Lenôtre
   "Hastings-Metropolis algorithm on Markov chains for small-probability estimation"
   ESAIM: Proceedings and Surveys 48 (2015) p.276
   [pdf] [arXiv]

Refereed national conference proceedings

1. F. Bachoc, D. Preinerstorfer and L. Steinberger
   "Uniformly valid confidence intervals post-model-selection"
   Proceedings of the 49e Journées de Statistique Avignon, May 29-June 2 2017
   [pdf]
2. F. Bachoc, F. Gamboa, J-M. Loubes and N. Venet
   "Gaussian process regression model for distribution inputs"
   Proceedings of the 49e Journées de Statistique Avignon, May 29-June 2 2017
   [pdf]
3. F. Bachoc, H. Leeb and B. Pötscher
   "Valid confidence intervals for post-model-selection predictors"
   Proceedings of the 47e Journées de Statistique Lille, 1-5 June 2015
   [pdf]
4. F. Bachoc, J. Garnier and J.M. Martinez
   "Maximum de vraisemblance et validation croisée pour l’estimation des hyper-paramètres de covariance pour le Krigeage",
   Proceedings of the 45e Journées de Statistique Toulouse, 27-31 Mai 2013
   [pdf]

Technical reports

1. J.M. Martinez, A. Marrel, N. Gilardi and F. Bachoc,
   "Krigeage par processus gaussiens Librairie gpLib",
   Internal report CEA DEN/DANS/DM2S/STMF/LGLS/RT/12-026/A. 50p. 2012
   Available upon request
2. F. Bachoc, G. Bois and J.M. Martinez
   "Contribution à la validation des codes de calcul par Processus Gaussiens. Application à la calibration du modèle de frottement pariétal de Flica 4",
   Internal report CEA DEN/DANS/DM2S/STMF/LGLS/RT/12-007/A. 42p. 2012
   Available upon request
3. F. Bachoc
   "Calibration de modèles physiques par méthodes probabilistes",
   Internal report CEA DEN/DANS/DM2S/SFME/LGLS/RT/10-015/A. 78p. 2010
   Available upon request

Software

1. J. Betancourt, F. Bachoc, T. Klein, D. Idier and J. Rohmer,
   "funGp: Gaussian process models for scalar and functional inputs",
   R package 2020
   [link]