This page contains all my publications; for more details, see my Google Scholar profile. For a non-technical overview of some of my work, see the webpage for the Fundamentals of Statistical Machine Learning project at the Turing Institute. Alternatively, if you would like a brief introduction to some of the fields I work in and have contributed to, you may prefer to have a look at the following project pages:


  • Kirby, A., Briol, F-X., Dunstan, T., Nishino, T. (2023). Data-driven modelling of turbine wake interactions and flow resistance in large wind farms. arXiv:2301.01699. (Preprint)

  • Zhang, M., Key, O., Hayes, P., Barber, D., Paige, B. & Briol, F-X. (2022). Towards healing the blindness of score matching. arXiv:2209.07396. (Preprint)
  • Matsubara, T., Knoblauch, J., Briol, F-X. & Oates, C. J. (2022). Generalised Bayesian inference for discrete intractable likelihood. arXiv:2206.08420. (Preprint) (Code)

  • Wenger, J., Krämer, N., Pförtner, M., Schmidt, J., Bosch, N., Effenberger, N., Zenn, J., Gessner, A., Karvonen, T., Briol, F-X, Mahsereci, M. & Hennig, P. (2021). ProbNum: Probabilistic numerics in Python. arXiv:2112.02100. (Preprint)
    • This paper is the reference for the open-source ProbNum software, which implements a range of probabilistic numerics methods in Python. Full details are available at
  • Key, O., Fernandez, T., Gretton, A. & Briol, F-X. (2021). Composite goodness-of-fit tests with kernels. arXiv.2111.10275. (Preprint)
  • Sun, Z., Barp, A. & Briol, F-X. (2021). Vector-valued control variates. arXiv:2109.08944. (Preprint)
    • This paper received a Student Paper Award from the section on Bayesian Statistical Science of the American Statistical Association in 2022.
    • Zhuo Sun was awarded a Silver Medal for his poster on this paper at the 2021 Fry conference at Bristol.
  • Niu, Z., Meier, J. & Briol, F-X. (2021). Discrepancy-based inference for intractable generative models using quasi-Monte Carlo. arXiv:2106.11561. (Preprint) (Code)

  • Briol, F-X., Barp, A., Duncan, A. B. & Girolami, M. (2019). Statistical inference for generative models with maximum mean discrepancy. arXiv:1906.05944. (Preprint) (Talk/Video)

Published Papers

  • Li, K., Giles, D., Karvonen, T., Guillas, S. & Briol, F-X. (2023). Multilevel Bayesian quadrature. arXiv:2209.07396. Accepted for publication at AISTATS 2023. (Preprint) (Code)

  • Anastasiou, A., Barp, A., Briol, F-X., Ebner, B., Gaunt, R. E., Ghaderinezhad, F., Gorham, J., Gretton, A., Ley, C., Liu, Q., Mackey, L., Oates, C. J., Reinert, G. & Swan, Y. (2023). Stein’s method meets Computational Statistics: A review of some recent developments. Statistical Science, Vol. 38, No. 1, 120-139. (Journal) (Preprint 1) (Preprint 2)

  • Mastubara, T., Knoblauch, J., Briol, F-X. & Oates, C. J. (2022). Robust generalised Bayesian inference for intractable likelihoods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 997– 1022. (Journal) (Preprint) (Code) (Video)
  • Dellaporta, C., Knoblauch, J., Damoulas, T. Briol. F-X. (2022). Robust Bayesian inference for simulator-based models via the MMD posterior bootstrap. Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 151:943-970. (Conference) (Preprint) (Code) (Video)
  • Bharti, A., Briol, F-X., Pedersen, T. (2022). A general method for calibrating stochastic radio channel models with kernels. IEEE Transactions on Antennas and Propagation, vol. 70, no. 6, pp. 3986-4001, June 2022. (Journal) (Preprint) (Code)
  • Si, S., Oates, C. J., Duncan, A. B., Carin, L. & Briol. F-X. (2021). Scalable control variates for Monte Carlo methods via stochastic optimization. Accepted for publication in the proceedings of the 14th Monte Carlo and Quasi-Monte Carlo Methods (MCQMC) conference 2020. arXiv:2006.07487. (Conference) (Preprint) (Video)

  • Mastubara, T., Oates, C. J., Briol, F-X. (2021). The ridgelet prior: A covariance function approach to prior specification for Bayesian neural networks. Journal of Machine Learning Research, 22 (157), 1-57. (Journal) (Preprint) (Video) (Code)

  • Wynne, G., Briol, F-X., Girolami, M. (2021). Convergence guarantees for Gaussian process means with misspecified likelihoods and smoothness. Journal of Machine Learning Research, 22 (123), 1-40. (Journal) (Preprint)

  • Bharti, A., Adeogun, R., Cai, X., Fan, W., Briol, F-X., Clavier, L., Pedersen, T. (2021). Joint modeling of received power, mean delay and delay spread for wideband radio channels. IEEE Transactions on Antennas and Propagation, vol. 69, no. 8, pp. 4871-4882, Aug. 2021. (Journal) (Preprint)

  • Zhu, H., Liu, X., Kang, R., Shen, Z., Flaxman, S., Briol, F-X. (2020). Bayesian probabilistic numerical integration with tree-based models. Neural Information Processing Systems, 5837-5849. (Conference) (Preprint) (Code)

  • Barp, A., Briol, F-X., Duncan, A. B., Girolami, M., Mackey, L. (2019). Minimum Stein discrepancy estimators. Neural Information Processing Systems, 12964-12976. (Conference) (Preprint) (Talk/Video)

  • Chen, W. Y., Barp, A., Briol, F-X., Gorham, J., Girolami, M., Mackey, L., Oates, C. J. (2019). Stein point Markov chain Monte Carlo. International Conference on Machine Learning, PMLR 97:1011-1021. (Conference) (Preprint) (Code)

  • Briol, F-X., Oates, C. J., Girolami, M., Osborne, M. A. & Sejdinovic, D. (2019). Probabilistic integration: a role in statistical computation? Statistical Science, Vol 34, Number 1, 1-22. (Journal) (Preprint) (Supplement)
  • Oates, C. J., Cockayne, J., Briol, F-X. & Girolami, M. (2019). Convergence rates for a class of estimators based on Stein’s identity. Bernoulli, Vol. 25, No. 2, 1141-1159. (Journal) (Preprint)

  • Xi, X., Briol, F-X. & Girolami, M. (2018). Bayesian quadrature for multiple related integrals. International Conference on Machine Learning, PMLR 80:5369-5378. (Conference) (Preprint)
    • This paper was accepted for a long talk (top 8% of submitted papers).
  • Chen, W. Y., Mackey, L., Gorham, J. Briol, F-X. & Oates, C. J. (2018). Stein points. International Conference on Machine Learning, PMLR 80:843-852. (Conference) (Preprint) (Code)

  • Barp, A., Briol, F-X., Kennedy, A. D. & Girolami, M. (2018). Geometry and dynamics for Markov chain Monte Carlo. Annual Review of Statistics and Its Applications, Vol. 5:451-471. (Journal) (Preprint)

  • Oates, C. J., Niederer, S., Lee, A., Briol, F-X. & Girolami, M. (2017). Probabilistic models for integration error in the assessment of functional cardiac models. Advances in Neural Information Processing Systems (NeurIPS), 109-117. (Conference) (Preprint)

  • Briol, F-X., Oates, C. J., Cockayne, J., Chen, W. Y. & Girolami, M. (2017). On the sampling problem for kernel quadrature. Proceedings of the 34th International Conference on Machine Learning, PMLR 70:586-595. (Conference) (Preprint)

  • Briol, F-X., Oates, C. J., Girolami, M. & Osborne, M. A. (2015). Frank-Wolfe Bayesian Quadrature: probabilistic integration with theoretical guarantees. Advances In Neural Information Processing Systems (NIPS), 1162-1170. (Preprint) (Conference)
    • This paper was accepted with a spotlight presentation (top 4.5% of submitted papers).
    • This paper was discussed in the blog of Ingmar Schuster.
  • Barp, A., Barp, E. G., Briol, F-X. & Ueltschi, D. (2015). A numerical study of the 3D random interchange and random loop models. Journal of Physics A: Mathematical and Theoretical, 48(34). (Journal) (Preprint)

Technical Discussions and Opinion Pieces

  • Zhu, H., Liu, X., Caron, A., Manolopoulou, I. Flaxman, S., Briol, F-X. (2020). Contributed Discussion of “Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects”. Bayesian Analysis, 15(3), 965-1056. (Journal (pp55-58)) (Preprint)

  • Briol, F-X., Diaz De la O, F. A., Hristov, P. O. (2019). Contributed Discussion of “A Bayesian Conjugate Gradient Method”. Bayesian Analysis, 14(3), 980-984. (Journal) (Preprint)

  • Briol, F-X., Oates, C. J., Girolami, M., Osborne, M. A. & Sejdinovic, D. (2019). Rejoinder for “Probabilistic integration: a role in statistical computation?” Statistical Science, Vol 34, Number 1, 38-42. (Journal) (Preprint)

  • Briol, F-X. & Girolami, M. (2018) Bayesian numerical methods as a case study for statistical data science, Statistical Data Science (Chapter 6): 99-110. (Book)

  • Briol, F-X., Cockayne, J. & Teymur, O. (2016). Contributed discussion on article by Chkrebtii, Campbell, Calderhead, and Girolami. Bayesian Analysis, 11(4), 1285-1293. (Journal) (Preprint)

Science Communication

  • Briol, F-X., Bharti, A. (2021). Using machine learning to improve the reliability of wireless communication systems. (Turing Institute Blog Post)


  • Briol, F-X. (2019). Statistical computation with kernels. PhD thesis, Department of Statistics, University of Warwick. (PDF)
    • I was awarded an Honorable Mention for the Savage Award in the section “Theory and Methodology” for this thesis. This is awarded by the International Society on Bayesian Analysis (ISBA) for “a dissertation that makes important original contributions to the foundations, theoretical developments, and/or general methodology of Bayesian analysis”.
  • Briol, F-X. (2014). Inference for Hawkes Processes. Masters thesis, Department of Statistics, University of Warwick.