Assistant Professor in Predictive Modelling (Mathematics Institute and School of Engineering) Office: C2.10 Phone: +44 (0)24 7615 0294 Email: t.j.sullivan@warwick.ac.uk

 

Teaching Responsibilities 2020/21:

Terms 1–3: Tutorial responsibilities in Mathematics and Engineering

Term 2: MA134 Geometry and Motion and MA4K0 Introduction to Uncertainty Quantification

For previous years see here.

Research Interests

Keywords: uncertainty quantification, inverse problems, probabilistic numerics, data science

Summary: My mathematical research interests are in uncertainty quantification (UQ), which lies at the intersection of applied mathematics and computational probability. The long-term vision underlying this line of research is to contribute to a paradigm shift in reasoning about complex systems under uncertainty, which is a pressing challenge in many application domains.
Particular topics of interest to me include the theoretical foundations of UQ; non-parametric Bayesian statistics, including inverse problems in function spaces; optimisation-based methods and their relationship to Bayesian methods (e.g. maximum-a-posteriori estimation); and computational methods for applied statistical problems, including dimension reduction and kernel-based machine learning techniques. A point of particular recent focus is probabilistic perspectives on numerical methods themselves, which is an emerging blend of statistical inference and numerical analysis. I have also contributed towards numerical implementation of all of these methods in open-source software packages.
I am a member of SIAM and GAMM, and have organised sections and minisymposia at multiple international conferences. I am an associate editor of the SIAM/ASA Journal on Uncertainty Quantification.

---

Selected Publications

See also this full list of publications.

1. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Bayesian probabilistic numerical methods.” SIAM Rev. 61(4):756–789, 2019. doi:10.1137/17M1139357
2. H. C. Lie, T. J. Sullivan, and A. L. Teckentrup. “Random forward models and log-likelihoods in Bayesian inverse problems.” SIAM/ASA J. Uncertain. Quantif. 6(4):1600–1629, 2018. doi:10.1137/18M1166523
3. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Probabilistic numerical methods for PDE-constrained Bayesian inverse problems” in Proceedings of the 36^th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. G. Verdoolaege. AIP Conference Proceedings 1853:060001-1–060001-8, 2017. doi:10.1063/1.4985359
4. T. J. Sullivan. “Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors.” Inverse Probl. Imaging 11(5):857–874, 2017. doi:10.3934/ipi.2017040
5. T. J. Sullivan. Introduction to Uncertainty Quantification, volume 63 of Texts in Applied Mathematics. Springer, 2015. ISBN 978-3-319-23394-9 (hardcover), 978-3-319-23395-6 (e-book). doi:10.1007/978-3-319-23395-6
6. H. Owhadi, C. Scovel, and T. J. Sullivan. “On the brittleness of Bayesian inference.” SIAM Rev. 57(4):566–582, 2015. doi:10.1137/130938633
7. H. Owhadi, C. Scovel, and T. J. Sullivan. “Brittleness of Bayesian inference under finite information in a continuous world.” Elec. J. Stat. 9(1):1–79, 2015. doi:10.1214/15-EJS989
8. T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi, and M. Ortiz. “Optimal uncertainty quantification for legacy data observations of Lipschitz functions.” ESAIM. Math. Mod. Num. Anal. 47(6):1657–1689, 2013. doi:10.1051/m2an/2013083
9. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns, and M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Rev. 55(2):271–345, 2013. doi:10.1137/10080782X
10. M. M. McKerns, L. Strand, T. J. Sullivan, A. Fang, and M. A. G. Aivazis. “Building a Framework for Predictive Science” in Proceedings of the 10th Python in Science Conference (SciPy 2011), June 2011, ed. S. van der Walt and J. Millman. 67–78, 2011. doi:10.25080/Majora-ebaa42b7-00d

Recent Research Grants

• Project 415980428 “Analysis of maximum a posteriori estimators: Common convergence theories for Bayesian and variational inverse problems”, as PI, funded by the German Research Foundation (DFG), 2020–2021.
• Project TrU-2 “Demand modelling and control for e-commerce using RKHS transfer operator approaches”, as co-PI, funded by Germany's Excellence Strategy, part of the Berlin Mathematics Research Center MATH+ (EXC-2046/1, project 390685689), 2019–2020.
• Project CH-15 “Analysis of Empirical Shape Trajectories”, as co-PI, funded by the Einstein Center for Mathematics ECMath and the Berlin Mathematics Research Center MATH+, 2017–2019.
• Project 337475393 (SFB1114/A06) “Enabling Bayesian uncertainty quantification for multiscale systems and network models via mutual likelihood-informed dimension reduction”, as project PI, funded by the German Research Foundation (DFG), part of SFB1114 Scaling Cascades in Complex Systems, 2017–2018.

Personal Homepage

www.tjsullivan.org.uk