Associate Professor in Predictive Modelling (Mathematics Institute and School of Engineering) Co-Director, Warwick Centre for Predictive Modelling Turing Fellow (Alan Turing Institute) Office: Zeeman Building, C2.10 Phone: +44 (0)24 7615 0294 Email: t.j.sullivan (at) warwick.ac.uk

 

Teaching Responsibilities 2021–2022:

Terms 1–3: Tutorial responsibilities in Mathematics and Engineering

Term 2: MA3H7 Control Theory

For previous years see here.

Research Interests

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

Summary: My mathematical research interests are in uncertainty quantificationLink opens in a new window (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 SIAMLink opens in a new window and GAMMLink opens in a new window, and have organised sections and minisymposia at multiple international conferences. I am an associate editor of the SIAM/ASA Journal on Uncertainty QuantificationLink opens in a new window.

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Selected Publications

See also this full list of publications.

1. F. Schäfer, T. J. Sullivan, and H. Owhadi. “Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity.” Multiscale Model. Simul. 19(2):688–730, 2021. doi:10.1137/19M129526XLink opens in a new window
2. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Bayesian probabilistic numerical methods.” SIAM Rev. 61(4):756–789, 2019. doi:10.1137/17M1139357Link opens in a new window
3. 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:10.1137/18M1166523Link opens in a new window
4. 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:10.1063/1.4985359Link opens in a new window
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:10.1007/978-3-319-23395-6Link opens in a new window
6. H. Owhadi, C. Scovel, and T. J. Sullivan. “On the brittleness of Bayesian inference.” SIAM Rev. 57(4):566–582, 2015. doi:10.1137/130938633Link opens in a new window
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-EJS989Link opens in a new window
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/2013083Link opens in a new window
9. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns, and M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Rev. 55(2):271–345, 2013. doi:10.1137/10080782XLink opens in a new window
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-ebaa42b7-00dLink opens in a new window

Recent Research Grants

• Project 415980428Link opens in a new window “Analysis of maximum a posteriori estimators: Common convergence theories for Bayesian and variational inverse problems”, as PI, funded by the German Research Foundation (DFG)Link opens in a new window, 2020–2022.
• Project TrU-2Link opens in a new window “Demand modelling and control for e-commerce using RKHS transfer operator approaches”, as co-PI, funded by Germany's Excellence StrategyLink opens in a new window, part of the Berlin Mathematics Research Center MATH+Link opens in a new window (EXC-2046/1, project 390685689Link opens in a new window), 2019–2020.
• Project CH-15 “Analysis of Empirical Shape Trajectories”Link opens in a new window, as co-PI, funded by the Einstein Center for Mathematics ECMathLink opens in a new window and the Berlin Mathematics Research Center MATH+Link opens in a new window, 2017–2019.
• Project 337475393Link opens in a new window (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)Link opens in a new window, part of SFB1114 Scaling Cascades in Complex SystemsLink opens in a new window, 2017–2018.

Personal Homepage

www.tjsullivan.org.ukLink opens in a new window