Dr Tim Sullivan
Assistant Professor in Predictive Modelling
(Mathematics Institute and School of Engineering)
Teaching Responsibilities 2020/21:
For previous years see here.
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.
See also this full list of publications.
- 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
- 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
- J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Probabilistic numerical methods for PDE-constrained Bayesian inverse problems” in Proceedings of the 36th 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.