Journal Article

Cockayne, Jon, Oates, Chris J., Sullivan, T. J. and Girolami, Mark (2019) Bayesian probabilistic numerical methods. SIAM Review, 61 (3). pp. 756-789. doi:10.1137/17M1139357

Girolami, M., Ipsen, I. C. F., Oates, C. J., Owen, A. B. and Sullivan, T. J. (2019) Editorial : special edition on probabilistic numerics. Statistics and Computing, 29 (6). pp. 1181-1183. doi:10.1007/s11222-019-09892-y

Lie, Han Cheng, Stuart, A. M. and Sullivan, T. J. (2019) Strong convergence rates of probabilistic integrators for ordinary differential equations. Statistics and Computing, 29 (6). pp. 1265-1283. doi:10.1007/s11222-019-09898-6

Oates, C. J. and Sullivan, T. J. (2019) A modern retrospective on probabilistic numerics. Statistics and Computing, 29 (6). pp. 1335-1351. doi:10.1007/s11222-019-09902-z

Lie, H. C., Sullivan, T. J. and Teckentrup, A. L. (2018) Random forward models and log-likelihoods in Bayesian inverse problems. SIAM/ASA Journal on Uncertainty Quantification, 6 (4). pp. 1600-1629. doi:10.1137/18M1166523

Lie, Han Cheng and Sullivan, T. J. (2018) Equivalence of weak and strong modes of measures on topological vector spaces. Inverse Problems, 34 (11). 115013. doi:10.1088/1361-6420/aadef2

Lie, Han Cheng and Sullivan, T. J. (2018) Quasi-invariance of countable products of Cauchy measures under non-unitary dilations. Electronic Communications in Probability, 23 . 8. doi:10.1214/18-ECP113

Sullivan, T. J. (2017) Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors. Proceedings in Applied Mathematics and Mechanics, 17 (1). pp. 871-874. doi:10.1002/pamm.201710402

Sullivan, T. J. (2017) Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors. Inverse Problems & Imaging, 11 (5). pp. 857-874. doi:10.3934/ipi.2017040

Owhadi, Houman, Scovel, Clint and Sullivan, T. J. (2015) On the brittleness of Bayesian inference. SIAM Review, 57 (4). pp. 566-582. doi:10.1137/130938633

Owhadi, Houman, Scovel, Clint and Sullivan, Tim J. (2015) Brittleness of Bayesian inference under finite information in a continuous world. Electronic Journal of Statistics, 9 (1). pp. 1-79. doi:10.1214/15-EJS989

Kamga, P-H. T., Li, B., McKerns, M., Nguyen, L. H., Ortiz, M., Owhadi, H. and Sullivan, T. J. (2014) Optimal uncertainty quantification with model uncertainty and legacy data. Journal of the Mechanics and Physics of Solids, 72 . pp. 1-19. doi:10.1016/j.jmps.2014.07.007

Sullivan, T. (2013) Optimal uncertainty quantification for legacy data observations of Lipschitz functions. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 47 (Number 6). pp. 1657-1689. doi:10.1051/m2an/2013083

Rast, L., Sullivan, T. and Tewary, V. K. (2013) Stratified graphene/noble metal systems for low-loss plasmonics applications. Physical Review B (Condensed Matter and Materials Physics), Volume 87 (Number 4). Article number 045428. doi:10.1103/PhysRevB.87.045428

Sullivan, T. and Owhadi, Houman (2012) Distances and diameters in concentration inequalities: from geometry to optimal assignment of sampling resources. International Journal for Uncertainty Quantification, Vol. 2 (No. 1). pp. 21-38. doi:10.1615/Int.J.UncertaintyQuantification.v2.i1.30

Kidane, A., Lashgari, A., Li, B., McKerns, M., Ortiz, M., Owhadi, H., Ravichandran, G., Stalzer, M. and Sullivan, T. (2012) Rigorous model-based uncertainty quantification with application to terminal ballistics, part I : systems with controllable inputs and small scatter. Journal of the Mechanics and Physics of Solids, Vol.60 (No.5). pp. 983-1001. doi:10.1016/j.jmps.2011.12.001

Ortiz, Michael, Theil, Florian, Koslowski, M. and Sullivan, T. (2012) Thermalization of rate-independent processes by entropic regularization. Discrete and Continuous Dynamical Systems - Series S, Vol. 6 (No. 1). pp. 215-233. doi:10.3934/dcdss.2013.6.215

Sullivan, T., Topcu, U., McKerns, M. and Owhadi, H. (2010) Uncertainty quantification via codimension-one partitioning. International Journal for Numerical Methods in Engineering, Vol.85 (No.12). pp. 1499-1521. doi:10.1002/nme.3030

Sullivan, T., Koslowski, M., Theil, Florian and Ortiz, M. (2009) On the behavior of dissipative systems in contact with a heat bath : application to Andrade creep. Journal of the Mechanics and Physics of Solids, Vol.57 (No.7). pp. 1058-1077. doi:10.1016/j.jmps.2009.03.006

Book Item

Scovel, Clint, Sullivan, Tim J. and Owhadi, Houman (2012) What is UQ? In: Theory, Simulation, and Computation Directorate Science Highlights 2012. Los Alamon, New Mexico: TSC publications, pp. 26-28.

Theil, Florian, Sullivan, Tim J. and Koslovski, Marisol (2010) Dissipative systems in contact with a heat bath : application to Andrade Creep. In: Hackl, K. (Klaus), (ed.) IUTAM symposium on variational concepts with applications to the mechanics of materials : Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, Bochum, Germany, September 22-26, 2008. IUTAM Bookseries, Volume 21 . Dordrecht ; New York: Springer, pp. 261-272. ISBN 9789048191956

Conference Item

Teymur, Onur, Calderhead, Ben, Lie , Hancheng and Sullivan, T. J. (2018) Implicit probabilistic integrators for ODEs. In: NIPS'18 : Neural Information Processing Systems 2018, Canada, 3-8 Dec 2018. Published in: Proceedings of the 32nd International Conference on Neural Information Processing Systems pp. 7255-7264. doi:10.5555/3327757.3327827

Cockayne, Jon, Oates, Chris J., Sullivan, T. J. and Girolami, Mark (2017) Probabilistic numerical methods for PDE-constrained Bayesian inverse problems. In: 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Ghent, Belgium, 10-15 Jul 2016. Published in: AIP Conference Proceedings, 1853 (1). ISSN 0094-243X. doi:10.1063/1.4985359