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Dr Tim Sullivan | Publications

This is a list of all publications, ordered reverse-chronologically; preprints that are later published after peer review are re-sorted according to their final publication date. See also this page for a categorised version of this list.

  1. I. Klebanov, B. Sprungk, and T. J. Sullivan. “The linear conditional expectation in Hilbert space.” Bernoulli 27(4):2267–2299, 2021. doi:10.3150/20-BEJ1308 arXiv:2008.12070
  2. B. Ayanbayev, I. Klebanov, H. C. Lie, and T. J. Sullivan. “Γ-convergence of Onsager–Machlup functionals. Part II: Infinite product measures on Banach spaces.” arXiv Preprint, 2021. arXiv:2108.04598
  3. B. Ayanbayev, I. Klebanov, H. C. Lie, and T. J. Sullivan. “Γ-convergence of Onsager–Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems.” arXiv Preprint, 2021. arXiv:2108.04597
  4. J. Wang, J. Cockayne, O. Chkrebtii, T. J. Sullivan, and C. J. Oates. “Bayesian numerical methods for nonlinear partial differential equations.” Stat. Comput. 31(5), 2021. doi:10.1007/s11222-021-10030-w arXiv:2104.12587
  5. H. C. Lie, T. J. Sullivan, and A. L. Teckentrup. “Error bounds for some approximate posterior measures in Bayesian inference” in Numerical Mathematics and Advanced Applications ENUMATH 2019, ed. F. J. Vermolen and C. Vuik. Lecture Notes in Computational Science and Engineering 139:275–283, 2021. doi:10.1007/978-3-030-55874-1_26 arXiv:1911.05669
  6. 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:10.1137/19M129526X arXiv:1706.02205
  7. H. C. Lie, M. Stahn, and T. J. Sullivan. “Randomised one-step time integration methods for deterministic operator differential equations.” arXiv Preprint, 2021. arXiv:2103.16506
  8. J. Cockayne, M. M. Graham, C. J. Oates, and T. J. Sullivan. “Testing whether a learning procedure is calibrated.” arXiv Preprint, 2020. arXiv:2012.12670
  9. H. Kersting, T. J. Sullivan, and P. Hennig. “Convergence rates of Gaussian ODE filters.” Stat. Comput. 30(6):1791–1816, 2020. doi:10.1007/s11222-020-09972-4 arXiv:1807.09737
  10. L. Bonnet, J.-L. Akian, É. Savin, and T. J. Sullivan. “Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification.” Algorithms 13(8):196, 2020. doi:10.3390/a13080196 arXiv:2007.05236
  11. I. Klebanov, I. Schuster, and T. J. Sullivan. “A rigorous theory of conditional mean embeddings.” SIAM J. Math. Data Sci. 2(3):583–606, 2020. doi:10.1137/19M1305069 arXiv:1912.00671
  12. M. McKerns, F. J. Alexander, K. S. Hickman, T. J. Sullivan, and D. E. Vaughan. “Optimal bounds on nonlinear partial differential equations in model certification, validation, and experimental design” in Handbook on Big Data and Machine Learning in the Physical Sciences, Volume 2: Advanced Analysis Solutions for Leading Experimental Techniques, ed. K. K. van Dam, K. G. Yager, S. I. Campbell, R. Farnsworth, and M. van Dam. World Scientific Series on Emerging Technologies 271–306, 2020. doi:10.1142/9789811204579_0014 arXiv:2009.06626
  13. C. J. Oates, J. Cockayne, D. Prangle, T. J. Sullivan, and M. Girolami. “Optimality criteria for probabilistic numerical methods” in Multivariate Algorithms and Information-Based Complexity, ed. F. J. Hickernell and P. Kritzer. Radon Series on Computational and Applied Mathematics 27:65–88, 2020. doi:10.1515/9783110635461-005 arXiv:1901.04326
  14. E. Nava-Yazdani, H.-C. Hege, T. J. Sullivan, and C. von Tycowicz. “Geodesic analysis in Kendall's shape space with epidemiological applications.” J. Math. Imaging Vis. 62(4):549–559, 2020. doi:10.1007/s10851-020-00945-w arXiv:1906.11950
  15. O. Ernst, F. Nobile, C. Schillings, and T. J. Sullivan (ed.). Uncertainty Quantification, 11–15 March 2019, Oberwolfach Reports 16(1):695–772, 2019. doi:10.4171/OWR/2019/12
  16. 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 arXiv:1702.03673
  17. M. Girolami, I. C. F. Ipsen, C. J. Oates, A. B. Owen, and T. J. Sullivan. “Editorial: Special Edition on Probabilistic Numerics.” Stat. Comput. 29(6):1181–1183, 2019. doi:10.1007/s11222-019-09892-y
  18. C. J. Oates and T. J. Sullivan. “A modern retrospective on probabilistic numerics.” Stat. Comput. 29(6):1335–1351, 2019. doi:10.1007/s11222-019-09902-z arXiv:1901.04457
  19. H. C. Lie, A. M. Stuart, and T. J. Sullivan. “Strong convergence rates of probabilistic integrators for ordinary differential equations.” Stat. Comput. 29(6):1265–1283, 2019. doi:10.1007/s11222-019-09898-6 arXiv:1703.03680
  20. T. J. Sullivan. “Contributed discussion on the article ‘A Bayesian conjugate gradient method’.” Bayesian Anal. 14(3):985–989, 2019. doi:10.1214/19-BA1145 arXiv:1906.10240
  21. O. Teymur, H. C. Lie, T. J. Sullivan, and B. Calderhead. “Implicit probabilistic integrators for ODEs” in Advances in Neural Information Processing Systems 31 (NIPS 2018), ed. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett. 7244–7253, 2018. http://papers.nips.cc/paper/7955-implicit-probabilistic-integrators-for-odes arXiv:1805.07970
  22. 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 arXiv:1712.05717
  23. H. C. Lie and T. J. Sullivan. “Erratum: Equivalence of weak and strong modes of measures on topological vector spaces (2018 Inverse Problems 34 115013).” Inverse Probl. 34(12):129601, 2018. doi:10.1088/1361-6420/aae55b
  24. H. C. Lie and T. J. Sullivan. “Equivalence of weak and strong modes of measures on topological vector spaces.” Inverse Probl. 34(11):115013, 2018. doi:10.1088/1361-6420/aadef2 arXiv:1708.02516
  25. H. C. Lie and T. J. Sullivan. “Quasi-invariance of countable products of Cauchy measures under non-unitary dilations.” Electron. Commun. Prob. 23(8):1–6, 2018. doi:10.1214/18-ECP113 arXiv:1611.10289
  26. I. Schuster, P. G. Constantine, and T. J. Sullivan. “Exact active subspace Metropolis–Hastings, with applications to the Lorenz-96 system.” arXiv Preprint, 2017. arXiv:1712.02749
  27. T. J. Sullivan. “Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors” in 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017, ed. C. Könke and C. Trunk. Proceedings in Applied Mathematics and Mechanics 17(1):871–874, 2017. doi:10.1002/pamm.201710402 arXiv:1710.05610
  28. 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 arXiv:1605.05898
  29. 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 arXiv:1701.04006
  30. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Probabilistic meshless methods for partial differential equations and Bayesian inverse problems.” arXiv Preprint, 2016. arXiv:1605.07811
  31. 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
  32. 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 arXiv:1308.6306
  33. H. Owhadi, C. Scovel, and T. J. Sullivan. “Brittleness of Bayesian inference under finite information in a continuous world.” Electron. J. Stat. 9(1):1–79, 2015. doi:10.1214/15-EJS989 arXiv:1304.6772
  34. P.-H. T. Kamga, B. Li, M. McKerns, L. H. Nguyen, M. Ortiz, H. Owhadi, and T. J. Sullivan. “Optimal uncertainty quantification with model uncertainty and legacy data.” J. Mech. Phys. Solids 72:1–19, 2014. doi:10.1016/j.jmps.2014.07.007
  35. T. J. Sullivan. “Optimal Uncertainty Quantification for Hypervelocity Impact” in Uncertainty Quantification in Computational Fluid Dynamics, 15–19 September 2014, von Karman Institute for Fluid Dynamics, Belgium, and 2–3 June 2014, Stanford University, United States. STO-AVT-VKI Lecture Series, AVT-235, , 2014.
  36. T. J. Sullivan, M. McKerns, M. Ortiz, H. Owhadi, and C. Scovel. “Optimal uncertainty quantification: Distributional robustness versus Bayesian brittleness.” ASME J. Med. Dev. 7(4):040920, 2013. doi:10.1115/1.4025786
  37. 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. Model. Numer. Anal. 47(6):1657–1689, 2013. doi:10.1051/m2an/2013083 arXiv:1202.1928
  38. 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 arXiv:1009.0679
  39. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. “Thermalization of rate-independent processes by entropic regularization.” Discrete Contin. Dyn. Syst. Ser. S 6(1):215–233, 2013. doi:10.3934/dcdss.2013.6.215 arXiv:1209.3619
  40. L. Rast, T. J. Sullivan, and V. K. Tewary. “Stratified graphene/noble metal systems for low-loss plasmonics applications.” Phys. Rev. B 87(4):045428, 2013. doi:10.1103/PhysRevB.87.045428 arXiv:1301.5620
  41. M. Ortiz, M. McKerns, H. Owhadi, T. J. Sullivan, and C. Scovel. “Optimal Uncertainty Quantification” in Advanced Computational Engineering, 12–18 February 2012, ed. O. Allix, C. Carstensen, J. Schröder, and P. Wriggers. Oberwolfach Reports 9(1):537–540, 2012. doi:10.4171/OWR/2012/09
  42. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. “Thermalization of rate-independent processes by entropic regularization” in Interplay of Analysis and Probability in Physics, 22–28 January 2012, ed. W. König, P. Mörters, M. Peletier, and J. Zimmer. Oberwolfach Reports 9(1):322–325, 2012. doi:10.4171/OWR/2012/06
  43. M. Adams, A. Lashgari, B. Li, M. McKerns, J. Mihaly, M. Ortiz, H. Owhadi, A. J. Rosakis, M. Stalzer, and T. J. Sullivan. “Rigorous model-based uncertainty quantification with application to terminal ballistics. Part II: Systems with uncontrollable inputs and large scatter.” J. Mech. Phys. Solids 60(5):1002–1019, 2012. doi:10.1016/j.jmps.2011.12.002
  44. A. A. Kidane, A. Lashgari, B. Li, M. McKerns, M. Ortiz, G. Ravichandran, M. Stalzer, and T. J. Sullivan. “Rigorous model-based uncertainty quantification with application to terminal ballistics. Part I: Systems with controllable inputs and small scatter.” J. Mech. Phys. Solids 60(5):983–1001, 2012. doi:10.1016/j.jmps.2011.12.001
  45. T. J. Sullivan and H. Owhadi. “Distances and diameters in concentration inequalities: from geometry to optimal assignment of sampling resources.” Int. J. Uncertain. Quantif. 2(1):21–38, 2012. doi:10.1615/Int.J.UncertaintyQuantification.v2.i1.30
  46. C. Scovel, H. Owhadi, T. J. Sullivan, M. McKerns, and M. Ortiz. “What is UQ?” in ADTSC Science Highlights 2012. Los Alamos National Laboratory, LA-UR 12-20429:26–27, 2012.
  47. 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 arXiv:1202.1056
  48. T. J. Sullivan, U. Topcu, M. McKerns, and H. Owhadi. “Uncertainty quantification via codimension-one partitioning.” Internat. J. Numer. Methods Engrg. 85(12):1499–1521, 2011. doi:10.1002/nme.3030
  49. T. J. Sullivan and F. Theil. “On gradient descents in random wiggly energies” in Microstructures in Solids: From Quantum Models to Continua, 14–20 March 2010, ed. A. Mielke and M. Ortiz. Oberwolfach Reports 7(1):739–741, 2010. doi:10.4171/OWR/2010/14
  50. M. McKerns, H. Owhadi, C. Scovel, T. J. Sullivan, and M. Ortiz. “The optimal uncertainty algorithm in the mystic framework.” Caltech CACR Technical Report No. 523, August 2010. arXiv:1202.1055
  51. T. J. Sullivan, M. McKerns, U. Topcu, and H. Owhadi. “Uncertainty quantification via codimension-one domain partitioning and a new concentration inequality.” Proc. Soc. Behav. Sci. 2(6):7751–7752, 2010. doi:10.1016/j.sbspro.2010.05.211
  52. F. Theil, T. J. Sullivan, M. Koslowski, and M. Ortiz. “Dissipative systems in contact with a heat bath: Application to Andrade creep” in Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, Bochum, Germany, September 22–26, 2008, ed. K. Hackl. IUTAM Bookseries 21:261–272, 2010. doi:10.1007/978-90-481-9195-6_20
  53. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. “On the behavior of dissipative systems in contact with a heat bath: Application to Andrade creep.” J. Mech. Phys. Solids 57(7):1058–1077, 2009. doi:10.1016/j.jmps.2009.03.006
  54. T. J. Sullivan and F. Theil. “Deterministic stick-slip dynamics in a one-dimensional random potential” in Analysis and Numerics for Rate-Independent Processes, 25 February–3 March 2007, ed. G. Dal Maso, G. Francfort, A. Mielke, and T. Roubíček. Oberwolfach Reports 4(1):652–655, 2007. doi:10.4171/OWR/2007/11