@article{LieSullivan2018, author = {Lie, Han Cheng and Sullivan, T. J.}, title = {Erratum: Equivalence of weak and strong modes of measures on topological vector spaces (2018 Inverse Problems 34 115013)}, volume = {34}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/aae55b}, pages = {129601}, year = {2018}, language = {en} } @article{OatesSullivan2019, author = {Oates, Chris and Sullivan, T. J.}, title = {A modern retrospective on probabilistic numerics}, volume = {29}, journal = {Statistics and Computing}, number = {6}, arxiv = {http://arxiv.org/abs/1901.04457}, doi = {10.1007/s11222-019-09902-z}, pages = {1335 -- 1351}, year = {2019}, abstract = {This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related to modern formal treatments and applications. We highlight in particular the parallel contributions of Sul'din and Larkin in the 1960s and how their pioneering early ideas have reached a degree of maturity in the intervening period, mediated by paradigms such as average-case analysis and information-based complexity. We provide a subjective assessment of the state of research in probabilistic numerics and highlight some difficulties to be addressed by future works.}, language = {en} } @misc{OatesCockaynePrangleetal.2020, author = {Oates, Chris and Cockayne, Jon and Prangle, Dennis and Sullivan, T. J. and Girolami, Mark}, title = {Optimality criteria for probabilistic numerical methods}, volume = {27}, journal = {Multivariate Algorithms and Information-Based Complexity}, editor = {Hickernell, F. J. and Kritzer, P.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/1901.04326}, doi = {10.1515/9783110635461-005}, pages = {65 -- 88}, year = {2020}, abstract = {It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.}, language = {en} } @article{KerstingSullivanHennig2020, author = {Kersting, Hans and Sullivan, T. J. and Hennig, Philipp}, title = {Convergence rates of Gaussian ODE filters}, volume = {30}, journal = {Statistics and Computing}, publisher = {Springer}, address = {Statistics and Computing}, arxiv = {http://arxiv.org/abs/1807.09737}, doi = {10.1007/s11222-020-09972-4}, pages = {1791 -- 1816}, year = {2020}, language = {en} } @article{LieSullivanTeckentrup2021, author = {Lie, Han Cheng and Sullivan, T. J. and Teckentrup, Aretha}, title = {Error bounds for some approximate posterior measures in Bayesian inference}, journal = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, publisher = {Springer}, arxiv = {http://arxiv.org/abs/1911.05669}, doi = {10.1007/978-3-030-55874-1_26}, pages = {275 -- 283}, year = {2021}, language = {en} } @article{LieSullivan2016, author = {Lie, Han Cheng and Sullivan, T. J.}, title = {Cameron--Martin theorems for sequences of Cauchy-distributed random variables}, journal = {arXiv}, arxiv = {http://arxiv.org/abs/1608.03784}, pages = {1608.03784}, year = {2016}, abstract = {Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random variables that is obtained by perturbing the location or scale parameter sequences. Using a result of Kakutani on equivalence of infinite product measures, we provide sufficient conditions for the equivalence of laws of the two sequences.}, language = {en} } @inproceedings{TeymurLieSullivanetal.2018, author = {Teymur, Onur and Lie, Han Cheng and Sullivan, T. J. and Calderhead, Ben}, title = {Implicit probabilistic integrators for ODEs}, booktitle = {Advances in Neural Information Processing Systems 31 (NIPS 2018)}, arxiv = {http://arxiv.org/abs/1805.07970}, year = {2018}, language = {en} } @article{KlebanovSchusterSullivan2020, author = {Klebanov, Ilja and Schuster, Ingmar and Sullivan, T. J.}, title = {A rigorous theory of conditional mean embeddings}, volume = {2}, journal = {SIAM Journal on Mathematics of Data Science}, number = {3}, arxiv = {http://arxiv.org/abs/1912.00671}, doi = {10.1137/19M1305069}, pages = {583 -- 606}, year = {2020}, language = {en} } @article{GirolamiIpsenOatesetal.2019, author = {Girolami, Mark A. and Ipsen, Ilse C. F. and Oates, Chris and Owen, Art B. and Sullivan, T. J.}, title = {Editorial: Special edition on probabilistic numerics}, volume = {29}, journal = {Statistics and Computing}, number = {6}, doi = {doi:10.1007/s11222-019-09892-y}, pages = {1181 -- 1183}, year = {2019}, language = {en} } @article{NavaYazdaniHegeSullivanetal.2020, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and Sullivan, T. J. and von Tycowicz, Christoph}, title = {Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications}, volume = {62}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, arxiv = {http://arxiv.org/abs/1906.11950}, doi = {10.1007/s10851-020-00945-w}, pages = {549 -- 559}, year = {2020}, abstract = {We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.}, language = {en} }