@article{AyanbayevKlebanovLieetal., author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, T. J.}, title = {Γ-convergence of Onsager-Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems}, series = {Inverse Problems}, volume = {38}, journal = {Inverse Problems}, number = {2}, doi = {10.1088/1361-6420/ac3f81}, pages = {32}, language = {en} } @article{AyanbayevKlebanovLieetal., author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, T. J.}, title = {Γ-convergence of Onsager-Machlup functionals: II. Infinite product measures on Banach spaces}, series = {Inverse Problems}, volume = {38}, journal = {Inverse Problems}, number = {2}, doi = {10.1088/1361-6420/ac3f82}, pages = {35}, language = {en} } @article{SchaeferSullivanOwhadi, author = {Sch{\"a}fer, Florian and Sullivan, T. J. and Owhadi, Houman}, title = {Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity}, series = {Multiscale Modeling and Simulation}, volume = {19}, journal = {Multiscale Modeling and Simulation}, number = {2}, doi = {10.1137/19M129526X}, pages = {688 -- 730}, language = {en} } @article{KlebanovSprungkSullivan, author = {Klebanov, Ilja and Sprungk, Bj{\"o}rn and Sullivan, T. J.}, title = {The linear conditional expectation in Hilbert space}, series = {Bernoulli}, volume = {27}, journal = {Bernoulli}, number = {4}, doi = {10.3150/20-BEJ1308}, pages = {2299 -- 2299}, language = {en} } @article{LieSullivanTeckentrup2020, author = {Lie, Han Cheng and Sullivan, T. J. and Teckentrup, Aretha}, title = {Error bounds for some approximate posterior measures in Bayesian inference}, series = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, journal = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-55874-1_26}, pages = {275 -- 283}, year = {2020}, language = {en} } @article{WangCockayneChkrebtiietal., author = {Wang, Junyang and Cockayne, Jon and Chkrebtii, Oksana and Sullivan, T. J. and Oates, Chris}, title = {Bayesian numerical methods for nonlinear partial differential equations}, series = {Statistics and Computing}, volume = {31}, journal = {Statistics and Computing}, number = {5}, doi = {10.1007/s11222-021-10030-w}, language = {en} } @article{KlebanovSchusterSullivan, author = {Klebanov, Ilja and Schuster, Ingmar and Sullivan, T. J.}, title = {A rigorous theory of conditional mean embeddings}, series = {SIAM Journal on Mathematics of Data Science}, volume = {2}, journal = {SIAM Journal on Mathematics of Data Science}, number = {3}, doi = {10.1137/19M1305069}, pages = {583 -- 606}, language = {en} } @article{NavaYazdaniHegeSullivanetal., 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}, series = {Journal of Mathematical Imaging and Vision}, volume = {62}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, doi = {10.1007/s10851-020-00945-w}, pages = {549 -- 559}, 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} } @article{BonnetAkianSavinetal., author = {Bonnet, Luc and Akian, Jean-Luc and Savin, {\´E}ric and Sullivan, T. J.}, title = {Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification}, series = {Algorithms}, volume = {13}, journal = {Algorithms}, number = {8}, doi = {10.3390/a13080196}, pages = {196}, abstract = {Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.}, language = {en} } @misc{OatesCockaynePrangleetal., author = {Oates, Chris and Cockayne, Jon and Prangle, Dennis and Sullivan, T. J. and Girolami, Mark}, title = {Optimality criteria for probabilistic numerical methods}, series = {Multivariate Algorithms and Information-Based Complexity}, volume = {27}, journal = {Multivariate Algorithms and Information-Based Complexity}, editor = {Hickernell, F. J. and Kritzer, P.}, publisher = {De Gruyter}, doi = {10.1515/9783110635461-005}, pages = {65 -- 88}, 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} }