@article{Sullivan, author = {Sullivan, T. J.}, title = {Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors}, series = {Inverse Problems and Imaging}, volume = {11}, journal = {Inverse Problems and Imaging}, number = {5}, doi = {10.3934/ipi.2017040}, pages = {857 -- 874}, language = {en} } @article{SchusterConstantineSullivan, author = {Schuster, Ingmar and Constantine, Paul and Sullivan, T. J.}, title = {Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system}, abstract = {We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We show that the original formulation, as proposed by Constantine, Kent, and Bui-Thanh (SIAM J. Sci. Comput., 38(5):A2779-A2805, 2016), possesses asymptotic bias. Using pseudo-marginal arguments, we develop an asymptotically unbiased variant. Our algorithm is applied to a synthetic multimodal target distribution as well as a Bayesian formulation of a parameter inference problem for a Lorenz-96 system.}, language = {en} }