TY - CHAP A1 - Sullivan, T. J. T1 - Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors T2 - 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017 Y1 - 2017 U6 - https://doi.org/10.1002/pamm.201710402 VL - 17 IS - 1 SP - 871 EP - 874 ER - TY - JOUR A1 - Sullivan, T. J. T1 - Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors JF - Inverse Problems and Imaging Y1 - 2017 U6 - https://doi.org/10.3934/ipi.2017040 VL - 11 IS - 5 SP - 857 EP - 874 ER - TY - CHAP A1 - Cockayne, Jon A1 - Oates, Chris A1 - Sullivan, T. J. A1 - Girolami, Mark T1 - Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems T2 - Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering N2 - This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model Y1 - 2017 U6 - https://doi.org/10.1063/1.4985359 VL - 1853 SP - 060001-1 EP - 060001-8 ER - TY - CHAP A1 - Schuster, Ingmar A1 - Strathmann, Heiko A1 - Paige, Brooks A1 - Sejdinovic, Dino T1 - Kernel Sequential Monte Carlo T2 - Joint European Conference on Machine Learning and Knowledge Discovery in Databases N2 - We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance structure and gradients of the target. The emulator's geometry is adaptively updated and subsequently used to inform local proposals. Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not compromise convergence of the sampler. KSMC combines the strengths of sequental Monte Carlo and kernel methods: superior performance for multimodal targets and the ability to estimate model evidence as compared to Markov chain Monte Carlo, and the emulator's ability to represent targets that exhibit high degrees of nonlinearity. As KSMC does not require access to target gradients, it is particularly applicable on targets whose gradients are unknown or prohibitively expensive. We describe necessary tuning details and demonstrate the benefits of the the proposed methodology on a series of challenging synthetic and real-world examples. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-71249-9_24 SP - 390 EP - 409 ER - TY - JOUR A1 - Klus, Stefan A1 - Schuster, Ingmar A1 - Muandet, Krikamol T1 - Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces JF - Journal of Machine Learning Research N2 - Transfer operators such as the Perron-Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the dynamics onto the dominant slow processes, or to separate superimposed signals. We extend transfer operator theory to reproducing kernel Hilbert spaces and show that these operators are related to Hilbert space representations of conditional distributions, known as conditional mean embeddings in the machine learning community. Moreover, numerical methods to compute empirical estimates of these embeddings are akin to data-driven methods for the approximation of transfer operators such as extended dynamic mode decomposition and its variants. In fact, most of the existing methods can be derived from our framework, providing a unifying view on the approximation of transfer operators. One main benefit of the presented kernel-based approaches is that these methods can be applied to any domain where a similarity measure given by a kernel is available. We illustrate the results with the aid of guiding examples and highlight potential applications in molecular dynamics as well as video and text data analysis. Y1 - 2017 ER - TY - THES A1 - Clausecker, Robert T1 - Notes on the Construction of Tablebases Y1 - 2017 ER - TY - CHAP A1 - Lange, Alexander T1 - A mathematical framework for predicting lifestyles of viral pathogens T2 - Modelling Biological Evolution 2017: Developing Novel Approaches Y1 - 2017 ER - TY - JOUR A1 - Kramer, Tobias A1 - Läuter, Matthias A1 - Rubin, Martin A1 - Altwegg, Kathrin T1 - Seasonal changes of the volatile density in the coma and on the surface of comet 67P/Churyumov-Gerasimenko JF - Monthly Notices of the Royal Astronomical Society N2 - Starting from several monthly data sets of Rosetta’s COmetary Pressure Sensor we reconstruct the gas density in the coma around comet 67P/Churyumov-Gerasimenko. The underlying inverse gas model is constructed by fitting ten thousands of measurements to thousands of potential gas sources distributed across the entire nucleus surface. The ensuing self-consistent solution for the entire coma density and surface activity reproduces the temporal and spatial variations seen in the data for monthly periods with Pearson correlation coefficients of 0.93 and higher. For different seasonal illumination conditions before and after perihelion we observe a systematic shift of gas sources on the nucleus. Y1 - 2017 U6 - https://doi.org/10.1093/mnras/stx866 VL - 469 SP - S20 EP - S28 ER - TY - GEN A1 - Aboulhassan, Amal A1 - Sicat, Ronell A1 - Baum, Daniel A1 - Wodo, Olga A1 - Hadwiger, Markus T1 - Comparative Visual Analysis of Structure-Performance Relations in Complex Bulk-Heterojunction Morphologies N2 - The structure of Bulk-Heterojunction (BHJ) materials, the main component of organic photovoltaic solar cells, is very complex, and the relationship between structure and performance is still largely an open question. Overall, there is a wide spectrum of fabrication configurations resulting in different BHJ morphologies and correspondingly different performances. Current state- of-the-art methods for assessing the performance of BHJ morphologies are either based on global quantification of morphological features or simply on visual inspection of the morphology based on experimental imaging. This makes finding optimal BHJ structures very challenging. Moreover, finding the optimal fabrication parameters to get an optimal structure is still an open question. In this paper, we propose a visual analysis framework to help answer these questions through comparative visualization and parameter space exploration for local morphology features. With our approach, we enable scientists to explore multivariate correlations between local features and performance indicators of BHJ morphologies. Our framework is built on shape-based clustering of local cubical regions of the morphology that we call patches. This enables correlating the features of clusters with intuition-based performance indicators computed from geometrical and topological features of charge paths. T3 - ZIB-Report - 17-16 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63239 SN - 1438-0064 ER - TY - JOUR A1 - Ritter, Zully A1 - Belavy, Daniel A1 - Baumann, Wolfgang A1 - Felsenberg, Dieter T1 - In vivo bone remodeling rates determination and compressive stiffness variations before, during 60 days bed rest and two years follow up: a micro-FE-analysis from HR-pQCT measurements of the Berlin bed rest study-2 JF - Acta Astronautica KW - finite-element analysis KW - bone structure KW - compressive stiffness KW - bed rest KW - HR-pQCT measurement Y1 - 2017 U6 - https://doi.org/10.1016/j.actaastro.2016.12.002 VL - 132 SP - 67 EP - 77 ER -