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Latest Publications


May 2021
Biomedical Optics Express
Mojiri S, Isbaner S, Mühle S, Jang H, Bae AJ, Gregor I, Golami A, Enderlein J
April 2021
Structure
Huang B, Guo Q, Niedermeier ML, Cheng J, Engler T, Maurer M, Pautsch A, Baumeister W, Stengel F, Kochanek S, Fernández-Busnadiego R
April 2021
bioRxiv
Baeuerlein FJB, Pastor-Pareja JC, Fernandez-Busnadiego R
April 2021
Nature Communications
Trinkaus VA, Riera-Tur I, Martínez-Sánchez A, Bäuerlein FJB, Guo Q, Arzberger T, Baumeister W, Dudanova I, Hipp MS, Hartl FU, Fernández-Busnadiego R
April 2021
Nature Structural & Molecular Biology
Farnung L, Ochmann M, Engeholm M, Cramer P
April 2021
European Biophysics Journal
Pein F, Eltzner B, Munk A
April 2021
Current Opinion in Virology
Hillen HS
April 2021
Proceedings of the National Academy of Sciences of the United States of America
Hillen HS, Markov DA, Wojtas ID, Hofmann KB, Lidschreiber M, Cowan AT, Jones JL, Temiakov D, Cramer P, Anikin M
March 2021
Acta Crystallographica Section D-Structural Biology
Hamann F, Zimmerningkat LC, Becker RA, Garbers TB, Neumann P, Hubc JS, Ficner R
March 2021
ArXiv
Hundrieser S, Klatt M, Munk A

Authors

Hundrieser S, Klatt M, Munk A

Journal

ArXiv

Citation

arXiv:2103.15426.

Abstract

Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to this are distributional limit laws and we derive a central limit theorem for the empirical OT distance of circular data. Our limit results require only mild assumptions in general and include prominent examples such as the von Mises or wrapped Cauchy family. Most notably, no assumptions are required when data are sampled from the probability measure to be compared with, which is in strict contrast to the real line. A bootstrap principle follows immediately as our proof relies on Hadamard differentiability of the OT functional. This paves the way for a variety of statistical inference tasks and is exemplified for asymptotic OT based goodness of fit testing for circular distributions. We discuss numerical implementation, consistency and investigate its statistical power. For testing uniformity, it turns out that this approach performs particularly well for unimodal alternatives and is almost as powerful as Rayleigh’s test, the most powerful invariant test for von Mises alternatives. For regimes with many modes the circular OT test is less powerful which is explained by the shape of the corresponding transport plan.

DOI

arXiv:2103.15426

 

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