Exploring Stickiness in CAT(κ) Spaces

Lammers, Lars

dc.contributor.advisor	Huckemann, Stephan F. Prof. Dr.
dc.contributor.author	Lammers, Lars
dc.date.accessioned	2024-10-10T16:48:51Z
dc.date.available	2024-10-17T00:50:09Z
dc.date.issued	2024-10-10
dc.identifier.uri	http://resolver.sub.uni-goettingen.de/purl?ediss-11858/15534
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-10795
dc.format.extent	156	de
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject.ddc	510	de
dc.title	Exploring Stickiness in CAT(κ) Spaces	de
dc.type	doctoralThesis	de
dc.contributor.referee	Huckemann, Stephan F. Prof. Dr.
dc.date.examination	2024-09-16	de
dc.description.abstracteng	The Fréchet mean is a natural generalization of the expectation to probability distributions on arbitrary metric spaces. In recent years, several seemingly related phenomena were observed for certain distributions on singular CAT(κ) spaces and are often collectively referred to as stickiness. Most notably, the sample Fréchet means of sticky distributions is confined to lower-dimensional subsets of the space. In addition, these distributions seem to be extraordinarily robust: the Fréchet mean remains in the lower-dimensional subset it sticks to when the distribution is perturbed by a point mass or when another distribution is considered which is sufficiently close in Wasserstein distance. Due to the restricted asymptotic variation of sample Fréchet means, stickiness limits the usefulness of sample Fréchet means for the discrimination between two distributions sticking to the same subset. Among the spaces affected by the phenomenon of stickiness are Billera-Holmes- Vogtmann (BHV) spaces of phylogenetic trees, in which stickiness manifests as the tendency of Fréchet means sticking to unresolved tree topologies. In that context, stickiness also causes computational issues. Conventional iterative methods for the computation of sample Fréchet means often fail in finding the correct tree topology when the topology is not binary. In this thesis, we introduce multiple sticky flavors capturing different phenomena commonly associated with the umbrella term of stickiness, and investigate their relationships in different scenarios, with a focus on CAT(κ) spaces and BHV-spaces, in particular. Furthermore, we develop hypothesis tests for sticky distributions on BHV spaces, and propose new methods for determining edges in Fréchet means of distributions on BHV spaces.	de
dc.contributor.coReferee	Luke, Russell Prof. Dr.
dc.subject.eng	Fréchet mean	de
dc.subject.eng	CAT(κ) spaces	de
dc.subject.eng	Stickiness	de
dc.subject.eng	Wasserstein distance	de
dc.subject.eng	Phylogenetic trees	de
dc.subject.eng	Statisical discrimination	de
dc.identifier.urn	urn:nbn:de:gbv:7-ediss-15534-8
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.description.embargoed	2024-10-17	de
dc.identifier.ppn	1906000719
dc.notes.confirmationsent	Confirmation sent 2024-10-10T19:45:01	de

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