Abstract
It has been observed that the sample mean of certain probability distributions in Billera-Holmes-Vogtmann (BHV) phylogenetic spaces is confined to a lower-dimensional subspace for large enough sample size. This non-standard behavior has been called stickiness and poses difficulties in statistical applications when comparing samples of sticky distributions. We extend previous results on stickiness to show the equivalence of this sampling behavior to topological conditions in the special case of BHV spaces. Furthermore, we propose to alleviate statistical comparision of sticky distributions by including the directional derivatives of the Fréchet function: the degree of stickiness.
Supported by DFG GK 2088 and DFG HU 1575/7.
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Acknowledgements
The 1st author gratefully acknowledges the DFG RTG 2088. The 2dn author gratefully acknowledges the DFG HU 1575/7. The 3rd author gratefully acknowledge the DFG CRC 1456. The work was done partially while the 2nd author was participating in the program of the Institute for Mathematical Sciences, National University of Singapore, in 2022.
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Lammers, L., Van, D.T., Nye, T.M.W., Huckemann, S.F. (2023). Types of Stickiness in BHV Phylogenetic Tree Spaces and Their Degree. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_35
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DOI: https://doi.org/10.1007/978-3-031-38271-0_35
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