Speaker
Description
Statistical inference in the field of phylogenetics requires the adaptiion of many classical methods to more general metric frameworks. The Fréchet-mean of a probability distribution is a generalisation of the expectation to metric spaces. 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. The umbrella term for such non-standard behavior is stickiness and poses difficulties in statistical applications when comparing samples of sticky distributions. We introduce multiple flavors of stickiness and extend previous results to show their equivalence 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.
