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 Fr\'echet function: the degree of stickiness.

翻译：已有研究表明，在Billera-Holmes-Vogtmann（BHV）系统发育空间中，当样本量足够大时，某些概率分布的样本均值会局限于低维子空间。这种非标准行为被称为粘性，并在比较粘性分布样本的统计应用中带来困难。我们扩展了关于粘性的现有结果，证实在BHV空间的特殊情形下，这种采样行为与拓扑条件等价。此外，我们提出通过引入Fréchet函数的方向导数——即粘性度——来缓解粘性分布的统计比较问题。