Related papers: A consistency lemma in statistical phylogenetics

We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

A mathematical theory on flocking serves the foundation for several ubiquitous multi-agent phenomena in biology, ecology, sensor networks, economy, as well as social behavior like language emergence and evolution. Directly inspired by the…

Many classes of phylogenetic networks have been proposed in the literature. A feature of several of these classes is that if one restricts a network in the class to a subset of its leaves, then the resulting network may no longer lie within…

The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth-death polytomy resolver is a method of…

This paper considers the question of the rate of convergence to ${\alpha}$- stable laws, using arguments based on the Zolotarev distance to prove bounds. We provide a rate of convergence to ${\alpha}$-stable random variable where 1 <…

An identity of conformal-projective curvature tensor of a statistical manifold is studied in this paper. The relation between the constancy of curvature and conformal-projective flatness of statistical manifolds is also discussed.

Selective inference is considered for testing trees and edges in phylogenetic tree selection from molecular sequences. This improves the previously proposed approximately unbiased test by adjusting the selection bias when testing many trees…

Estimating the phylogeny of the genus Homo is entering a new phase of vastly improved data and methodology. There is increasing evidence of 6 to 10 competing species/lineages at any point in the last half million years, making the…

We study the reconfiguration of plane spanning trees on point sets in the plane in convex position, where a reconfiguration step (flip) replaces one edge with another, yielding again a plane spanning tree. The flip distance between two…

In this paper, we study the asymptotic behaviour of the number of subtrees and the subtree density for a sequence of trees that converges in the Benjamini-Schramm sense. Benjamini-Schramm convergence, also called local weak convergence,…

In a landmark paper, Abadie and Imbens (2008) showed that the naive bootstrap is inconsistent when applied to nearest neighbor matching estimators of the average treatment effect with a fixed number of matches. Since then, this finding has…

A phylogenetic birth-and-death model is a probabilistic graphical model for a so-called phylogenetic profile, i.e., the size distribution for a homolog gene family at the terminal nodes of a phylogeny. Profile datasets are used in…

Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…

Constructing tests or confidence regions that control over the error rates in the long-run is probably one of the most important problem in statistics. Yet, the theoretical justification for most methods in statistics is asymptotic. The…

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular the fossilized…

The rich and varied ways that genetic material can be passed between species has motivated extensive research into the theory of phylogenetic networks. Features that align with biological processes, or with desirable mathematical…

In a recent study, Bryant, Francis and Steel investigated the concept of \enquote{future-proofing} consensus methods in phylogenetics. That is, they investigated if such methods can be robust against the introduction of additional data like…

One of the basic questions of phylogenomics is how gene function evolves, whether among species or inside gene families. In this chapter, we provide a brief overview of the problems associated with defining gene function in a manner which…

Coalescent histories are combinatorial structures that describe for a given gene tree and species tree the possible lists of branches of the species tree on which the gene tree coalescences take place. Properties of the number of coalescent…