相关论文: A consistency lemma in statistical phylogenetics
We describe the use of the Frechet mean and variance in the Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Frechet mean is comparable to other summary methods,…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
An important and well-studied problem in phylogenetics is to compute a \emph{consensus tree} so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
It is proposed that the co-expression of statistically significant motifs among the sequences of a proteome is a phylogenetic trait. From the co-expression matrix of such motifs in a group of prokaryotic proteomes a suitable definition of a…
We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection…
We show the consistency of a threshold dynamics type algorithm for the anisotropic motion by fractional mean curvature, in the presence of a time dependent forcing term. Beside the consistency result, we show that convex sets remain convex…
Phylogenomics, even more so than traditional phylogenetics, needs to represent the uncertainty in evolutionary trees due to systematic error. Here we illustrate the analysis of genome-scale alignments of yeast, using robust measures of the…
We use a combination of analytic models and computer simulations to gain insight into the dynamics of evolution. Our results suggest that certain interesting phenomena should eventually emerge from the fossil record. For example, there…
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and…
This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more…
These notes are a self-contained short proof of the stability of persistence diagrams.
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.
We devise a general result on the consistency of model-based bootstrap methods for U- and V-statistics under easily verifiable conditions. For that purpose, we derive the limit distributions of degree-2 degenerate U- and V-statistics for…