Related papers: Necessary and sufficient conditions for consistent…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
This paper provides answers to questions regarding the almost sure limiting behavior of rooted, binary tree-structured rules for regression. Examples show that questions raised by Gordon and Olshen in 1984 have negative answers. For these…
The ancestral maximum-likelihood and phylogeography problems are two fundamental problems involving evolutionary studies. The ancestral maximum-likelihood problem involves identifying a rooted tree alongside internal node sequences that…
We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very…
We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
The $k$-cut number of rooted graphs was introduced by Cai et al. as a generalization of the classical cutting model by Meir and Moon. In this paper, we show that all moments of the k-cut number of conditioned Galton-Watson trees converges…
The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…
We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes…
For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motivated by signal processing problems and metastability studies…
In this work, we study a family of non-Markovian trees modeling populations where individuals live and reproduce independently with possibly time-dependent birth-rate and lifetime distribution. To this end, we use the coding process…
In this paper we consider the reconstruction problem on the tree for the hardcore model. We determine new bounds for the non-reconstruction regime on the k-regular tree showing non-reconstruction when lambda < (ln 2-o(1))ln^2(k)/(2 lnln(k))…
We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say,…
We introduce a simple algorithm for reconstructing phylogenies from multiple gene trees in the presence of incomplete lineage sorting, that is, when the topology of the gene trees may differ from that of the species tree. We show that our…
We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks…
We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies…