Related papers: Topology and inference for multi-type Yule trees
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights…
Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…
RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate…
A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify…
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively,…
The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual…
Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant…
A uniform recursive tree on $n$ vertices is a random tree where each possible $(n-1)!$ labeled recursive rooted tree is selected with equal probability. In this paper we introduce and study weighted trees, a non-uniform recursive tree model…
Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this paper, we consider a Hidden Markov Model involving several correlated hidden processes at the same time.…
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…
Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively…
In mathematical phylogenetics, the time-consistent galled trees provide a simple class of rooted binary network structures that can be used to represent a variety of different biological phenomena. We study the enumerative combinatorics of…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
Networks are ubiquitous in economic research on organizations, trade, and many other areas. However, while economic theory extensively considers networks, no general framework for their empirical modeling has yet emerged. We thus introduce…
Maximum likelihood estimation (MLE) methods are widely used for evolutionary tree. As evolutionary tree is not a smooth parameter, the consistency of its MLE has been a topic of debate. It has been noted without proof that the classical…