Related papers: Identifying evolutionary trees and substitution pa…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for…
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer.…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
The goal of branch length estimation in phylogenetic inference is to estimate the divergence time between a set of sequences based on compositional differences between them. A number of software is currently available facilitating branch…
We propose a new topological invariant of unlabeled trees of N nodes. The invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i as the matrix elements, where d_{i,j} are the elements of the distance matrix and v_i…
This paper describes the Context Tree Switching technique, a modification of Context Tree Weighting for the prediction of binary, stationary, n-Markov sources. By modifying Context Tree Weighting's recursive weighting scheme, it is possible…
We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of…
It has become increasingly common nowadays to collect observations of feature and response pairs from different environments. As a consequence, one has to apply learned predictors to data with a different distribution due to distribution…
We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We…
In this paper, we investigate tree-indexed Markov chains (Gibbs measures) defined by a Hamiltonian that couples two Ising layers: hidden spins \(s(x) \in \{\pm 1\}\) and observed spins \(\sigma(x) \in \{\pm 1\}\) on a Cayley tree. The…
Stochastic models of evolution (Markov random fields on trivalent trees) generally assume that different characters (different runs of the stochastic process) are independent and identically distributed. In this paper we take the first…
The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the…
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings,…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…
DAG models are statistical models satisfying a collection of conditional independence relations encoded by the nonedges of a directed acyclic graph (DAG) $\mathcal{G}$. Such models are used to model complex cause-effect systems across a…
Because biological processes can make different loci have different evolutionary histories, species tree estimation requires multiple loci from across the genome. While many processes can result in discord between gene trees and species…