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Molecular phylogenetic and phylogeographic reconstructions generally assume time-homogeneous substitution processes. Motivated by computational convenience, this assumption sacrifices biological realism and offers little opportunity to…
In Bayesian phylogenetics, our goal is to estimate the posterior distribution over phylogenetic trees. Markov chain Monte Carlo methods are widely used to approximate the phylogenetic posterior distributions. For large-scale sequence data,…
The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a…
Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in…
We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown.…
Scientific studies in many areas of biology routinely employ evolutionary analyses based on the probabilistic inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly…
Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
Phylogenetic inference is an intractable statistical problem on a complex space. Markov chain Monte Carlo methods are the primary tool for Bayesian phylogenetic inference but it is challenging to construct efficient schemes to explore the…
Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…
Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…
Phylogenetic mixture models, in which the sites in sequences undergo different substitution processes along the same or different trees, allow the description of heterogeneous evolutionary processes. As data sets consisting of longer…
When the process underlying DNA substitutions varies across evolutionary history, the standard Markov models underlying standard phylogenetic methods are mathematically inconsistent. The most prominent example is the general time reversible…
The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant…
Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes…
We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…
Mutation rate variation across loci is well known to cause difficulties, notably identifiability issues, in the reconstruction of evolutionary trees from molecular sequences. Here we introduce a new approach for estimating general…
The parameters of many classes of birth-death processes cannot be inferred uniquely from phylogenetic trees: infinitely many parameter combinations yield the same distribution of phylogenetic trees. Here, we show that parameter…