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Hidden Markov Models (HMMs) are powerful tools for modeling sequential data, where the underlying states evolve in a stochastic manner and are only indirectly observable. Traditional HMM approaches are well-established for linear sequences,…
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.…
Phylogenetics, the inference of evolutionary trees from molecular sequence data such as DNA, is an enterprise that yields valuable evolutionary understanding of many biological systems. Bayesian phylogenetic algorithms, which approximate a…
We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…
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…
We introduce a hierarchical nonparametric model for probability measures based on a multi-resolution transformation of probability distributions. The model allows a varying amount of shrinkage to be applied to data features of different…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…
We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version…
We provide a new approach for proving the indistinguishability of connected components of random one-or-two-ended oriented forests on unimodular random graphs. In particular, this approach leads to a new and simpler proof for the wired…
Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic…
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…
We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root state estimator is said to be consistent if the probability…
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…
Bayesian inference has predominantly relied on the Markov chain Monte Carlo (MCMC) algorithm for many years. However, MCMC is computationally laborious, especially for complex phylogenetic models of time trees. This bottleneck has led to…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…