Related papers: Sequential Markov coalescent algorithms for popula…
We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
A large offspring number diploid biparental multilocus population model of Moran type is our object of study. At each timestep, a pair of diploid individuals drawn uniformly at random contribute offspring to the population. The number of…
The sequentially Markov coalescent (SMC) is a Markov jump process which models correlations in local genealogies across a chromosome. It has been used as a theoretical tool for studying linkage disequilibrium and identity-by-descent, and it…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
We define a Markov process in a forward population model with backward genealogy given by the $\Lambda$-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two…
Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r=0, this reduces to the study of a single…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics. Kingman's coalescent process enables inference of past population dynamics directly from…
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting.…
We introduce a general diploid population model with self-fertilization and possible overlapping generations, and study the genealogy of a sample of $n$ genes as the population size $N$ tends to infinity. Unlike traditional approach in…
The coalescent revolutionised theoretical population genetics, simplifying, or making possible for the first time, many analyses, proofs, and derivations, and offering crucial insights about the way in which the structure of data in samples…
Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus,…
Coalescents with multiple collisions (also called Lambda-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with…
We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed…
We study coalescent processes conditional on the population pedigree under the exchangeable diploid bi-parental population model of \citet{BirknerEtAl2018}. While classical coalescent models average over all reproductive histories, thereby…