Related papers: Bayesian nonparametric analysis of Kingman's coale…
The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman's coalescent process, which produces a binary tree, universally emerges from many microscopic models in which the…
We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibit so-called shallow gene genealogies, potentially…
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…
In a series of recent works it has been shown that a class of simple models of evolving populations under selection leads to genealogical trees whose statistics are given by the Bolthausen-Sznitman coalescent rather than by the well known…
Multiple-merger coalescents, e.g. $\Lambda$-$n$-coalescents, have been proposed as models of the genealogy of $n$ sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's…
Identifiability of evolutionary tree models has been a recent topic of discussion and some models have been shown to be non-identifiable. A coalescent-based rooted population tree model, originally proposed by Nielsen et al. 1998 [2], has…
The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics,…
The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends…
We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…
Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and…
The development of statistical approaches for the joint modelling of the temporal changes of imaging, biochemical, and clinical biomarkers is of paramount importance for improving the understanding of neurodegenerative disorders, and for…
Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large…
We consider the tree-valued Fleming-Viot process, $(\mathcal X_t)_{t\geq 0}$, with mutation and selection as studied in Depperschmidt, Greven, Pfaffelhuber (2012). This process models the stochastic evolution of the genealogies and…
Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…
Population genetics theory has laid the foundations for genomics analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species.…
A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the…
Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…
The Galton-Watson process is a model for population growth which assumes that individuals reproduce independently according to the same offspring distribution. Inference usually focuses on the offspring average as it allows to classify the…