Related papers: Sampling probabilities, diffusions, ancestral grap…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads…
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…
Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are defined by a degenerate second order operator on the interval [0, 1], where the coefficient of the second order term…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…
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…
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
With novel developments in sequencing technologies, time-sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these datasets. Here, we compare…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…
We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…
Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…