Related papers: Tractable diffusion and coalescent processes for w…

In this paper we consider a model based on branching process theory for the proliferation and the dissemination network of T cells in the adaptive immune response. A multi-type Galton Watson branching process is assumed as the basic…

We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may…

Prior social contagion models consider the spread of either one contagion at a time on interdependent networks or multiple contagions on single layer networks or under assumptions of competition. We propose a new threshold model for the…

Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…

We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…

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…

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

When an infectious disease outbreak is of a relatively small size, describing the ancestry of a sample of infected individuals is difficult because most ancestral models assume large population sizes. Given a set of infected individuals, we…

Galaxy populations at different cosmic epochs are often linked together by comoving cumulative number density in observational studies. Many theoretical works, however, have shown that the number densities of tracked galaxy populations…

Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…

Consider the Markov process taking values in the partitions of N such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate d. This is a special case of exchangeable…

We consider a model of a population in which individuals are sampled from different species. The Yule-Kingman nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a…

From the Poisson-Dirichlet diffusions to the $Z$-measure diffusions, they all have explicit transition densities. In this paper, we will show that the transition densities of the $Z$-measure diffusions can also be expressed as a mixture of…

The development of coalescent theory paved the way to statistical inference from population genetic data. In the genomic era, however, coalescent models are limited due to the complexity of the underlying ancestral recombination graph. The…

We extend the spatial $\Lambda$-Fleming-Viot process introduced in [Electron. J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models allele frequencies in a population which is distributed over the two-dimensional…

Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…

We construct a new class of infinite-dimensional diffusions taking values in a generalized Kingman simplex. Our model describes the temporal evolution of the relative frequencies of infinitely-many types which are "labeled" by an arbitrary…

We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the…

This paper explores the challenges and benefits of a trainable destruction process in diffusion samplers -- diffusion-based generative models trained to sample an unnormalised density without access to data samples. Contrary to the majority…