Related papers: An R package for nonparametric inference on dynami…
This paper provides a construction of a Fleming--Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the…
In populations competing for resources, it is natural to ask whether consuming fewer resources provides any selective advantage. To answer this question, we propose a Wright- Fisher model with two types of individuals: the inefficient…
Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently…
The Random Variable Transformation (RVT) method is a fundamental tool for determining the probability distribution function associated with a Random Variable (RV) Y=g(X), where X is a RV and g is a suitable transformation. In the usual…
We construct a constant size population model allowing for general selective interactions and extreme reproductive events. It generalizes the idea of (Krone and Neuhauser 1997) who represented the selection by allowing individuals to sample…
We are interested in populations in which the fitness of different genetic types fluctuates in time and space, driven by temporal and spatial fluctuations in the environment. For simplicity, our population is assumed to be composed of just…
Consider a continuous time Markov chain with rates Q in the state space \Lambda\cup\{0\} with 0 as an absorbing state. In the associated Fleming-Viot process N particles evolve independently in \Lambda with rates Q until one of them…
The R Package IBMPopSim aims to simulate the random evolution of heterogeneous populations using stochastic Individual-Based Models (IBMs). The package enables users to simulate population evolution, in which individuals are characterized…
Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop…
This paper studies a branching-selection model of motionless particles in $\mathbb{R}^d$, with nonlocal branching, introduced by Durrett and Remenik in dimension $1$. The assumptions on the fitness function, $F$, and on the inhomogeneous…
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently…
In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations. This well known criterion involves a simple necessary and…
Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated…
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero…
Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in [0,1]^\N: \sum_{i\ge 1} x_i=1\}$ with GEM…
Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing…