Related papers: Intertwining of the Wright-Fisher diffusion
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path.…
The long time behavior of an absorbed Markov process is well described by the limiting distribution of the process conditioned to not be killed when it is observed. Our aim is to give an approximation's method of this limit, when the…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods…
The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of…
Coupled Wright-Fisher diffusions have been recently introduced to model the temporal evolution of finitely-many allele frequencies at several loci. These are vectors of multidimensional diffusions whose dynamics are weakly coupled among…
The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in…
This paper generalizes the strong seed-bank model introduced in arXiv:1411.4747 to allow for more general dormancy time distributions, such as a type of Pareto distribution. Inspired by the method of approximation using models with…
The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that…
In this paper an exact rejection algorithm for simulating paths of the coupled Wright-Fisher diffusion is introduced. The coupled Wright-Fisher diffusion is a family of multidimensional Wright-Fisher diffusions that have drifts depending on…
In this article we consider a family of real-valued diffusion processes on the time interval $[0,1]$ indexed by their prescribed initial value $x \in \mathbb{R}$ and another point in space, $y \in \mathbb{R}$. We first present an…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the…
The Wright-Fisher process with selection is an important tool in population genetics theory. Traditional analysis of this process relies on the diffusion approximation. The diffusion approximation is usually studied in a partial…
The Wright--Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation, and genetic drift. Simulating paths of…
It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
We investigate the properties of a Wright-Fisher diffusion process started from frequency x at time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge. Bridges arise naturally in the analysis of selection…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…