Related papers: Filtering the Wright-Fisher diffusion
Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional…
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…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
We study voter models defined on large sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright-Fisher diffusion only involves certain averages of…
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.…
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…
In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright-Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation…
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…
The stationary 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 to…
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…
We study a generalization of the Wright--Fisher model in which some individuals adopt a behavior that is harmful to others without any direct advantage for themselves. This model is motivated by studies of spiteful behavior in nature,…
In a (two-type) Wright-Fisher diffusion with directional selection and two-way mutation, let $x$ denote today's frequency of the beneficial type, and given $x$, let $h(x)$ be the probability that, among all individuals of today's…
The Moran discrete process and the Wright-Fisher modelare the most popular models in population genetics. It is common tounderstand the dynamics of these models to use an approximating diffusionprocess, called Wright-Fisher diffusion. Here,…
Wright-Fisher diffusions describe the evolution of the type composition of an infinite haploid population with two types (say type $0$ and type $1$) subject to neutral reproductions, and possibly selection and mutations. In the present…
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…
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…
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…
A new class of time-dependent Dirichlet priors is introduced as a generalisation of the Wright-Fisher diffusion, allowing discontinuities in the trajectories, as well as non-Markovian memory. This class is obtained as a simple stochastic…
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…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…