Related papers: Analysis and rejection sampling of Wright-Fisher d…
{\bf Abstract} The trajectory of the frequency of an allele which begins at $x$ at time $0$ and is known to have frequency $z$ at time $T$ can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when $x=z=0$ are…
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…
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…
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…
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…
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 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,…
A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
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.…
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…
The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of…
It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth…
Motivated by a biased diffusion of molecular motors with the bias dependent on the state of the substrate, we investigate a random walk on a one-dimensional lattice that contains weak links (called "bridges'') which are affected by the…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
Whisking is a rhythmic and adaptive behavior that rodents use to probe and interact with their environment, and the frequency of movement reflects both sensorimotor processing and internal brain states. A robust and traditional method of…
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…
We study the small-time asymptotics for hypoelliptic diffusion processes conditioned by their initial and final positions, in a model class of diffusions satisfying a weak H\"ormander condition where the diffusivity is constant and the…
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent…