15 citations · 18 across the 12 of their papers we have counts for
12 papers
Poisson-Dirichlet approximation for the stationary distribution of the inclusion process
Han L. Gan
We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson-Dirichlet distribution. Using Stein's method, we derive an explicit bo…
Stationary distribution approximations of Two-island Wright-Fisher and seed-bank models using Stein's method
Han L. Gan, Maite Wilke-Berenguer
We consider two finite population Markov chain models, the two-island Wright-Fisher model with mutation, and the seed-bank model with mutation. Despite the relatively simple descri…
Steady-state Dirichlet approximation of the Wright-Fisher model using the prelimit generator comparison approach of Stein's method
Anton Braverman, Han L. Gan
The Wright-Fisher model, originating in Wright (1931) is one of the canonical probabilistic models used in mathematical population genetics to study how genetic type frequencies ev…
Arcsine laws for random walks generated from random permutations with applications to genomics
Xiao Fang, Han Liang Gan, Susan Holmes +4
A classical result for the simple symmetric random walk with steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the…
Stein's method for the Poisson-Dirichlet distribution and the Ewens Sampling Formula, with applications to Wright-Fisher models
Han L. Gan, Nathan Ross
We provide a general theorem bounding the error in the approximation of a random measure of interest--for example, the empirical population measure of types in a Wright-Fisher mode…
Stein's method and duality of Markov processes
Han L. Gan
One of the key ingredients to successfully apply Stein's method for distributional approximation are solutions to the Stein equations and their derivatives. Using Barbour's generat…
Approximation of the difference of two Poisson-like counts with Skellam
H. L. Gan, Eric D. Kolaczyk
Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of a…
Improving approximation error bounds via truncation
H. L. Gan
One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we wi…
Dirichlet approximation of equilibrium distributions in Cannings models with mutation
H. L. Gan, Adrian Röllin, Nathan Ross
Consider a haploid population of fixed finite size with a finite number of allele types and having Cannings exchangeable genealogy with neutral mutation. The stationary distributio…
Conditional Poisson process approximation
H. L. Gan
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Ov…
Fragility Distributions and their approximations
H. L. Gan, A. Xia
Given a sequence of identically distributed random variables with common distribution , the \emph{fragility distribution of order }, represented by $\FD$, is the limit co…
Stein factors for negative binomial approximation in Wasserstein distance
A. D. Barbour, H. L. Gan, A. Xia
The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The pro…