Stein's method for the Poisson-Dirichlet distribution and the Ewens sampling formula, with applications to Wright-Fisher models

DOI10.1214/20-AAP1600zbMath1476.60025arXiv1910.04976OpenAlexW3146324326MaRDI QIDQ2240828

Nathan Ross, Han L. Gan

Publication date: 4 November 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.04976

zbMATH Keywords

Stein's methodDirichlet processEwens sampling formulaWright-Fisher processPoisson-Dirichlet approximation

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Probability distributions: general theory (60E05) Population dynamics (general) (92D25) Convergence of probability measures (60B10)

Related Items (5)

The Prelimit Generator Comparison Approach of Stein’s Method ⋮ Concentration inequalities using approximate zero bias couplings with applications to Hoeffding’s statistic under the Ewens distribution ⋮ Bounding Kolmogorov distances through Wasserstein and related integral probability metrics ⋮ Stein's method, Gaussian processes and palm measures, with applications to queueing ⋮ The leftmost column of ordered Chinese restaurant process up-down chains: intertwining and convergence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fundamentals of Stein's method
• Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model
• The transition function of a Fleming-Viot process
• Markov chains and stochastic stability
• On the rate of convergence in the multivariate CLT
• Two-parameter family of infinite-dimensional diffusions on the Kingman simplex
• Stein's method of exchangeable pairs for the Beta distribution and generalizations
• A note on the exchangeability condition in Stein's method
• Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
• Exchangeable pairs and Poisson approximation
• Stein's method for diffusion approximations
• Wandering random measures in the Fleming-Viot model
• Convergence to Fleming-Viot processes in the weak atomic topology
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• Mathematical population genetics. I: Theoretical introduction.
• Logarithmic combinatorial structures: A probabilistic approach
• Compositions of random functions on a finite set
• Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models
• Central limit theorem for the size of the range of a renewal process
• Stein's method, Palm theory and Poisson process approximation.
• Approximation of Hilbert-valued gaussians on Dirichlet structures
• Stein's method for multivariate Brownian approximations of sums under dependence
• Measuring sample quality with diffusions
• T. E. Harris's contributions to recurrent Markov processes and stochastic flows
• Translated Poisson approximation using exchangeable pair couplings
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• Exact coalescent for the Wright-Fisher model
• Exponential approximation and Stein's method of exchangeable pairs
• Random Measures, Theory and Applications
• The infinitely-many-neutral-alleles diffusion model by ages
• The Poisson-Dirichlet Distribution and Related Topics
• Normal Approximation by Stein’s Method
• Expected coalescence time for a nonuniform allocation process
• The infinitely-many-neutral-alleles diffusion model
• The time back to the most recent common ancestor in exchangeable population models
• A short survey of Stein's method
• Fleming–Viot Processes in Population Genetics
• Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models
• Dirichlet approximation of equilibrium distributions in Cannings models with mutation

This page was built for publication: Stein's method for the Poisson-Dirichlet distribution and the Ewens sampling formula, with applications to Wright-Fisher models