The Rescaled Pólya Urn and the Wright—Fisher Process with Mutation

In recent papers the authors introduce, study and apply a variant of the Eggenberger—Pólya urn, called the “rescaled” Pólya urn, which, for a suitable choice of the model parameters, exhibits a reinforcement mechanism mainly based on the last observations, a random persistent fluctuation of the pred...

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Autores principales: Giacomo Aletti, Irene Crimaldi
Formato: article
Lenguaje:EN
Publicado: MDPI AG 2021
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Acceso en línea:https://doaj.org/article/9c59a411d040471eb47fbc05a11bc6c9
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Sumario:In recent papers the authors introduce, study and apply a variant of the Eggenberger—Pólya urn, called the “rescaled” Pólya urn, which, for a suitable choice of the model parameters, exhibits a reinforcement mechanism mainly based on the last observations, a random persistent fluctuation of the predictive mean and the almost sure convergence of the empirical mean to a deterministic limit. In this work, motivated by some empirical evidence, we show that the multidimensional Wright—Fisher diffusion with mutation can be obtained as a suitable limit of the predictive means associated to a family of rescaled Pólya urns.