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.

The Rescaled Pólya Urn and the Wright-Fisher Process with Mutation / G. Aletti, I. Crimaldi. - In: MATHEMATICS. - ISSN 2227-7390. - 9:22(2021 Nov 15), pp. 2909.1-2909.11. [10.3390/math9222909]

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

G. Aletti
Primo
;
2021-11-15

Abstract

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.
Pólya urn; predictive mean; urn model; Wright-Fisher diffusion
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/01 - Statistica
Centro di Ricerca Interdisciplinare su Modellistica Matematica, Analisi Statistica e Simulazione Computazionale per la Innovazione Scientifica e Tecnologica ADAMSS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/886158
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