Analyzing Generalized Pólya Urn Models using Martingales, with an Application to Viral Evolution

06/30/2023

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by   Ivan Specht, et al.

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The randomized play-the-winner (RPW) model is a generalized Pólya Urn process with broad applications ranging from viral genomics to clinical trials. We derive an exact expression for the variance of the RPW model as well as an approximation of its full probability mass function. We then demonstrate an application of the model to viral replication processes, and provide a novel method of estimating viral mutation rates.