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A Journey from Process Algebra via Timed Automata to Model Learning pp 339–357Cite as

A Reconstruction of Ewens’ Sampling Formula via Lists of Coins

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13560))

Abstract

This overview paper starts from an elementary fact about lists of numbers (coins) for which a simple arithmetical proof is lacking. The paper does provide a proof, but via probabilistic reasoning, using iterations of probabilistic functions (channels), or equivalently, using iteration of transitions in a probabilistic automaton. The formulas involved capture mutations, with a rate parameter, as developed some fifty years ago in population biology by Warren Ewens. Here, this formula is reconstructed, in a theoretical computer science setting, first for lists and then also for multisets—like in the original work. The methods for describing such mutations have wider significance, beyond biology, for instance in machine learning, when the number of clusters in a classification problem may grow.

Dedicated to my dear colleague Frits Vaandrager, on the occasion of his 60th birthday.

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Acknowledgements

Thanks are due to Ceel Pierik for helpful discussion on the material in Sect. 5.

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Authors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud University, Nijmegen, The Netherlands

    Bart Jacobs

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  1. Bart Jacobs
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Correspondence to Bart Jacobs .

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Editors and Affiliations

  1. Radboud University Nijmegen, Nijmegen, The Netherlands

    Nils Jansen

  2. University of Twente, Enschede, The Netherlands

    Mariëlle Stoelinga

  3. University of Twente, Enschede, The Netherlands

    Petra van den Bos

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Jacobs, B. (2022). A Reconstruction of Ewens’ Sampling Formula via Lists of Coins. In: Jansen, N., Stoelinga, M., van den Bos, P. (eds) A Journey from Process Algebra via Timed Automata to Model Learning . Lecture Notes in Computer Science, vol 13560. Springer, Cham. https://doi.org/10.1007/978-3-031-15629-8_18

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  • DOI: https://doi.org/10.1007/978-3-031-15629-8_18

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  • Online ISBN: 978-3-031-15629-8

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