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In this chapter, we extend the Pólya urn model to the multicolor urn. The EwensEwens, W.J. sampling formula is a one-parameter probability distribution on the set of all partitions of an integer (Ewens 1990)Ewens, W.J.. The Pitman sampling formula is a two-parameter extension of the EwensEwens, W.J. sampling formula (Pitman 2006)Pitman, J.. The Pitman-Yor process (Pitman and Yor 1997)Pitman, J. and a generalized Pólya urnGeneralized Pólya urn (Yamato and Shibuya 2001) are the non-equilibrium stochastic processes that derive the Pitman sampling formula (Pitman 2006)Pitman, J.. These processes permit new entries of individuals and an increasing number of them.

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Multicolor Urn Process and Equilibrium

  • 章节

  • 发表日期：

    2025年

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  • Masato Hisakado

摘要

In this chapter, we extend the Pólya urn model to the multicolor urn. The EwensEwens, W.J. sampling formula is a one-parameter probability distribution on the set of all partitions of an integer (Ewens 1990)Ewens, W.J.. The Pitman sampling formula is a two-parameter extension of the EwensEwens, W.J. sampling formula (Pitman 2006)Pitman, J.. The Pitman-Yor process (Pitman and Yor 1997)Pitman, J. and a generalized Pólya urnGeneralized Pólya urn (Yamato and Shibuya 2001) are the non-equilibrium stochastic processes that derive the Pitman sampling formula (Pitman 2006)Pitman, J.. These processes permit new entries of individuals and an increasing number of them.