Abstract
For a Pólya urn model with a continuum of colors introduced by Blackwell and MacQueen ((1973),Ann. Statist.,2, 1152–1174), we show the joint distribution of colors aftern draws from which several properties of the urn model are derived. The similar results hold for the case where the initial distribution of colors is invariant under a finite group of transformations.
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References
Antoniak, C. A. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems,Ann. Statist.,2, 1152–1174.
Blackwell, D. and MacQueen, J. (1973). Ferguson distribution via Pólya urn schemes,Ann. Statist.,1, 353–355.
Charalambides, Ch. A. and Singh, J. (1988). A review of the Stirling numbers, their generalization and a statistical applications,Comm. Statist. Theory Methods,17, 2533–2593.
Comtet, L. (1974).Advanced Combinatorics, Reidel, Dordrecht.
Dalal, S. R. (1979). Dirichlet invariant processes and applications to nonparametric estimation of symmetric distribution functions,Stochastic Process. Appl.,9, 99–107.
Korwar, R. M. and Hollander, M. (1973). Contributions to the theory of Dirichlet processes,Ann. Probab.,1, 705–711.
Sibuya, M. (1991). A cluster-number distribution and its application to the analysis of homonyms,Japanese Journal of Applied Statistics,20, 139–153 (in Japanese).
Yamato, H. (1987). On samples from distributions chosen from a Dirichlet invariant process,Bull. Inform. Cybernet.,22, 199–207.
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Yamato, H. A pólya urn model with a continuum of colors. Ann Inst Stat Math 45, 453–458 (1993). https://doi.org/10.1007/BF00773347
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DOI: https://doi.org/10.1007/BF00773347