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Prediction rules for exchangeable sequences related to species sampling

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  • Hansen, Ben
  • Pitman, Jim

Abstract

Suppose an exchangable sequence with values in a nice measurable space S admits a prediction rule of the following form: given the first n terms of the sequence, the next term equals the jth distinct value observed so far with probability pj,n, for j=1,2,... , and otherwise is a new value with distribution [nu] for some probability measure [nu] on S with no atoms. Then the pj,n depend only on the partitition of the first n integers induced by the first n values of the sequence. All possible distributions for such an exchangeable sequence are characterized in terms of constraints on the pj,n and in terms of their de Finetti representations.

Suggested Citation

  • Hansen, Ben & Pitman, Jim, 2000. "Prediction rules for exchangeable sequences related to species sampling," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 251-256, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:3:p:251-256
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    Citations

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    Cited by:

    1. U. Garibaldi & D. Costantini & P. Viarengo, 2007. "The two-parameter Ewens distribution: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 2(2), pages 147-161, December.
    2. Masanao Aoki & Hiroshi Yoshikawa, 2012. "Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(1), pages 1-22, May.
    3. Martínez-Ovando Juan Carlos & Olivares-Guzmán Sergio I. & Roldán-Rodríguez Adriana, 2014. "Predictive Inference on Finite Populations Segmented in Planned and Unplanned Domains," Working Papers 2014-04, Banco de México.
    4. Wenpin Tang, 2022. "Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions," Papers 2206.02227, arXiv.org.
    5. Ali Amiryousefi & Ville Kinnula & Jing Tang, 2022. "Bayes in Wonderland! Predictive Supervised Classification Inference Hits Unpredictability," Mathematics, MDPI, vol. 10(5), pages 1-11, March.
    6. Bissiri, Pier Giovanni, 2010. "Characterization of the law of a finite exchangeable sequence through the finite-dimensional distributions of the empirical measure," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1306-1312, September.
    7. Andrea Collevecchio & Codina Cotar & Marco LiCalzi, 2011. "On a preferential attachment and generalized Pólya's urn model," Working Papers 8, Department of Management, Università Ca' Foscari Venezia, revised Oct 2012.
    8. Cerquetti, Annalisa, 2007. "A note on Bayesian nonparametric priors derived from exponentially tilted Poisson-Kingman models," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1705-1711, December.

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