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On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

Author

Listed:
  • Federico Camerlenghi

    (Department of Economics, Management and Statistics, University of Milano-Bicocca, Piazza dell’Ateneo Nuovo 1, 20126 Milano, Italy
    Collegio Carlo Alberto, Piazza V. Arbarello 8, 10122 Torino, Italy
    BIDSA, Bocconi University, via Röntgen 1, 20136 Milano, Italy)

  • Stefano Favaro

    (Collegio Carlo Alberto, Piazza V. Arbarello 8, 10122 Torino, Italy
    Department of Economics, Social Studies, Applied Mathematics and Statistics, University of Torino, Corso Unione Sovietica 218/bis, 10134 Torino, Italy
    IMATI-CNR “Enrico Magenes”, 20133 Milano, Italy)

Abstract

In the 1920s, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson’s “sufficientness” postulate, and it has been the subject of many contributions in Bayesian statistics, leading to predictive characterization for infinite-dimensional generalizations of the Dirichlet distribution, i.e., species-sampling models. In this paper, we review “sufficientness” postulates for species-sampling models, and then investigate analogous predictive characterizations for the more general feature-sampling models. In particular, we present a “sufficientness” postulate for a class of feature-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of feature-sampling models.

Suggested Citation

  • Federico Camerlenghi & Stefano Favaro, 2021. "On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models," Mathematics, MDPI, vol. 9(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2891-:d:678546
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