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Finite-dimensional Discrete Random Structures and Bayesian Clustering

Author

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  • Antonio Lijoi
  • Igor Prünster
  • Tommaso Rigon

Abstract

Discrete random probability measures stand out as effective tools for Bayesian clustering. The investigation in the area has been very lively, with a strong emphasis on nonparametric procedures based on either the Dirichlet process or on more flexible generalizations, such as the normalized random measures with independent increments (NRMI). The literature on finite-dimensional discrete priors is much more limited and mostly confined to the standard Dirichlet-multinomial model. While such a specification may be attractive due to conjugacy, it suffers from considerable limitations when it comes to addressing clustering problems. In order to overcome these, we introduce a novel class of priors that arise as the hierarchical compositions of finite-dimensional random discrete structures. Despite the analytical hurdles such a construction entails, we are able to characterize the induced random partition and determine explicit expressions of the associated urn scheme and of the posterior distribution. A detailed comparison with (infinite-dimensional) NRMIs is also provided: indeed, informative bounds for the discrepancy between the partition laws are obtained. Finally, the performance of our proposal over existing methods is assessed on a real application where we study a publicly available dataset from the Italian education system comprising the scores of a mandatory nationwide test.

Suggested Citation

  • Antonio Lijoi & Igor Prünster & Tommaso Rigon, 2024. "Finite-dimensional Discrete Random Structures and Bayesian Clustering," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 929-941, April.
  • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:546:p:929-941
    DOI: 10.1080/01621459.2022.2149406
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