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Enriched Pitman-Yor processes.

Tommaso Rigon1, Sonia Petrone2, Bruno Scarpa3

  • 1Department of Economics, Management and Statistics, University of Milano-Bicocca, Italy.

Scandinavian Journal of Statistics, Theory and Applications
|August 13, 2025
PubMed
Summary
This summary is machine-generated.

We introduce the enriched Pitman-Yor process, a novel Bayesian nonparametric prior offering greater flexibility for nested clustering structures. This unified framework enhances modeling capabilities for complex data partitions in various applications.

Keywords:
Bayesian nonparametricsEnriched Dirichlet processMixture of mixturesNested random partitionsSpecies sampling modelsSpike and slab processes

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Area of Science:

  • Bayesian nonparametrics
  • Statistical modeling
  • Machine learning

Background:

  • Bayesian nonparametrics offers flexible methods for inference and data reduction.
  • Discrete prior laws are crucial but existing options like the Dirichlet process have limitations for nested clustering.
  • Need for more flexible priors to handle complex data partition structures.

Purpose of the Study:

  • Introduce a novel discrete nonparametric prior: the enriched Pitman-Yor process.
  • Enhance flexibility in modeling elaborate nested partition structures.
  • Provide a unified probabilistic framework for existing Bayesian nonparametric priors.

Main Methods:

  • Investigate theoretical properties of the enriched Pitman-Yor process.
  • Establish connections with enriched Dirichlet process and normalized random measures.
  • Utilize a square-breaking representation and derive closed-form expressions for posterior law and urn schemes.

Main Results:

  • The enriched Pitman-Yor process offers higher flexibility for nested clustering.
  • Established models like Dirichlet processes and mixture of mixtures are special cases.
  • Demonstrated practical utility in a species-sampling ecological problem.

Conclusions:

  • The enriched Pitman-Yor process serves as a unified framework for Bayesian nonparametrics.
  • Provides a powerful tool for modeling complex hierarchical data structures.
  • Applicable to diverse fields requiring flexible clustering and partitioning.