Bayesian non-parametrics has evolved into a broad area encompassing flexible methods for Bayesian inference, combinatorial structures, tools for complex data reduction, and more. Discrete prior laws play an important role in these developments, and various choices are available nowadays. However, many existing priors, such as the Dirichlet process, have limitations if data require nested clustering structures. Thus, we introduce a discrete non-parametric prior, termed the enriched Pitman–Yor process, which offers higher flexibility in modeling such elaborate partition structures. We investigate the theoretical properties of this novel prior and establish its formal connection with the enriched Dirichlet process and normalized random measures. Additionally, we present a square-breaking representation and derive closed-form expressions for the posterior law and associated urn schemes. Furthermore, we demonstrate that several established models, including Dirichlet processes with a spike-and-slab base measure and mixture of mixtures models, emerge as special instances of the enriched Pitman–Yor process, which therefore serves as a unified probabilistic framework for various Bayesian non-parametric priors. To illustrate its practical utility, we employ the enriched Pitman–Yor process for a species-sampling ecological problem.

Enriched Pitman–Yor processes

Rigon, Tommaso
;
Petrone, Sonia;Scarpa, Bruno
In corso di stampa

Abstract

Bayesian non-parametrics has evolved into a broad area encompassing flexible methods for Bayesian inference, combinatorial structures, tools for complex data reduction, and more. Discrete prior laws play an important role in these developments, and various choices are available nowadays. However, many existing priors, such as the Dirichlet process, have limitations if data require nested clustering structures. Thus, we introduce a discrete non-parametric prior, termed the enriched Pitman–Yor process, which offers higher flexibility in modeling such elaborate partition structures. We investigate the theoretical properties of this novel prior and establish its formal connection with the enriched Dirichlet process and normalized random measures. Additionally, we present a square-breaking representation and derive closed-form expressions for the posterior law and associated urn schemes. Furthermore, we demonstrate that several established models, including Dirichlet processes with a spike-and-slab base measure and mixture of mixtures models, emerge as special instances of the enriched Pitman–Yor process, which therefore serves as a unified probabilistic framework for various Bayesian non-parametric priors. To illustrate its practical utility, we employ the enriched Pitman–Yor process for a species-sampling ecological problem.
In corso di stampa
2025
Rigon, Tommaso; Petrone, Sonia; Scarpa, Bruno
File in questo prodotto:
File Dimensione Formato  
Scandinavian J Statistics - 2025 - Rigon - Enriched Pitman Yor processes.pdf

accesso aperto

Descrizione: article
Tipologia: Pdf editoriale (Publisher's layout)
Licenza: Creative commons
Dimensione 996.79 kB
Formato Adobe PDF
996.79 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4071318
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact