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.

Rigon, T., Petrone, S., Scarpa, B. (2025). Enriched Pitman-Yor processes. SCANDINAVIAN JOURNAL OF STATISTICS [10.1111/sjos.12765].

Enriched Pitman-Yor processes

Rigon, T
;
Scarpa, B
2025

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.
Articolo in rivista - Articolo scientifico
Bayesian non-parametrics; enriched Dirichlet process; mixture of mixtures; nested random partitions; species sampling models; spike and slab processes;
English
19-gen-2025
2025
none
Rigon, T., Petrone, S., Scarpa, B. (2025). Enriched Pitman-Yor processes. SCANDINAVIAN JOURNAL OF STATISTICS [10.1111/sjos.12765].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/538961
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