Vectors of hierarchical random probability measures are popular tools in Bayesian nonparametrics. They may be used as priors whenever partial exchangeability is assumed at the level of either the observations or of some latent variables involved in the model. The first contribution in this direction can be found in Teh et al. (2006), who introduced the hierarchical Dirichlet process. Recently, Camerlenghi et al. (2018) have developed a general distribution theory for hierarchical processes, which includes the derivation of the partition structure, the posterior distribution and the prediction rules. The present paper is a review of these theoretical findings for vectors of hierarchies of Pitman--Yor processes.

Camerlenghi, F., Lijoi, A., Pruenster, I. (2017). On some distributional properties of hierarchical processes. In 2017 JSM proceedings (pp.853-860).

On some distributional properties of hierarchical processes

Camerlenghi, F;
2017

Abstract

Vectors of hierarchical random probability measures are popular tools in Bayesian nonparametrics. They may be used as priors whenever partial exchangeability is assumed at the level of either the observations or of some latent variables involved in the model. The first contribution in this direction can be found in Teh et al. (2006), who introduced the hierarchical Dirichlet process. Recently, Camerlenghi et al. (2018) have developed a general distribution theory for hierarchical processes, which includes the derivation of the partition structure, the posterior distribution and the prediction rules. The present paper is a review of these theoretical findings for vectors of hierarchies of Pitman--Yor processes.
No
paper
Bayesian Nonparametrics, hierarchical processes, partial exchangeablity, Pitman-Yor process, partition structure, posterior distribution
English
Joint Statistical Meeting 2017
9780983937579
Camerlenghi, F., Lijoi, A., Pruenster, I. (2017). On some distributional properties of hierarchical processes. In 2017 JSM proceedings (pp.853-860).
Camerlenghi, F; Lijoi, A; Pruenster, I
File in questo prodotto:
File Dimensione Formato  
versione_ufficiale.pdf

Solo gestori archivio

Dimensione 313.56 kB
Formato Adobe PDF
313.56 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/10281/183362
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
Social impact