Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical problems, these methods may suffer from some limitations if used to estimate non-linear functionals of the posterior distribution. The main goal is to develop a novel methodology that extends a well-established marginal procedure designed for hazard mixture models, in order to draw approximate inference on survival functions that is not limited to the posterior mean but includes, as remarkable examples, credible intervals and median survival time. The proposed approach relies on a characterization of the posterior moments that, in turn, is used to approximate the posterior distribution by means of a technique based on Jacobi polynomials. The inferential performance of this methodology is analyzed by means of an exten- sive study of simulated data and real data consisting of leukemia remission times. Although tailored to the survival analysis context, the proposed procedure can be adapted to a range of other models for which moments of the posterior distribution can be estimated.

Full Bayesian inference with hazard mixture models

ARBEL, JULYAN;LIJOI, ANTONIO;
2016

Abstract

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical problems, these methods may suffer from some limitations if used to estimate non-linear functionals of the posterior distribution. The main goal is to develop a novel methodology that extends a well-established marginal procedure designed for hazard mixture models, in order to draw approximate inference on survival functions that is not limited to the posterior mean but includes, as remarkable examples, credible intervals and median survival time. The proposed approach relies on a characterization of the posterior moments that, in turn, is used to approximate the posterior distribution by means of a technique based on Jacobi polynomials. The inferential performance of this methodology is analyzed by means of an exten- sive study of simulated data and real data consisting of leukemia remission times. Although tailored to the survival analysis context, the proposed procedure can be adapted to a range of other models for which moments of the posterior distribution can be estimated.
2016
2014
Arbel, Julyan; Lijoi, Antonio; Nipoti, Bernardo
File in questo prodotto:
File Dimensione Formato  
CSDA_2016.pdf

non disponibili

Tipologia: Pdf editoriale (Publisher's layout)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 531.47 kB
Formato Adobe PDF
531.47 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/11565/3998870
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 9
social impact