Bayesian inference under imprecise prior information is studied: the starting point is a precise strategy $σ$ and a full B-conditional prior belief function $Bel_B$, conveying ambiguity in probabilistic prior information. In finite spaces, we give a closed form expression for the lower envelope $\underlineP$ of the class of full conditional probabilities dominating $(Bel_B,σ)$ and, in particular, for the related “posterior probabilities”. The assessment $(Bel_B,σ)$ is a coherent lower conditional probability in the sense of Williams and the characterized lower envelope $\underlineP$ coincides with its natural extension.

Bayesian Inference under Ambiguity: Conditional Prior Belief Functions

COLETTI, Giulianella;PETTURITI, DAVIDE;VANTAGGI, BARBARA
2017

Abstract

Bayesian inference under imprecise prior information is studied: the starting point is a precise strategy $σ$ and a full B-conditional prior belief function $Bel_B$, conveying ambiguity in probabilistic prior information. In finite spaces, we give a closed form expression for the lower envelope $\underlineP$ of the class of full conditional probabilities dominating $(Bel_B,σ)$ and, in particular, for the related “posterior probabilities”. The assessment $(Bel_B,σ)$ is a coherent lower conditional probability in the sense of Williams and the characterized lower envelope $\underlineP$ coincides with its natural extension.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11391/1419555
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact