On fuzzy Bayesian inference
type: Item
instance of: scholarly article
title: On fuzzy Bayesian inference
zbMATH Open document ID: 0796.62003
DOI: 10.1016/0165-0114(93)90288-S
published in: Fuzzy Sets and Systems
publication date: 1994-04-19T00:00:00Z
review text: The author applies Zadeh's extension principle to Bayes' theorem for both fuzzy data and fuzzy priors resulting in fuzzyfied versions of some classical tools in Bayesian statistics, like fuzzy posterior densities, fuzzy Bayes estimators, fuzzy predictive densities and fuzzy highest posterior density regions. For illustration, the exponential density with (conjugate) gamma priors is considered. In my opinion, one question remains open: To what extent is the fuzzyfied classical Bayesian inference indeed a Bayesian inference for random fuzzy variables with random fuzzy priors?
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62F99
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 550098
zbMATH Keywords: Zadeh's extension principle
zbMATH Keywords: Bayes' theorem
zbMATH Keywords: fuzzy data
zbMATH Keywords: fuzzy posteriori densities
zbMATH Keywords: fuzzy Bayes estimators
zbMATH Keywords: fuzzy predictive densities
zbMATH Keywords: fuzzy highest posterior density regions
zbMATH Keywords: exponential density
zbMATH Keywords: gamma priors
zbMATH Keywords: random fuzzy variables
zbMATH Keywords: random fuzzy priors
author: Sylvia Frühwirth-Schnatter
reviewed by: Wolfgang Näther
MaRDI profile type: Publication
cites work: Fuzzy sets and systems. Theory and applications
cites work: On statistical inference for fuzzy data with applications to descriptive statistics
cites work: Statistics with vague data
cites work: Q3888406
cites work: Q4395075
cites work: On Bayes' theorem for fuzzy data
full work available at URL: 0165-0114(93)90288-s
OpenAlex ID: W2093952795
description: scientific article; zbMATH DE number 550098