Independence assumptions and Bayesian updating
type: Item
instance of: scholarly article
title: Independence assumptions and Bayesian updating
zbMATH Open document ID: 0576.62007
DOI: 10.1016/0004-3702(85)90043-8
author: Clark Glymour
published in: Artificial Intelligence
publication date: 1985-01-01T00:00:00Z
review text: \textit{E. P. D. Pednault}, \textit{S. W. Zucker} and \textit{L. V. Muresan} [ibid. 16, 213-222 (1981; Zbl 0465.62005)] proved the following theorem: If the hypotheses \(H_ 1,H_ 2,...,H_ N\) with \(N>2\) are complete and mutually exclusive, i.e. \(\sum^{N}_{i=1}P(H_ i)=1\), and if the assumptions \(P(E_ 1,...,E_ m| H_ i)=\prod^{n}_{j=1}P(F_ j| H_ i)\) and \(P(E_ 1,...,E_ m| H_ i)=\prod^{m}_{j=1}P(E_ j| H_ i)\) are satisfied then for any sequence of evidence sentences \(E_ 1,...,E_ m\) and for every subsequence \(E_ i,...,E_ k\) and every \(H_ i\) we have \[ P(H_ i| E_ i,...,E_ k)/P(\bar H_ i| E_ i,...,E_ k)=P(H_ i)/P(\bar H_ i) \] (no updating occurs). The author proves by using a simple counterexample that the above theorem is false. The error in the proof of Pendault et al. lies in their use of an incorrect result by \textit{A. B. S. Hussain} [IEEE Trans. Comput. C-21, 318-320 (1972; Zbl 0242.68072)]. It is not clear whether the result claimed by Pendault et al. holds if in addition for all i, \(P(H_ i| E_ 1,...,E_ k)\neq 0\).
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 68T05
zbMATH DE Number: 3921702
zbMATH Keywords: Bayesian updating
zbMATH Keywords: independence
zbMATH Keywords: counterexample
MaRDI profile type: Publication
full work available at URL: 0004-3702(85)90043-8
OpenAlex ID: W2119741725
cites work: On the Correctness of Some Sequential Classification Schemes in Pattern Recognition
cites work: On the independence assumption underlying subjective Bayesian updating
description: scientific article; zbMATH DE number 3921702