Arbres de Markov triplet et fusion de Dempster-Shafer. (Triplet Markov trees and Dempster-Shafer fusion)
type: Item
instance of: scholarly article
title: Arbres de Markov triplet et fusion de Dempster-Shafer. (Triplet Markov trees and Dempster-Shafer fusion)
zbMATH Open document ID: 1030.60028
DOI: 10.1016/S1631-073X(03)00188-2
author: Wojciech Pieczynski
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-09-15T00:00:00Z
review text: Let \(Z= (X, Y)\) be a hidden Markov chain with \[ p(x, y)= p(x_1) p(x_2/x_1)\cdots p(x_n/x_{n-1}) p(y_1/x_1)\cdots p(y_n/x_n) \] distribution. It may be considered that \(p(x/y)\) is the Dempster-Shaefer fusion result of \(p(x)= p(x_1) p(x_2/x_1)\cdots p(x_n/x_{n-1})\) probability with \(q(x)\propto p(y_1/x_1)\cdots p(y_n/x_n)\) probability, \(y\) fixed. This result remains valid even if \(q\) is replaced with ``mass function''. The author established in a previous paper that \(M\) fusion with \(q\) is a triplet Markov chain. In the present paper, the author gives different generalizations of this last result.
Mathematics Subject Classification ID: 60G20
zbMATH DE Number: 1981333
zbMATH Keywords: hidden Markov chain
zbMATH Keywords: triplet Markov chain
reviewed by: Ion C. Vladimirescu
MaRDI profile type: Publication
cites work: Signal and Image Segmentation Using Pairwise Markov Chains
cites work: Discrete Markov image modeling and inference on the quadtree
cites work: Pairwise Markov trees
cites work: Triplet Markov chains
cites work: Q4131415
cites work: Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem
full work available at URL: s1631-073x(03)00188-2
OpenAlex ID: W2085243994
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description: scientific article; zbMATH DE number 1981333