## Axioms for probability and belief-function propagation (1990)

Venue: | Uncertainty in Artificial Intelligence |

Citations: | 135 - 17 self |

### BibTeX

@INPROCEEDINGS{Shenoy90axiomsfor,

author = {Prakash P. Shenoy and Glenn Shafer},

title = {Axioms for probability and belief-function propagation},

booktitle = {Uncertainty in Artificial Intelligence},

year = {1990},

pages = {169--198},

publisher = {Morgan Kaufmann}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework. 1.

### Citations

2249 |
A mathematical theory of evidence
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(Show Context)
Citation Context ...e decomposition of evidence into independent items, each involving only a fewsvariables. We represent each item of evidence by a belief function and combine these belief functions by Dempster's rule [=-=Shafer 1976-=-]. It is shown in Shenoy [1989b] that Spohn's [1988, 1990] theory of epistemic beliefs also fits in the abstract framework described here. This framework is extended in Shenoy and Shafer [1988a,b] to ... |

1290 | Local computation with probabilities on graphical structures and their application to expert systems - Lauritzen, Spiegelhalter - 1988 |

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(Show Context)
Citation Context ...eventually provided only that all the processors act eventually. It will get done, for example, if each processor checks on its inputs periodically or at random times and acts if it has those inputs [=-=Pearl 1986-=-]. If we tell each processor who its neighbors are and which one of these neighbors lies on the path towards the goal, then no further global control or synchronization is needed. Each processor knows... |

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(Show Context)
Citation Context ... firings, one for each vertex in the Markov tree. Production systems are usually implemented so that a rule will fire only once for a given instantiation of its antecedent; this is called refraction [=-=Brownston et al. 1985-=-, pp. 62-63]. If our simple production system is implemented with refraction, there will be no unnecessary firings of rules; only the n firings that are needed will occur. Even without refraction, how... |

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New methods for reasoning toward posterior distributions based on sample data
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(Show Context)
Citation Context ...te the extension of h to g. For example, if a is a subset of W{W,X}, then the vacuous extension of a to {W,X,Y,Z} is a×W{Y,Z}. Combination. For superpotentials, combination is called Dempster's rule [=-=Dempster 1966-=-]. Consider two superpotentials G and H on g and h, respectively. If Σ{G(a)H(b)|(a ↑(g∪h) )∩(b ↑(g∪h) ) ≠ ∅} ≠ 0, (5.1) 32sthen their combination, denoted by G⊕H, is the superpotential on g∪h given by... |

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