ISSN:0028-3045    

DOI:10.1002/net.3230200502

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractWe investigate directed Markov fields over finite graphs without positivity assumptions on the densities involved. A criterion for conditional independence of two groups of variables given a third is given and named as the directed, global Markov property. We give a simple proof of the fact that the directed, local Markov property and directed, global Markov property are equivalent and – in the case of absolute continuity w. r. t. a product measure – equivalent to the recursive factorization of densities. It is argued that our criterion is easy to use, it is sharper than that given by Kiiveri, Speed, and Carlin and equivalent to that of Pearl. It follows that our criterion cannot be sharpe

ISSN:0028-3045    

DOI:10.1002/net.3230200503

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractAn important feature of Bayesian networks is that they facilitate explicit encoding of information about independencies in the domain, information that is indispensable for efficient inferencing. This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions. The algorithm's correctness is based on the soundness of a graphical criterion, calledd‐separation, and its optimality stems from the completeness ofd‐separation. An enhanced version ofd‐separation, calledD‐separation, is defined, extending the algorithm to networks that encode functional dependencies. Finally, the algorithm is shown to work for a broad class of nonprobabilistic indepen

ISSN:0028-3045    

DOI:10.1002/net.3230200504

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractInfluence diagrams are a directed network representation for decision making under uncertainty. The nodes in the diagram represent uncertain and decision variables, and the arcs indicate probabilistic dependence and observability. This paper examines the graphical orderings underlying the influence diagram and the primitive interchange operations that can reorder the network. These operations are sufficient to determine the maximal independent set and minimal relevant sets for any given inference problem, and a linear time algorithm is developed to obtain those sets. This framework is also used to examine and explain properties of the time structure of general influence diagrams with decisions.

ISSN:0028-3045    

DOI:10.1002/net.3230200505

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractInfluence diagrams are used to illustrate how the probability of having a disease can be updated given the results from two or more clinical tests. The problem of calibrating a register using results from a survey, as discussed by Heldal and Spjøtvoll (1988), is solved using a Bayesian approach

ISSN:0028-3045    

DOI:10.1002/net.3230200506

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractA directed acyclic graph or influence diagram is frequently used as a representation for qualitative knowledge in some domains in which expert system techniques have been applied, and conditional probability tables on appropriate sets of variables form the quantitative part of the accumulated experience. It is shown how one can introduce imprecision into such probabilities as a data base of cases accumulates. By exploiting the graphical structure, the updating can be performed locally, either approximately or exactly, and the setup makes it possible to take advantage of a range of well‐established statistical techniques. As examples we discuss discrete models, models based on Dirichlet distributions and models of the logistic regression typ

ISSN:0028-3045    

DOI:10.1002/net.3230200507

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractWe address the pragmatics of constructing normative expert systems and examine the influence diagram as a potential framework for representing knowledge in such systems. We introduce an extension of the influence‐diagram representation called asimilarity network.A similarity network is a tool for constructing large and complex influence diagrams. The representation allows a user to construct independent influence diagrams for subsets of a given domain. A valid influence diagram for the entire domain can then be constructed from the individual diagrams. Similarity networks represent forms of conditional independence that are not represented conveniently in an ordinary influence diagram. We discuss in detail one such conditional independence, calledsubset independence, and examine how similarity networks exploit this form of independence to facilitate the construction of an influence diagram. Also, we investigate the assessment of probability distributions for influence diagrams. We see that similarity networks exploit subset independence to simplify such probability assessments. We introduce a representation that is closely related to similarity networks, called apartition.This representation further exploits subset independence to simplify probability assessment. Finally, we examine a real‐world normative expert system for the diagnosis of lymph‐node pathology, called Pathfinder. The similarity‐network and partition representations played a crucial role in the construction of this expert

ISSN:0028-3045    

DOI:10.1002/net.3230200508

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractCausal probabilistic networks (CPNs) have proved to be a useful knowledge representation tool for modeling domains where causal relations‐in a broad sense‐are a natural way of relating domain concepts and where uncertainty is inherited in these relations. The domain is modeled in a CPN by use of a directed graph where the nodes represent concepts in the domain and the arcs represent causal relations. Furthermore, the quantitative relation between a node and its immediate causes is expressed as conditional probabilities. During the last few years, several schemes based on probability theory for incorporating and propagating new information throughout a CPN has emerged. As long as the domain can be modeled by use of a singly connected CPN (i. e., no more than one path between any pair of nodes), the schemes operate directly in the CPN and perform conceptually simple operations in this structure. When it comes to more complicated structures such as multiply connected CPNs (i. e., more than one path is allowed between pairs of nodes), the schemes operate in derived structures where the embedded domain knowledge no longer is as explicit and transparent as in the CPN. Furthermore, the simplicity in the operations is lost also. This report outlines a scheme‐the algebra ofBayesian belief universes‐for absorbing and propagating evidence in multiply connected CPNs. The scheme provides a secondary structure,a junction tree, and a simple set of algebraic operations between objects in this structure,Collect EvidenceandDistribute Evidence.These are the basic tools for making inference in a CPN domain model and yield a calculus as simple as in the case of singly connect

ISSN:0028-3045    

DOI:10.1002/net.3230200509

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractResearchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build probabilistic expert systems. Using standard methods drawn from the theory of computational complexity, workers in the field have shown that the problem of probabilistic inference in belief networks is difficult and almost certainly intractable. We have developed a randomized approximation scheme, BN‐RAS, for doing probabilistic inference in belief networks. The algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models. Unlike previously described stochastic algorithms for probabilistic inference, the randomized approximation scheme (ras) computes a priori bounds on running time by analyzing the structure and contents of the belief network. In this article, we describe BN‐RAS precisely and analyze its performance mathematica

ISSN:0028-3045    

DOI:10.1002/net.3230200510

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractQualitative probabilistic networks (QPNs) are abstractions of influence diagrams that encode constraints on the probabilistic relation among variables rather than precise numeric distributions.Qualitative relationsexpress monotonicity constraints on direct probabilistic relations between variables or on interactions among the direct relations. Like their numeric counterpart, QPNs facilitate graphical inference: methods for deriving qualitative relations of interest via graphical transformations of the network model. However, query processing in QPNs exhibits, computational properties quite different from basic influence diagrams. In particular, the potential for information loss due to the incomplete specification of probabilities poses the new challenge of minimizing ambiguity. Analysis of the properties of QPN transformations reveals several characteristics of admissible graphical inference procedures.

ISSN:0028-3045    

DOI:10.1002/net.3230200511

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY