An axiomatic framework for propagating uncertainty in directed acyclic networks

Cano, José; Delgado, Miguel; Moral, Serafı́n

doi:10.1016/0888-613x(93)90026-a

Cited by 41 publications

(25 citation statements)

References 3 publications

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“…Developing a BN involves: defining a directed acyclic graph that specifies a network of conditional probability dependencies; defining prior probability distributions for all graph nodes (i.e., sources of uncertainty); and defining a likelihood function and sampling strategy (e.g., MCMC) for inducing posterior distributions from prior distributions. Credal networks can supplement BNs by allowing variables to be associated with interval and set valued probabilities [ Cano et al , 1993; Cozman , 2000], leading to studies of robustness and incomplete knowledge of uncertainties.…”

Section: Methodsmentioning

confidence: 99%

Evaluating uncertainty in integrated environmental models: A review of concepts and tools

Matott

Babendreier

Purucker

2009

Water Resources Research

237

149

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[1] This paper reviews concepts for evaluating integrated environmental models and discusses a list of relevant software-based tools. A simplified taxonomy for sources of uncertainty and a glossary of key terms with ''standard'' definitions are provided in the context of integrated approaches to environmental assessment. These constructs provide a reference point for cataloging 65 different model evaluation tools. Each tool is described briefly (in the auxiliary material) and is categorized for applicability across seven thematic model evaluation methods. Ratings for citation count and software availability are also provided, and a companion Web site containing download links for tool software is introduced. The paper concludes by reviewing strategies for tool interoperability and offers guidance for both practitioners and tool developers.

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Section: Methodsmentioning

confidence: 99%

Evaluating uncertainty in integrated environmental models: A review of concepts and tools

Matott

Babendreier

Purucker

2009

Water Resources Research

237

149

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“…the variables with known values. Our task is to find the conditional probability p * (x|E) = p(X * )/p(E) (1) for a variable x ∈ (X* -E).…”

Section: Introductionmentioning

confidence: 99%

“…It appears that both the problems (1) and (2) are extremely difficult from the numerical standpoint. To be illustrative assume that X* contains 56 binary variables.…”

Section: Introductionmentioning

confidence: 99%

Reasoning and Facts Explanation in Valuation Based Systems

Wierzchoń

Kłopotek

Michalewicz

1997

Fundamenta Informaticae

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In the literature, the optimization problem to identify a set of composite hypotheses H, which will yield the k largest P (H|S e ) where a composite hypothesis is an instantiation of all the nodes in the network except the evidence nodes [14] is of significant interest. This problem is called "finding the k Most Plausible Explanation (MPE) of a given evidence S e in a Bayesian belief network". The problem of finding k most probable hypotheses is generally NP-hard [2]. Therefore in the past various simplifications of the task by restricting k (to 1 or 2), restricting the structure (e.g. to singly connected networks), or shifting the complexity to spatial domain have been investigated.A genetic algorithm is proposed in this paper to overcome some of these restrictions while stepping out from probabilistic domain onto the general Valuation based System (VBS) framework is also proposed by generalizing the genetic algorithm approach to the realm of Dempster-Shafer belief calculus.

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“…3 The problem with this definition is that the consideration of a global valuation and the combination without normalization allows the propagation of partial inconsistency. Our approach will be to use the components of the global valuation, the elementary valuations giving rise thereto, instead of the global valuation itself trying to normalize before combining.…”

Section: N͖ and O I Is An Absorbent Valuation On U Imentioning

confidence: 99%

“…The objective of this paper is to make an abstract study of partial inconsistency and of the strategies to remove it. In Section 2, we shall start by considering general valuation systems in which the last axiom proposed by Cano et al 3 is not necessarily verified. In Section 3, we shall show that this axiomatic system is verified by probability theory, the theory of infinitesimal probabilities, possibility theory, and the so called symbolic evidence theory.…”

Section: Introductionmentioning

confidence: 99%

Removing partial inconsistency in valuation-based systems

Campos

Moral

1997

Int. J. Intell. Syst.

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This paper presents an abstract definition of partial inconsistency and one operator used to remove it: normalization. When there is partial inconsistency in the combination of two pieces of information, this partial inconsistency is propagated to all the information in the system thereby degrading it. To avoid this effect, it is necessary to apply normalization. Four different formalisms are studied as particular cases of the axiomatic framework presented in this paper: probability theory, infinitesimal probabilities, possibility theory, and symbolic evidence theory. It is shown how, in one of these theories (probability), normalization is not an important problem: a property which is verified in this case gives rise to the equivalence of all the different normalization strategies. Things are very different for the other three theories: there are a number of different normalization procedures. The main objective of this paper will be to determine conditions based on general principles indicating how and when the normalization operator should be applied.

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An axiomatic framework for propagating uncertainty in directed acyclic networks

Cited by 41 publications

References 3 publications

Evaluating uncertainty in integrated environmental models: A review of concepts and tools

Evaluating uncertainty in integrated environmental models: A review of concepts and tools

Reasoning and Facts Explanation in Valuation Based Systems

Removing partial inconsistency in valuation-based systems

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