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Title:

Probabilistic-possibilistic belief networks

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The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the dat...

The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuzzy probabilities to describe the uncertain knowledge about the values of the nodes of belief networks. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-18

Source:

http://epub.ub.uni-muenchen.de/4448/1/report.pdf

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text

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en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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http://www.stat.uni-muenchen.de Probabilistic-Possibilistic Belief Networks

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The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the dat...

The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuzzy probabilities to describe the uncertain knowledge about the values of the nodes of belief networks. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-24

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/lmu32.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/lmu32.pdf Minimize

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text

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en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Probabilistic-possibilistic belief networks

Description:

Abstract: The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided ...

Abstract: The interpretation of membership functions of fuzzy sets as statistical likelihood functions leads to a probabilistic-possibilistic hierarchical description of uncertain knowledge. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. This paper studies the possibility of using fuzzy probabilities to describe the uncertain knowledge about the values of the nodes of belief networks. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-05-08

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/vsim09.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/vsim09.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Fuzzy probabilities based on the likelihood function. In Soft Methods for Handling Variability and Imprecision

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Abstract If we interpret the statistical likelihood function as a measure of the relative plausibility of the probabilistic models considered, then we obtain a hierarchical description of uncertain knowledge, offering a unified approach to the combination of probabilistic and possibilistic uncertainty. The fundamental advantage of the resulting ...

Abstract If we interpret the statistical likelihood function as a measure of the relative plausibility of the probabilistic models considered, then we obtain a hierarchical description of uncertain knowledge, offering a unified approach to the combination of probabilistic and possibilistic uncertainty. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. Key words: likelihood function, hierarchical model, fuzzy probabilities, imprecise probabilities, statistical inconsistency 1 Minimize

Publisher:

Springer

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-17

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/smps08-uv.pdf

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text

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en

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Title:

Foundations of Probability

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Probability theory is that part of mathematics that is concerned with the description and modeling of random phenomena, or in a more general — but not unanimously accepted — sense, of any kind of uncertainty. Probability is assigned to random events, expressing their tendency to occur in a random experiment, or more generally to propositions, ch...

Probability theory is that part of mathematics that is concerned with the description and modeling of random phenomena, or in a more general — but not unanimously accepted — sense, of any kind of uncertainty. Probability is assigned to random events, expressing their tendency to occur in a random experiment, or more generally to propositions, characterizing the degree of Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-17

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/iess-uv.pdf

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text

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en

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Title:

7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Likelihood-Based Naive Credal Classifier

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The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by consideri...

The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by considering any possible quantification (each one defining a naive Bayes classifier) apart from those assigning to the available data a probability below a given threshold level. Besides the available supervised data, in the likelihood evaluation we also consider the instance to be classified, for which the value of the class variable is assumed missingat-random. We obtain a closed formula to compute the dominance according to the maximality criterion for any threshold level. As there are currently no well-established metrics for comparing credal classifiers which have considerably different determinacy, we compare the two classifiers when they have comparable determinacy, finding that in those cases they generate almost equivalent classifications. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-30

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-1.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

naive credal classifier

naive credal classifier Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Combining Belief Functions Issued from Dependent Sources

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Dempster's rule for combining two belief functions assumes the independence of the sources of information. If this assumption is questionable, I suggest to use the least specific combination minimizing the conflict among the ones allowed by a simple generalization of Dempster's rule. This increases the monotonicity of the reasoning and helps us ...

Dempster's rule for combining two belief functions assumes the independence of the sources of information. If this assumption is questionable, I suggest to use the least specific combination minimizing the conflict among the ones allowed by a simple generalization of Dempster's rule. This increases the monotonicity of the reasoning and helps us to manage situations of dependence. Some properties of this combination rule and its usefulness in a generalization of Bayes' theorem are then considered. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-18

Source:

http://www.carleton-scientific.com/isipta/PDF/011.pdf

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Document Type:

text

Language:

en

Subjects:

propositional logic ; combination ; Dempster’s rule ; independence ; conflict ; monotonicity ; nonspecificity ; idempotency ; associativity ; Bayes ’ theorem

propositional logic ; combination ; Dempster’s rule ; independence ; conflict ; monotonicity ; nonspecificity ; idempotency ; associativity ; Bayes ’ theorem Minimize

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Title:

Likelihood-based inference for probabilistic graphical models: Some preliminary results

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A method for calculating some profile likelihood inferences in probabilistic graphical models is presented and applied to the problem of classification. It can also be interpreted as a method for obtaining inferences from hierarchical networks, a kind of imprecise probabilistic graphical models. 1

A method for calculating some profile likelihood inferences in probabilistic graphical models is presented and applied to the problem of classification. It can also be interpreted as a method for obtaining inferences from hierarchical networks, a kind of imprecise probabilistic graphical models. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-05-08

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/pgm10.pdf

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Document Type:

text

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en

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Title:

7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Likelihood-Based Naive Credal Classifier

Author:

Description:

The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by consideri...

The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by considering any possible quantification (each one defining a naive Bayes classifier) apart from those assigning to the available data a probability below a given threshold level. Besides the available supervised data, in the likelihood evaluation we also consider the instance to be classified, for which the value of the class variable is assumed missingat-random. We obtain a closed formula to compute the dominance according to the maximality criterion for any threshold level. As there are currently no well-established metrics for comparing credal classifiers which have considerably different determinacy, we compare the two classifiers when they have comparable determinacy, finding that in those cases they generate almost equivalent classifications. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-07

Source:

http://www.idsia.ch/%7Egiorgio/pdf/isipta11-likelihood.pdf

http://www.idsia.ch/%7Egiorgio/pdf/isipta11-likelihood.pdf Minimize

Document Type:

text

Language:

en

Subjects:

naive credal classifier

naive credal classifier Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Regression with Imprecise Data: A Robust Approach

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We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominanc...

We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominance: interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. In the application to social survey data, the resulting set of plausible descriptions is relatively large, reflecting the amount of uncertainty inherent in the analyzed data set. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-25

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-2.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-2.pdf Minimize

Document Type:

text

Language:

en

Subjects:

imprecise data

imprecise data Minimize

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