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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

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Description:

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

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

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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:

Likelihood-Based Statistical Decisions

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In this paper, a nonadditive quantitative description of uncertain knowledge about statistical models is obtained by extending the likelihood function to sets and allowing the use of prior information. This description, which has the distinctive feature of not being calibrated, is called relative plausibility. It can be updated when new informat...

In this paper, a nonadditive quantitative description of uncertain knowledge about statistical models is obtained by extending the likelihood function to sets and allowing the use of prior information. This description, which has the distinctive feature of not being calibrated, is called relative plausibility. It can be updated when new information is obtained, and it can be used for inference and decision making. As regards inference, the well-founded theory of likelihoodbased statistical inference can be exploited, whereas decisions can be based on the minimax plausibilityweighted loss criterion. In the present paper, this decision criterion is introduced and some of its properties are studied, both from the conditional and from the repeated sampling point of view. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-19

Source:

http://leo.ugr.es/sipta/isipta05/proceedings/papers/s044.pdf.gz

http://leo.ugr.es/sipta/isipta05/proceedings/papers/s044.pdf.gz Minimize

Document Type:

text

Language:

en

Subjects:

imprecise probabilities

imprecise probabilities Minimize

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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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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

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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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8th International Symposium on Imprecise Probability: Theories and Applications, Compiègne, France, 2013 On the Robustness of Imprecise Probability Methods

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Imprecise probability methods are often claimed to be robust, or more robust than conventional methods. In particular, the higher robustness of the resulting methods seems to be the principal argument supporting the imprecise probability approach to statistics over the Bayesian one. The goal of the present paper is to investigate the robustness ...

Imprecise probability methods are often claimed to be robust, or more robust than conventional methods. In particular, the higher robustness of the resulting methods seems to be the principal argument supporting the imprecise probability approach to statistics over the Bayesian one. The goal of the present paper is to investigate the robustness of imprecise probability methods, and in particular to clarify the terminology used to describe this fundamental issue of the imprecise probability approach. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-28

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/isipta13.pdf

http://www.stat.uni-muenchen.de/~cattaneo/publications/isipta13.pdf Minimize

Document Type:

text

Language:

en

Subjects:

sensitivity analysis ; imprecise

sensitivity analysis ; imprecise Minimize

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Title:

Belief functions combination without the assumption of independence of the information sources

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-13

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/ijar1-uv.pdf

http://www.stat.uni-muenchen.de/~cattaneo/publications/ijar1-uv.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Key words ; Dempster-Shafer theory ; belief functions ; combination rule ; dependence ; conflict ; cautious combination

Key words ; Dempster-Shafer theory ; belief functions ; combination rule ; dependence ; conflict ; cautious combination Minimize

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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

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

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

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

Document Type:

text

Language:

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:

2012-05-07

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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Title:

A Generalization of Credal Networks

Description:

The likelihood approach to statistics can be interpreted as a theory of fuzzy probability. This paper presents a generalization of credal networks obtained by generalizing imprecise probabilities to fuzzy probabilities; that is, by additionally considering the relative plausibility of different values in the probability intervals.

The likelihood approach to statistics can be interpreted as a theory of fuzzy probability. This paper presents a generalization of credal networks obtained by generalizing imprecise probabilities to fuzzy probabilities; that is, by additionally considering the relative plausibility of different values in the probability intervals. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-24

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta09.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta09.pdf Minimize

Document Type:

text

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en

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