**
**

**Cattaneo, Marco E. G. V. (29. February 2008): Probabilistic-possibilistic belief networks. Department of Statistics: Technical Reports, No.32 [PDF, 308kB]**

## 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.

Item Type: | Paper |
---|---|

Form of publication: | Preprint |

Keywords: | likelihood function, hierarchical model, fuzzy probabilities, imprecise probabilities, updating, Bayesian networks, credal networks, conditional irrelevance, d-separation, possibilistic uncertainty |

Faculties: | Mathematics, Computer Science and Statistics > Statistics > Technical Reports |

URN: | urn:nbn:de:bvb:19-epub-4448-8 |

Language: | English |

Item ID: | 4448 |

Date Deposited: | 17. Jun 2008 07:38 |

Last Modified: | 04. Nov 2020 12:48 |

References: | Cano, A., and Moral, S. (1996). A Genetic algorithm to approximate convex sets of probabilities. In IPMU ’96. Vol. 2. Universidad de Granada, 859–864. Cattaneo, M. (2005). Likelihood-based statistical decisions. In ISIPTA ’05. SIPTA, 107–116. Cattaneo, M. (2007). Statistical Decisions Based Directly on the Likelihood Function. PhD thesis, ETH Zurich. Available online at e-collection.ethz.ch. Cozman, F. G. (2000). Credal networks. Artif. Intell. 120, 199–233. Cozman, F. G. (2005). Graphical models for imprecise probabilities. Int. J. Approx. Reasoning 39, 167–184. Dahl, F. A. (2005). Representing human uncertainty by subjective likelihood estimates. Int. J. Approx. Reasoning 39, 85–95. Dubois, D. (2006). Possibility theory and statistical reasoning. Comput. Stat. Data Anal. 51, 47–69. Dubois, D., Moral, S., and Prade, H. (1997). A semantics for possibility theory based on likelihoods.J. Math. Anal. Appl. 205, 359–380. Dubois, D., and Prade, H. (1993). Fuzzy sets and probability: Misunderstandings, bridges and gaps. In Second IEEE International Conference on Fuzzy Systems. Vol. 2. IEEE Service Center, 1059–1068. Fisher, R. A. (1921). On the “probable error” of a coefficient of correlation deduced from a small sample. Metron 1, 3–32. Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philos. Trans. R. Soc. Lond., Ser. A 222, 309–368. Good, I. J. (1950). Probability and the Weighing of Evidence. Charles Griffin. Hisdal, E. (1988). Are grades of membership probabilities? Fuzzy Sets Syst. 25, 325–348. Jensen, F. V. (2001). Bayesian Networks and Decision Graphs. Springer. Kullback, S., and Leibler, R. A. (1951). On information and sufficiency. Ann. Math. Stat. 22, 79–86. Moral, S. (1992). Calculating uncertainty intervals from conditional convex sets of probabilities. In UAI ’92. Morgan Kaufmann, 199–206. Pearl, J. (1988). Probabilistic Inference in Intelligent Systems. Morgan Kaufmann. Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. Chapman and Hall. Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62. Wilson, N. (2001). Modified upper and lower probabilities based on imprecise likelihoods. In ISIPTA ’01. Shaker, 370–378. Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28. |