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Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application

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  • Coletti, Giulianella
  • Gervasi, Osvaldo
  • Tasso, Sergio
  • Vantaggi, Barbara

Abstract

A generalized Bayesian inference framework in order to embed fuzzy sets and partial probabilistic information is provided. The general framework of reference is that of coherent conditional probabilities, which allows giving a rigorous interpretation of membership function as a conditional probability, regarded as a function of the conditioning event. The inferential problem needs to be studied in situations where the prior can be partial; moreover, membership and prior can be given on different classes of events. This inferential model is applied for the virtual representation of a female avatar.

Suggested Citation

  • Coletti, Giulianella & Gervasi, Osvaldo & Tasso, Sergio & Vantaggi, Barbara, 2012. "Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 967-980.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:967-980
    DOI: 10.1016/j.csda.2011.06.020
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    References listed on IDEAS

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    1. Coletti, Giulianella & Scozzafava, Romano, 2006. "Conditional probability and fuzzy information," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 115-132, November.
    2. Coppi, Renato & D’Urso, Pierpaolo & Giordani, Paolo, 2012. "Fuzzy and possibilistic clustering for fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 915-927.
    3. Nozer D. Singpurwalla & Jane M. Booker, 2004. "Membership Functions and Probability Measures of Fuzzy Sets," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 867-877, January.
    4. Patrizia Berti & Lorenzo Fattorini & Pietro Rigo, 2000. "Eliminating nuisance parameters: two characterizations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 133-148, June.
    5. Ramos-Guajardo, Ana Belén & Lubiano, María Asunción, 2012. "K-sample tests for equality of variances of random fuzzy sets," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 956-966.
    6. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
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    Cited by:

    1. G. Coletti & D. Petturiti & B. Vantaggi, 2014. "Bayesian inference: the role of coherence to deal with a prior belief function," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 519-545, November.

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