Abstract
We are interested in whether or not there exist any advantages of utilizing credal set theory for the discrete state estimation problem. We present an experiment where we compare in total six different methods, three based on Bayesian theory and three on credal set theory. The results show that Bayesian updating performed on centroids of operand credal sets significantly outperforms the other methods. We analyze the result based on degree of imprecision, position of extreme points, and second-order distributions.
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References
Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. John Wiley and Sons, Chichester (2000)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, Boca Raton (1991)
Levi, I.: The enterprise of knowledge. The MIT press, Cambridge (1983)
Cozman, F.G.: Credal networks. Artificial Intelligence 120, 199–233 (2000)
Cozman, F.: Decision Making Based on Convex Sets of Probability Distributions: Quasi-Bayesian Networks and Outdoor Visual Position Estimation. PhD thesis, The Robotics Institute, Carnegie Mellon University (1997)
Zaffalon, M., Fagiuoli, E.: Tree-based credal networks for classification. Reliable Computing 9, 487–509 (2003)
Corani, G., Zaffalon, M.: Learning reliable classifiers from small or incomplete data sets: The naive credal classifier 2. Journal of Machine Learning Research 9, 581–621 (2008)
Arnborg, S.: Robust Bayesianism: Imprecise and paradoxical reasoning. In: Proceedings of the 7th International Conference on Information fusion, pp. 407–414 (2004)
Arnborg, S.: Robust Bayesianism: Relation to evidence theory. Journal of Advances in Information Fusion 1, 63–74 (2006)
Karlsson, A., Johansson, R., Andler, S.F.: On the behavior of the robust Bayesian combination operator and the significance of discounting. In: 6th International Symposium on Imprecise Probability: Theories and Applications, pp. 259–268 (2009)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)
Brier, G.W.: Verification of forecasts expressed in terms of probability. Monthly Weather Review 78, 1–3 (1950)
Demšar, J.: Statistical comparisons of classifiers over multiple data sets. The Journal of Machine Learning Research 7, 1–30 (2006)
R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2009)
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Karlsson, A., Johansson, R., Andler, S.F. (2010). An Empirical Comparison of Bayesian and Credal Set Theory for Discrete State Estimation. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_9
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DOI: https://doi.org/10.1007/978-3-642-14055-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14054-9
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