Abstract
We consider the problem of transforming a coherent lower probability into another one that (i) belongs to some subclass with better mathematical properties, such as 2- or complete monotonicity; (ii) is at least as informative as the original model, while being as close as possible to it. We show that the problem can be approached in terms of linear programming and that it can be connected with the one of determining the incenter of a credal set. Finally, we compare the performance of the original and the transformed model in a decision problem.
Supported by grant PGC2018-098623-B-I00.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Augustin, T., Coolen, F., de Cooman, G., Troffaes, M. (eds.) Introduction to Imprecise Probabilities. In: Wiley Series in Probability and Statistics. Wiley (2014)
Baroni, P., Vicig, P.: An uncertainty interchange format with imprecise probabilities. Int. J. Approx. Reason. 40, 147–180 (2005)
Berger, J.: Robust Bayesian analysis: sensitivity to the prior. J. Statist. Plan. Inference 25, 303–328 (1990)
Bronevich, A.: Necessary and sufficient consensus conditions for the eventwise aggregation of lower probabilities. Fuzzy Sets Syst. 158, 881–894 (2007)
Destercke, S., Montes, I., Miranda, E.: Processing distortion models: a comparative study. Int. J. Approx. Reason. 145(C), 91–120 (2022)
Huber, P.: Robust Statistics. Wiley, New York (1981)
Miranda, E., Montes, I.: Centroids of Credal sets: a comparative study. In: Vejnarová, J., Wilson, N. (eds.) ECSQARU 2021. LNCS (LNAI), vol. 12897, pp. 427–441. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-86772-0_31
Miranda, E., Montes, I.: Centroids of credal sets: a comparative study. Submitted for publication (2021)
Miranda, E., Montes, I., Vicig, P.: On the selection of an optimal outer approximation of a coherent lower probability. Fuzzy Sets Syst. 424C, 1–36 (2021)
Montes, I., Miranda, E., Destercke, S.: Unifying neighbourhood and distortion models: Part I- New results on old models. Int. J. Gen. Syst. 49(6), 605–635 (2020)
Montes, I., Miranda, E., Destercke, S.: Unifying neighbourhood and distortion models: Part II- New models and synthesis. Int. J. Gen. Syst. 49(6), 636–674 (2020)
Montes, I., Miranda, E., Vicig, P.: 2-Monotone outer approximations of coherent lower probabilities. Int. J. Approx. Reason. 101, 181–205 (2018)
Montes, I., Miranda, E., Vicig, P.: Outer approximating coherent lower probabilities with belief functions. Int. J. Approx. Reason. 110, 1–30 (2019)
Pelessoni, R., Vicig, P., Zaffalon, M.: Inference and risk measurement with the pari-mutuel model. Int. J. Approx. Reason. 51, 1145–1158 (2010)
Seidenfeld, T., Wasserman, L.: Dilation for sets of probabilities. Ann. Statist. 21, 1139–54 (1993)
Troffaes, M.C.M.: Decision making under uncertainty using imprecise probabilities. Int. J. Approx. Reason. 45(1), 17–29 (2007)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Miranda, E., Montes, I., Presa, A. (2022). Inner Approximations of Credal Sets by Non-additive Measures. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_60
Download citation
DOI: https://doi.org/10.1007/978-3-031-08971-8_60
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-08970-1
Online ISBN: 978-3-031-08971-8
eBook Packages: Computer ScienceComputer Science (R0)