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Articles

Unifying neighbourhood and distortion models: part I – new results on old models

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Pages 602-635 | Received 10 Jan 2020, Accepted 21 Apr 2020, Published online: 24 Jun 2020

References

  • Benavoli, A., and M. Zaffalon. 2013. “Density-ratio Robustness in Dynamic State Estimation.” Mechanical Systems and Signal Processing 37 (1–2): 54–75. doi: 10.1016/j.ymssp.2012.09.004
  • Berger, J. 1990. “Robust Bayesian Analysis: Sensitivity to the Prior.” Journal of Statistical Planning and Inference 25: 303–328. doi: 10.1016/0378-3758(90)90079-A
  • Bronevich, A. 2005. “On the Closure of Families of Fuzzy Measures Under Eventwise Aggregations.” Fuzzy Sets and Systems 153: 45–70. doi: 10.1016/j.fss.2004.12.005
  • Bronevich, A. 2007. “Necessary and Sufficient Consensus Conditions for the Eventwise Aggregation of Lower Probabilities.” Fuzzy Sets and Systems 158: 881–894. doi: 10.1016/j.fss.2006.10.020
  • Chateauneuf, A. 1996. “Decomposable Capacities, Distorted Probabilities and Concave Capacities.” Mathematical Social Sciences 31: 19–37. doi: 10.1016/0165-4896(95)00794-6
  • Choquet, G. 1953–1954. “Theory of Capacities.” Annales De L'Institut Fourier 5: 131–295. doi: 10.5802/aif.53
  • Corsato, C., R. Pelessoni, and P. Vicig. 2019. “Nearly-linear Uncertainty Measures.” International Journal of Approximate Reasoning 114: 1–28. doi: 10.1016/j.ijar.2019.08.001
  • Csiszár, I. 2008. “Axiomatic Characterization of Information Measures.” Entropy 10: 261–273. doi: 10.3390/e10030261
  • De Bock, J., C. De Campos, and A. Antonucci. 2014. “Global Sensitivity Analysis for Map Inference in Graphical Models.” Advances in Neural Information Processing Systems, New York, 2690–2698.
  • de Campos, L. M., J. F. Huete, and S. Moral. 1994. “Probability Intervals: a Tool for Uncertain Reasoning.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2: 167–196. doi: 10.1142/S0218488594000146
  • Denneberg, D. 1994. Non-Additive Measure and Integral. Dordrecht: Kluwer Academic.
  • Filippi, S., O. Cappé, and A. Garivier. 2010. “Optimism in reinforcement learning and Kullback-Leibler divergence.” 48th Annual Allerton Conference on Communication, Control, and Computing, Urbana-Champaign, USA, 115–122. IEEE.
  • Herron, T., T. Seidenfeld, and L. Wasserman. 1997. “Divisive Conditioning: Further Results on Dilation.” Philosophy of Science 64: 411–444. doi: 10.1086/392559
  • Hourbracq, M., C. Baudrit, P.-H. Wuillemin, and S. Destercke. 2013. “Dynamic credal networks: introduction and use in robustness analysis.” Eighth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2013), Compiègne, France, 159–169.
  • Huber, P. J. 1981. Robust Statistics. New York: Wiley.
  • Huber, P. J., and V. Strassen. 1973. “Minimax Tests and the Neyman–Pearson Lemma for Capacities.” The Annals of Statistics 1: 251–263. doi: 10.1214/aos/1176342363
  • Levi, I. 1980. The Enterprise of Knowledge. Cambridge: MIT Press.
  • Miranda, E. 2008. “A Survey of the Theory of Coherent Lower Previsions.” International Journal of Approximate Reasoning 48 (2): 628–658. doi: 10.1016/j.ijar.2007.12.001
  • Miranda, E., and I. Montes. 2015. “Coherent Updating of Non-additive Measures.” International Journal of Approximate Reasoning 56 (B): 159–177. doi: 10.1016/j.ijar.2014.05.003
  • Miranda, E., I. Montes, and S. Destercke. 2019. “A Unifying Frame for Neighbourhood and Distortion Models.” Proceedings of Machine Learning Research 103: 304–313. Proceedings of ISIPTA Conference.
  • Montes, I., E. Miranda, and S. Destercke. 2019. “Pari-mutuel Probabilities As An Uncertainty Model.” Information Sciences 481: 550–573. doi: 10.1016/j.ins.2019.01.005
  • Montes, I., E. Miranda, and S. Destercke. 2020. “Unifying Neighbourhood and Distortion Models: Part II- New Models and Synthesis.” International Journal of General Systems. Accepted for publication. doi:10.1080/03081079.2020.1778683.
  • Moral, S. 2018. “Discounting Imprecise Probabilities.” In The Mathematics of the Uncertain, edited by E. Gil, J. Gil, and M. Gil, Studies in Systems, Decision and Control. Vol. 142. Cham: Springer.
  • Pelessoni, R., P. Vicig, and M. Zaffalon. 2010. “Inference and Risk Measurement with the Pari-mutuel Model.” International Journal of Approximate Reasoning 51: 1145–1158. doi: 10.1016/j.ijar.2010.08.005
  • Pericchi, L. R., and P. Walley. 1991. “Robust Bayesian Credible Intervals and Prior Ignorance.” International Statistical Review 59: 1–23. doi: 10.2307/1403571
  • Rieder, H. 1997. “Least Favourable Pairs for Special Capacities.” Annals of Statistics 5 (5): 909–921. doi: 10.1214/aos/1176343947
  • Schmeidler, D. 1989. “Subjective Probability and Expected Utility Without Additivity.” Econometrica 57: 571–587. doi: 10.2307/1911053
  • Shafer, G. 1976. A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press.
  • Utkin, L. 2014. “A Framework for Imprecise Robust One-class Classification Models.” Journal of Machine Learning Research and Cybernetics 5 (3): 379–393. doi: 10.1007/s13042-012-0140-6
  • Utkin, L., and A. Wiencierz. 2015. “Improving Over-fitting in Ensemble Regression by Imprecise Probabilities.” Information Sciences 317: 315–328. doi: 10.1016/j.ins.2015.04.037
  • Walley, P. 1981. Coherent lower (and upper) probabilities. Technical Report 22, University of Warwick, Coventry.
  • Walley, P. 1991. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall. London.
  • Wallner, A. 2003. “Bi-elastic neighbourhood models.” In Proceedings of the 3rd International Symposium on Imprecise Probability: Theories and Applications (ISIPTA'2003), edited by J.-M-Bernard, T. Seidenfeld, and M. Zaffalon, Vol. 18, 593–607. Lugano: Carleton Scientific.

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