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In Search of a Global Belief Model for Discrete-Time Uncertain Processes

Natan T'Joens (UGent) , Jasper De Bock (UGent) and Gert De Cooman (UGent)
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Abstract
To model discrete-time uncertain processes, we argue for the use of a global belief model in the form of an upper expectation that satisfies a number of simple and intuitive axioms. We motivate these axioms on the basis of two possible interpretations for this upper expectation: a behavioural interpretation similar to that of Walley’s, and an interpretation in terms of upper envelopes of linear expectations. Subsequently, we show that the most conservative upper expectation satisfying our axioms coincides with a particular version of the game-theoretic upper expectation introduced by Shafer and Vovk. This has two important implications. On the one hand, it guarantees that there is a unique most conservative global belief model satisfying our axioms. On the other hand, it shows that Shafer and Vovk’s model can be given an axiomatic characterisation, thereby providing an alternative motivation for adopting this model, even outside their framework.
Keywords
Game-theoretic probability, Upper expectations, Uncertain processes, Coherence

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MLA
T’Joens, Natan, Jasper De Bock, and Gert De Cooman. “In Search of a Global Belief Model for Discrete-Time Uncertain Processes.” Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications. Ed. Jasper De Bock et al. Vol. 103. Proceedings of Machine Learning Research, 2019. 377–385. Print.
APA
T’Joens, N., De Bock, J., & De Cooman, G. (2019). In Search of a Global Belief Model for Discrete-Time Uncertain Processes. In Jasper De Bock, C. P. de Campos, G. De Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications (Vol. 103, pp. 377–385). Presented at the International Symposium on Imprecise Probabilities: Theories and Applications, Proceedings of Machine Learning Research.
Chicago author-date
T’Joens, Natan, Jasper De Bock, and Gert De Cooman. 2019. “In Search of a Global Belief Model for Discrete-Time Uncertain Processes.” In Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, ed. Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:377–385. Proceedings of Machine Learning Research.
Chicago author-date (all authors)
T’Joens, Natan, Jasper De Bock, and Gert De Cooman. 2019. “In Search of a Global Belief Model for Discrete-Time Uncertain Processes.” In Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, ed. Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:377–385. Proceedings of Machine Learning Research.
Vancouver
1.
T’Joens N, De Bock J, De Cooman G. In Search of a Global Belief Model for Discrete-Time Uncertain Processes. In: De Bock J, de Campos CP, De Cooman G, Quaeghebeur E, Wheeler G, editors. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications. Proceedings of Machine Learning Research; 2019. p. 377–85.
IEEE
[1]
N. T’Joens, J. De Bock, and G. De Cooman, “In Search of a Global Belief Model for Discrete-Time Uncertain Processes,” in Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, Ghent, 2019, vol. 103, pp. 377–385.
@inproceedings{8627442,
  abstract     = {To model discrete-time uncertain processes, we argue for the use of a global belief model in the form of an upper expectation that satisfies a number of simple and intuitive axioms. We motivate these axioms on the basis of two possible interpretations for this upper expectation: a behavioural interpretation similar to that of Walley’s, and an interpretation in terms of upper envelopes of linear expectations. Subsequently, we show that the most conservative upper expectation satisfying our axioms coincides with a particular version of the game-theoretic upper expectation introduced by Shafer and Vovk. This has two important implications. On the one hand, it guarantees that there is a unique most conservative global belief model satisfying our axioms. On the other hand, it shows that Shafer and Vovk’s model can be given an axiomatic characterisation, thereby providing an alternative motivation for adopting this model, even outside their framework.},
  author       = {T'Joens, Natan and De Bock, Jasper and De Cooman, Gert},
  booktitle    = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications},
  editor       = {De Bock, Jasper and de Campos, Cassio P. and De Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory},
  keywords     = {Game-theoretic probability,Upper expectations,Uncertain processes,Coherence},
  language     = {eng},
  location     = {Ghent},
  pages        = {377--385},
  publisher    = {Proceedings of Machine Learning Research},
  title        = {In Search of a Global Belief Model for Discrete-Time Uncertain Processes},
  volume       = {103},
  year         = {2019},
}