Computable randomness is about more than probabilities
- Author
- Floris Persiau (UGent) , Jasper De Bock (UGent) and Gert de Cooman (UGent)
- Organization
- Abstract
- We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer.
- Keywords
- computable randomness, coherent lower expectations, imprecise probabilities, supermartingales, computability
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8675897
- MLA
- Persiau, Floris, et al. “Computable Randomness Is about More than Probabilities.” Scalable Uncertainty Management, 14th International Conference, SUM 2020, edited by J Davis and K Tabia, vol. 12322, Springer, 2020, pp. 172–86, doi:10.1007/978-3-030-58449-8_12.
- APA
- Persiau, F., De Bock, J., & de Cooman, G. (2020). Computable randomness is about more than probabilities. In J. Davis & K. Tabia (Eds.), Scalable Uncertainty Management, 14th International Conference, SUM 2020 (Vol. 12322, pp. 172–186). https://doi.org/10.1007/978-3-030-58449-8_12
- Chicago author-date
- Persiau, Floris, Jasper De Bock, and Gert de Cooman. 2020. “Computable Randomness Is about More than Probabilities.” In Scalable Uncertainty Management, 14th International Conference, SUM 2020, edited by J Davis and K Tabia, 12322:172–86. Springer. https://doi.org/10.1007/978-3-030-58449-8_12.
- Chicago author-date (all authors)
- Persiau, Floris, Jasper De Bock, and Gert de Cooman. 2020. “Computable Randomness Is about More than Probabilities.” In Scalable Uncertainty Management, 14th International Conference, SUM 2020, ed by. J Davis and K Tabia, 12322:172–186. Springer. doi:10.1007/978-3-030-58449-8_12.
- Vancouver
- 1.Persiau F, De Bock J, de Cooman G. Computable randomness is about more than probabilities. In: Davis J, Tabia K, editors. Scalable Uncertainty Management, 14th International Conference, SUM 2020. Springer; 2020. p. 172–86.
- IEEE
- [1]F. Persiau, J. De Bock, and G. de Cooman, “Computable randomness is about more than probabilities,” in Scalable Uncertainty Management, 14th International Conference, SUM 2020, Bozen-Bolzano, Italy, virtual event, 2020, vol. 12322, pp. 172–186.
@inproceedings{8675897,
abstract = {{We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer.}},
author = {{Persiau, Floris and De Bock, Jasper and de Cooman, Gert}},
booktitle = {{Scalable Uncertainty Management, 14th International Conference, SUM 2020}},
editor = {{Davis, J and Tabia, K}},
isbn = {{9783030584481}},
issn = {{0302-9743}},
keywords = {{computable randomness,coherent lower expectations,imprecise probabilities,supermartingales,computability}},
language = {{eng}},
location = {{Bozen-Bolzano, Italy, virtual event}},
pages = {{172--186}},
publisher = {{Springer}},
title = {{Computable randomness is about more than probabilities}},
url = {{http://doi.org/10.1007/978-3-030-58449-8_12}},
volume = {{12322}},
year = {{2020}},
}
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