A Remarkable Equivalence between Non-Stationary Precise and Stationary Imprecise Uncertainty Models in Computable Randomness

Floris Persiau, Jasper De Bock, Gert de Cooman
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:244-253, 2021.

Abstract

The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, such randomness involves precise uncertainty models, and it is only recently that imprecision has been introduced into this field. As a consequence, the investigation into how imprecision alters our view on random sequences has only just begun. In this contribution, we establish a close and surprising connection between precise and imprecise uncertainty models in this randomness context. In particular, we show that there are stationary imprecise models and non-stationary precise models that have the exact same set of computably random sequences. We also discuss the possible implications of this result for a statistics based on imprecise probabilities.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-persiau21a, title = {A Remarkable Equivalence between Non-Stationary Precise and Stationary Imprecise Uncertainty Models in Computable Randomness}, author = {Persiau, Floris and De Bock, Jasper and de Cooman, Gert}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {244--253}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/persiau21a/persiau21a.pdf}, url = {https://proceedings.mlr.press/v147/persiau21a.html}, abstract = {The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, such randomness involves precise uncertainty models, and it is only recently that imprecision has been introduced into this field. As a consequence, the investigation into how imprecision alters our view on random sequences has only just begun. In this contribution, we establish a close and surprising connection between precise and imprecise uncertainty models in this randomness context. In particular, we show that there are stationary imprecise models and non-stationary precise models that have the exact same set of computably random sequences. We also discuss the possible implications of this result for a statistics based on imprecise probabilities.} }
Endnote
%0 Conference Paper %T A Remarkable Equivalence between Non-Stationary Precise and Stationary Imprecise Uncertainty Models in Computable Randomness %A Floris Persiau %A Jasper De Bock %A Gert de Cooman %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-persiau21a %I PMLR %P 244--253 %U https://proceedings.mlr.press/v147/persiau21a.html %V 147 %X The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, such randomness involves precise uncertainty models, and it is only recently that imprecision has been introduced into this field. As a consequence, the investigation into how imprecision alters our view on random sequences has only just begun. In this contribution, we establish a close and surprising connection between precise and imprecise uncertainty models in this randomness context. In particular, we show that there are stationary imprecise models and non-stationary precise models that have the exact same set of computably random sequences. We also discuss the possible implications of this result for a statistics based on imprecise probabilities.
APA
Persiau, F., De Bock, J. & de Cooman, G.. (2021). A Remarkable Equivalence between Non-Stationary Precise and Stationary Imprecise Uncertainty Models in Computable Randomness. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:244-253 Available from https://proceedings.mlr.press/v147/persiau21a.html.

Related Material