Imprecision in martingale-theoretic prequential randomness

Floris Persiau, Gert de Cooman
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:390-400, 2023.

Abstract

In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast ‘on the fly’ without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the more standard approach. We take the first steps in allowing for probability intervals instead of precise probabilities in this prequential approach, based on ideas from our earlier imprecise-probabilistic and martingale-theoretic account of algorithmic randomness. We define what it means for an infinite sequence $(I_1,x_1,I_2,x_2,…)$ of successive interval forecasts $I_k$ and subsequent binary outcomes $x_k$ to be random. We compare the resulting prequential randomness notion with the more standard one, and investigate where both randomness notions coincide, as well as where their properties correspond.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-persiau23a, title = {Imprecision in martingale-theoretic prequential randomness}, author = {Persiau, Floris and de Cooman, Gert}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {390--400}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/persiau23a/persiau23a.pdf}, url = {https://proceedings.mlr.press/v215/persiau23a.html}, abstract = {In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast ‘on the fly’ without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the more standard approach. We take the first steps in allowing for probability intervals instead of precise probabilities in this prequential approach, based on ideas from our earlier imprecise-probabilistic and martingale-theoretic account of algorithmic randomness. We define what it means for an infinite sequence $(I_1,x_1,I_2,x_2,…)$ of successive interval forecasts $I_k$ and subsequent binary outcomes $x_k$ to be random. We compare the resulting prequential randomness notion with the more standard one, and investigate where both randomness notions coincide, as well as where their properties correspond.} }
Endnote
%0 Conference Paper %T Imprecision in martingale-theoretic prequential randomness %A Floris Persiau %A Gert de Cooman %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-persiau23a %I PMLR %P 390--400 %U https://proceedings.mlr.press/v215/persiau23a.html %V 215 %X In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast ‘on the fly’ without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the more standard approach. We take the first steps in allowing for probability intervals instead of precise probabilities in this prequential approach, based on ideas from our earlier imprecise-probabilistic and martingale-theoretic account of algorithmic randomness. We define what it means for an infinite sequence $(I_1,x_1,I_2,x_2,…)$ of successive interval forecasts $I_k$ and subsequent binary outcomes $x_k$ to be random. We compare the resulting prequential randomness notion with the more standard one, and investigate where both randomness notions coincide, as well as where their properties correspond.
APA
Persiau, F. & de Cooman, G.. (2023). Imprecision in martingale-theoretic prequential randomness. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:390-400 Available from https://proceedings.mlr.press/v215/persiau23a.html.

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