Towards a Strictly Frequentist Theory of Imprecise Probability
Abstract
Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to statistical phenomena that exhibit diverging relative frequencies. In doing so, we develop a close connection with imprecise probability: the cluster points of relative frequencies yield a coherent upper prevision. We show that a natural frequentist definition of conditional probability recovers the generalized Bayes rule. We prove constructively that, for a finite set of elementary events, there exists a sequence for which the cluster points of relative frequencies coincide with a prespecified set, thereby providing strictly frequentist semantics for coherent upper previsions.
Cite
Text
Fröhlich et al. "Towards a Strictly Frequentist Theory of Imprecise Probability." Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, 2023.Markdown
[Fröhlich et al. "Towards a Strictly Frequentist Theory of Imprecise Probability." Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, 2023.](https://mlanthology.org/isipta/2023/frohlich2023isipta-strictly/)BibTeX
@inproceedings{frohlich2023isipta-strictly,
title = {{Towards a Strictly Frequentist Theory of Imprecise Probability}},
author = {Fröhlich, Christian and Derr, Rabanus and Williamson, Robert C.},
booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications},
year = {2023},
pages = {230-240},
volume = {215},
url = {https://mlanthology.org/isipta/2023/frohlich2023isipta-strictly/}
}