Empirical Interpretation of Imprecise Probabilities

Marco E. G. V. Cattaneo
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:61-72, 2017.

Abstract

This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise probabilities can be satisfactorily estimated from data. In fact, estimability on the basis of finite amounts of data is a necessary condition for imprecise probabilities in order to have a clear empirical meaning. Unfortunately, imprecise probabilities can be estimated arbitrarily well from data only in very limited settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-cattaneo17a, title = {Empirical Interpretation of Imprecise Probabilities}, author = {Cattaneo, Marco E. G. V.}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {61--72}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/cattaneo17a/cattaneo17a.pdf}, url = {https://proceedings.mlr.press/v62/cattaneo17a.html}, abstract = {This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise probabilities can be satisfactorily estimated from data. In fact, estimability on the basis of finite amounts of data is a necessary condition for imprecise probabilities in order to have a clear empirical meaning. Unfortunately, imprecise probabilities can be estimated arbitrarily well from data only in very limited settings.} }
Endnote
%0 Conference Paper %T Empirical Interpretation of Imprecise Probabilities %A Marco E. G. V. Cattaneo %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-cattaneo17a %I PMLR %P 61--72 %U https://proceedings.mlr.press/v62/cattaneo17a.html %V 62 %X This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise probabilities can be satisfactorily estimated from data. In fact, estimability on the basis of finite amounts of data is a necessary condition for imprecise probabilities in order to have a clear empirical meaning. Unfortunately, imprecise probabilities can be estimated arbitrarily well from data only in very limited settings.
APA
Cattaneo, M.E.G.V.. (2017). Empirical Interpretation of Imprecise Probabilities. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:61-72 Available from https://proceedings.mlr.press/v62/cattaneo17a.html.

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