Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same!

Natan T’Joens, Jasper De Bock
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:310-319, 2021.

Abstract

We consider three different types of global uncertainty models for discrete-time stochastic processes: measure-theoretic upper expectations, game-theoretic upper expectations and axiomatic upper expectations. The last two are known to be identical. We show that they coincide with measure-theoretic upper expectations on two distinct domains: monotone pointwise limits of finitary gambles, and bounded below Borel-measurable variables. We argue that these domains cover most practical inferences, and that therefore, in practice, it does not matter which model is used.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-t-joens21a, title = {Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same!}, author = {T'Joens, Natan and De Bock, Jasper}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {310--319}, 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/t-joens21a/t-joens21a.pdf}, url = {https://proceedings.mlr.press/v147/t-joens21a.html}, abstract = {We consider three different types of global uncertainty models for discrete-time stochastic processes: measure-theoretic upper expectations, game-theoretic upper expectations and axiomatic upper expectations. The last two are known to be identical. We show that they coincide with measure-theoretic upper expectations on two distinct domains: monotone pointwise limits of finitary gambles, and bounded below Borel-measurable variables. We argue that these domains cover most practical inferences, and that therefore, in practice, it does not matter which model is used.} }
Endnote
%0 Conference Paper %T Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same! %A Natan T’Joens %A Jasper De Bock %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-t-joens21a %I PMLR %P 310--319 %U https://proceedings.mlr.press/v147/t-joens21a.html %V 147 %X We consider three different types of global uncertainty models for discrete-time stochastic processes: measure-theoretic upper expectations, game-theoretic upper expectations and axiomatic upper expectations. The last two are known to be identical. We show that they coincide with measure-theoretic upper expectations on two distinct domains: monotone pointwise limits of finitary gambles, and bounded below Borel-measurable variables. We argue that these domains cover most practical inferences, and that therefore, in practice, it does not matter which model is used.
APA
T’Joens, N. & De Bock, J.. (2021). Global Upper Expectations for Discrete-Time Stochastic Processes: In Practice, They Are All The Same!. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:310-319 Available from https://proceedings.mlr.press/v147/t-joens21a.html.

Related Material