Monte Carlo Estimation for Imprecise Probabilities: Basic Properties

Arne Decadt, Gert de Cooman, Jasper De Bock
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:135-144, 2019.

Abstract

We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly practical techniques for proving strong consistency of the estimators and use these to prove the consistency of an example in the literature. We also provide an example where there is no consistency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-decadt19a, title = {Monte Carlo Estimation for Imprecise Probabilities: Basic Properties}, author = {Decadt, Arne and {de Cooman}, Gert and De Bock, Jasper}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {135--144}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/decadt19a/decadt19a.pdf}, url = {https://proceedings.mlr.press/v103/decadt19a.html}, abstract = {We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly practical techniques for proving strong consistency of the estimators and use these to prove the consistency of an example in the literature. We also provide an example where there is no consistency.} }
Endnote
%0 Conference Paper %T Monte Carlo Estimation for Imprecise Probabilities: Basic Properties %A Arne Decadt %A Gert de Cooman %A Jasper De Bock %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-decadt19a %I PMLR %P 135--144 %U https://proceedings.mlr.press/v103/decadt19a.html %V 103 %X We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly practical techniques for proving strong consistency of the estimators and use these to prove the consistency of an example in the literature. We also provide an example where there is no consistency.
APA
Decadt, A., de Cooman, G. & De Bock, J.. (2019). Monte Carlo Estimation for Imprecise Probabilities: Basic Properties. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:135-144 Available from https://proceedings.mlr.press/v103/decadt19a.html.

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