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Monte Carlo estimation for imprecise probabilities : basic properties

Arne Decadt (UGent) , Gert De Cooman (UGent) and Jasper De Bock (UGent)
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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.
Keywords
Monte Carlo simulation, Imprecise probabilities, Bias, Consistency, Lower expectation operator, Estimation

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MLA
Decadt, Arne, et al. “Monte Carlo Estimation for Imprecise Probabilities : Basic Properties.” International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, edited by Jasper De Bock et al., vol. 103, PMLR, 2019, pp. 135–44.
APA
Decadt, A., De Cooman, G., & De Bock, J. (2019). Monte Carlo estimation for imprecise probabilities : basic properties. In J. De Bock, C. P. de Campos, G. De Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings (Vol. 103, pp. 135–144). Ghent: PMLR.
Chicago author-date
Decadt, Arne, Gert De Cooman, and Jasper De Bock. 2019. “Monte Carlo Estimation for Imprecise Probabilities : Basic Properties.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, edited by Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:135–44. PMLR.
Chicago author-date (all authors)
Decadt, Arne, Gert De Cooman, and Jasper De Bock. 2019. “Monte Carlo Estimation for Imprecise Probabilities : Basic Properties.” In International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, ed by. Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:135–144. PMLR.
Vancouver
1.
Decadt A, De Cooman G, De Bock J. Monte Carlo estimation for imprecise probabilities : basic properties. In: De Bock J, de Campos CP, De Cooman G, Quaeghebeur E, Wheeler G, editors. International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings. PMLR; 2019. p. 135–44.
IEEE
[1]
A. Decadt, G. De Cooman, and J. De Bock, “Monte Carlo estimation for imprecise probabilities : basic properties,” in International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings, Ghent, 2019, vol. 103, pp. 135–144.
@inproceedings{8626742,
  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.},
  author       = {Decadt, Arne and De Cooman, Gert and De Bock, Jasper},
  booktitle    = {International Symposium on Imprecise Probabilities : Theories and Applications, ISIPTA 2019, Proceedings},
  editor       = {De Bock, Jasper and de Campos, Cassio P. and De Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory},
  issn         = {2640-3498},
  keywords     = {Monte Carlo simulation,Imprecise probabilities,Bias,Consistency,Lower expectation operator,Estimation},
  language     = {eng},
  location     = {Ghent},
  pages        = {135--144},
  publisher    = {PMLR},
  title        = {Monte Carlo estimation for imprecise probabilities : basic properties},
  url          = {http://proceedings.mlr.press/v103/decadt19a/decadt19a.pdf},
  volume       = {103},
  year         = {2019},
}