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Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions.

Troffaes, Matthias C. M. (2018) 'Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions.', International journal of approximate reasoning., 101 . pp. 31-48.

Abstract

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We link consistency of these estimators to Glivenko-Cantelli classes, and for the sub-Gaussian case we show how the correlation structure of this process can be used to bound the bias and prove consistency. We also propose a new upper estimator, which can be used along with the standard lower estimator, in order to provide a simple confidence interval. As a case study of this framework, we then discuss how importance sampling can be exploited to provide accurate numerical estimates of lower previsions. We propose an iterative importance sampling method to drastically improve the performance of imprecise importance sampling. We demonstrate our results on the imprecise Dirichlet model.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
First Live Deposit - 05 December 2017
File format - PDF
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Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.ijar.2018.06.009
Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Record Created:05 Dec 2017 09:28
Last Modified:06 Jul 2018 09:27

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