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

Troffaes, Matthias C.M.

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.

Citation

Troffaes, M. C. (2018). Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions. International Journal of Approximate Reasoning: Uncertainty in Intelligent Systems, 101, 31-48. https://doi.org/10.1016/j.ijar.2018.06.009

• Journal Article Type: Article
• Acceptance Date: Jun 27, 2018
• Online Publication Date: Jun 30, 2018
• Publication Date: Oct 1, 2018
• Deposit Date: Dec 4, 2017
• Publicly Available Date: Jun 30, 2019
• Journal: International Journal of Approximate Reasoning
• Print ISSN: 0888-613X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 101
• Pages: 31-48
• DOI: https://doi.org/10.1016/j.ijar.2018.06.009
• Public URL: https://durham-repository.worktribe.com/output/1343383
• Related Public URLs: https://arxiv.org/abs/1806.10404