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Product-form estimators : exploiting independence to scale up Monte Carlo
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Kuntz, Juan, Crucinio, Francesca R. and Johansen, Adam M. (2022) Product-form estimators : exploiting independence to scale up Monte Carlo. Statistics and Computing, 32 (1). 12. doi:10.1007/s11222-021-10069-9 ISSN 0960-3174.
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Official URL: http://dx.doi.org/10.1007/s11222-021-10069-9
Abstract
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target’s independence structure. We identify the most basic incarnations of these estimators with a class of generalized U-statistics and thus establish their unbiasedness, consistency, and asymptotic normality. Moreover, we show that they obtain the minimum possible variance amongst a broad class of estimators, and we investigate their computational cost and delineate the settings in which they are most efficient. We exemplify the merger of these estimators with other well known Monte Carlo estimators so as to better adapt the latter to the target’s independence structure and improve their performance. We do this via three simple mergers: one with importance sampling, another with importance sampling squared, and a final one with pseudo-marginal Metropolis–Hastings. In all cases, we show that the resulting estimators are well founded and achieve lower variances than their standard counterparts. Lastly, we illustrate the various variance reductions through several examples.
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Dimension reduction (Statistics), Monte Carlo method, Sampling (Statistics) | ||||||||||||||||||
| Journal or Publication Title: | Statistics and Computing | ||||||||||||||||||
| Publisher: | Springer | ||||||||||||||||||
| ISSN: | 0960-3174 | ||||||||||||||||||
| Official Date: | 2022 | ||||||||||||||||||
| Dates: |
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| Volume: | 32 | ||||||||||||||||||
| Number: | 1 | ||||||||||||||||||
| Article Number: | 12 | ||||||||||||||||||
| DOI: | 10.1007/s11222-021-10069-9 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
| Date of first compliant deposit: | 21 January 2022 | ||||||||||||||||||
| Date of first compliant Open Access: | 24 January 2022 | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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