A Note on Monte Carlo Integration in High Dimensions.
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo integration using techniques from the high-dimensional statistics lit...
| Publicado en: | American Statistician Vol. 78; no. 3; pp. 290 - 297 |
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| Formato: | Artículo |
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Taylor & Francis Ltd
Aug2024
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=178594369&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 178594369 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Aug2024 vid: 78 iid: 3 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 178594369 10.1080/00031305.2023.2267637 ppf: 290 ppct: 7 formats: tig: atl: A Note on Monte Carlo Integration in High Dimensions. aug: au: Tang, Yanbo affil: Department of Mathematics, Imperial College London, London, UK su: Monte Carlo method Approximation error Concentration functions Confidence intervals High-dimensional model representation sug: subj: Monte Carlo method Approximation error Concentration functions Confidence intervals High-dimensional model representation keyword: Concentration inequalities High-dimensional statistics Numerical integration Concentration inequalities High-dimensional statistics Numerical integration ab: Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo integration using techniques from the high-dimensional statistics literature by allowing the dimension of the integral to increase. In doing so, we derive nonasymptotic bounds for the relative and absolute error of the approximation for some general classes of functions through concentration inequalities. We provide concrete examples in which the magnitude of the number of points sampled needed to guarantee a consistent estimate varies between polynomial to exponential, and show that in theory arbitrarily fast or slow rates are possible. This demonstrates that the behavior of Monte Carlo integration in high dimensions is not uniform. Through our methods we also obtain nonasymptotic confidence intervals which are valid regardless of the number of points sampled. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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