Gilks, WR, Cironis, L and Barber, S orcid.org/0000-0002-7611-7219 (Cover date: October 2023) Wavelet Monte Carlo: a principle for sampling from complex distributions. Statistics and Computing, 33 (5). 92. ISSN 0960-3174
Abstract
We present Wavelet Monte Carlo (WMC), a new method for generating independent samples from complex target distributions. The methodology is based on wavelet decomposition of the difference between the target density and a user-specified initial density, and exploits both wavelet theory and survival analysis. In practice, WMC can process only a finite range of wavelet scales. We prove that the resulting L1 approximation error converges to zero geometrically as the scale range tends to (−∞,+∞). This provides a principled approach to trading off accuracy against computational efficiency. We offer practical suggestions for addressing some issues of implementation, but further development is needed for a computationally efficient methodology. We illustrate the methodology in one- and two-dimensional examples, and discuss challenges and opportunities for application in higher dimensions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Monte-Carlo integration; Statistical sampling algorithm; Survival analysis; Wavelet decomposition |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 May 2023 13:37 |
Last Modified: | 07 Aug 2024 02:09 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s11222-023-10256-w |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:199136 |