{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:21Z","timestamp":1740123921264,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T00:00:00Z","timestamp":1687564800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T00:00:00Z","timestamp":1687564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present <jats:italic>Wavelet Monte Carlo<\/jats:italic> (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\u00a0can process only a finite range of wavelet scales. We prove that the resulting <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> approximation error converges to zero geometrically as the scale range tends to <jats:inline-formula><jats:alternatives><jats:tex-math>$$(-\\infty ,+\\infty )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mi>\u221e<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mi>\u221e<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. 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.<\/jats:p>","DOI":"10.1007\/s11222-023-10256-w","type":"journal-article","created":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T11:39:02Z","timestamp":1687606742000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Wavelet Monte Carlo: a principle for sampling from complex distributions"],"prefix":"10.1007","volume":"33","author":[{"given":"Walter R.","family":"Gilks","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lukas","family":"Cironis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7611-7219","authenticated-orcid":false,"given":"Stuart","family":"Barber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,24]]},"reference":[{"key":"10256_CR1","unstructured":"Cironis, L.: Theory, Analysis and implementation of Wavelet Monte Carlo. 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