{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T23:30:11Z","timestamp":1711755011520},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The assessment of the probability of a rare event with a naive Monte Carlo method is computationally intensive, so faster estimation or variance reduction methods are needed. We focus on one of these methods which is the interacting particle system (IPS) method.\nThe method is not intrusive in the sense that the random Markov system under consideration is simulated with its original distribution, but\nselection steps are introduced that favor trajectories (particles) with high potential values.\nAn unbiased estimator with reduced variance can then be proposed.\nThe method requires to specify a set of potential functions. The choice of these functions is crucial because it determines the magnitude of the variance reduction. So far, little information was available on how to choose the potential functions. This paper provides the expressions of the optimal potential functions minimizing the asymptotic variance of the estimator of the IPS method and it proposes recommendations for the practical design of the potential\nfunctions.<\/jats:p>","DOI":"10.1515\/mcma-2021-2086","type":"journal-article","created":{"date-parts":[[2021,4,29]],"date-time":"2021-04-29T21:52:40Z","timestamp":1619733160000},"page":"137-152","source":"Crossref","is-referenced-by-count":3,"title":["Optimal potential functions for the interacting particle system method"],"prefix":"10.1515","volume":"27","author":[{"given":"Hassane","family":"Chraibi","sequence":"first","affiliation":[{"name":"\u00c9lectricit\u00e9 de France (EDF) , PERICLES Department, 7 Boulevard Gaspard Monge, 91120 Palaiseau , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anne","family":"Dutfoy","sequence":"additional","affiliation":[{"name":"\u00c9lectricit\u00e9 de France (EDF) , PERICLES Department, 7 Boulevard Gaspard Monge, 91120 Palaiseau , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Galtier","sequence":"additional","affiliation":[{"name":"CMAP , \u00c9cole polytechnique , Institut Polytechnique de Paris , 91128 Palaiseau Cedex , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Josselin","family":"Garnier","sequence":"additional","affiliation":[{"name":"CMAP , \u00c9cole polytechnique , Institut Polytechnique de Paris , 91128 Palaiseau Cedex , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2021,4,30]]},"reference":[{"key":"2021053122092011094_j_mcma-2021-2086_ref_001_w2aab3b7e1393b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"D.  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Lai,\nA general theory of particle filters in hidden Markov models and some applications,\nAnn. Statist. 41 (2013), no. 6, 2877\u20132904.","DOI":"10.1214\/13-AOS1172"},{"key":"2021053122092011094_j_mcma-2021-2086_ref_008_w2aab3b7e1393b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"N.  Chopin,\nCentral limit theorem for sequential Monte Carlo methods and its application to Bayesian inference,\nAnn. Statist. 32 (2004), no. 6, 2385\u20132411.","DOI":"10.1214\/009053604000000698"},{"key":"2021053122092011094_j_mcma-2021-2086_ref_009_w2aab3b7e1393b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"H.  Chraibi, A.  Dutfoy, T.  Galtier and J.  Garnier,\nOn the optimal importance process for piecewise deterministic Markov process,\nESAIM Probab. Stat. 23 (2019), 893\u2013921.","DOI":"10.1051\/ps\/2019015"},{"key":"2021053122092011094_j_mcma-2021-2086_ref_010_w2aab3b7e1393b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"P.  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