{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:43:22Z","timestamp":1765039402227,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"6-8","license":[{"start":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T00:00:00Z","timestamp":1525305600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura Cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["GA14-19213S"],"award-info":[{"award-number":["GA14-19213S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Technologias de juegos para la creaci\u00f3n de contenidos digitales, gesti\u00f3n, visualizaci\u00f3n y sonificaci\u00f3n","award":["TIN2016-75866-C3-3-R"],"award-info":[{"award-number":["TIN2016-75866-C3-3-R"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61471561","61771335"],"award-info":[{"award-number":["61471561","61771335"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National research, development and innovation office","award":["OTKA K-124124"],"award-info":[{"award-number":["OTKA K-124124"]}]},{"name":"Reinvent systems for science and discovery","award":["VKSZ-14 PET\/MRI 7T"],"award-info":[{"award-number":["VKSZ-14 PET\/MRI 7T"]}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-17-CE40-0031-01"],"award-info":[{"award-number":["ANR-17-CE40-0031-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100011264","name":"FP7 People: Marie-Curie Actions","doi-asserted-by":"publisher","award":["FP7\/2007-2013"],"award-info":[{"award-number":["FP7\/2007-2013"]}],"id":[{"id":"10.13039\/100011264","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Prestige postdoctoral research fellowsips","award":["PCOFUND-GA-2013-609102"],"award-info":[{"award-number":["PCOFUND-GA-2013-609102"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Vis Comput"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s00371-018-1522-x","type":"journal-article","created":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T03:48:38Z","timestamp":1525319318000},"page":"843-852","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Multiple importance sampling characterization by weighted mean invariance"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2164-6858","authenticated-orcid":false,"given":"Mateu","family":"Sbert","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3329-8814","authenticated-orcid":false,"given":"Vlastimil","family":"Havran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8523-2315","authenticated-orcid":false,"given":"L\u00e1szl\u00f3","family":"Szirmay-Kalos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8967-4866","authenticated-orcid":false,"given":"V\u00edctor","family":"Elvira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,5,3]]},"reference":[{"key":"1522_CR1","doi-asserted-by":"publisher","unstructured":"Belzunce, F., Martinez-Riquelme, C., Mulero, J.: An Introduction to Stochastic Orders. Academic Press (2016). \n                    https:\/\/doi.org\/10.1016\/B978-0-12-803768-3.09977-4","DOI":"10.1016\/B978-0-12-803768-3.09977-4"},{"issue":"4","key":"1522_CR2","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1109\/MSP.2017.2699226","volume":"34","author":"MF Bugallo","year":"2017","unstructured":"Bugallo, M.F., Elvira, V., Martino, L., Luengo, D., M\u00edguez, J., Djuric, P.M.: Adaptive importance sampling: the past, the present, and the future. IEEE Signal Process. Mag. 34(4), 60\u201379 (2017)","journal-title":"IEEE Signal Process. Mag."},{"key":"1522_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0399-4","volume-title":"Handbook of Means and Their Inequalities","author":"P Bullen","year":"2003","unstructured":"Bullen, P.: Handbook of Means and Their Inequalities. Springer, Dordrecht (2003)"},{"issue":"4","key":"1522_CR4","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1198\/106186004X12803","volume":"13","author":"O Capp\u00e9","year":"2004","unstructured":"Capp\u00e9, O., Guillin, A., Marin, J.M., Robert, C.P.: Population Monte Carlo. J. Comput. Graph. Stat. 13(4), 907\u2013929 (2004)","journal-title":"J. Comput. Graph. Stat."},{"issue":"4","key":"1522_CR5","doi-asserted-by":"publisher","first-page":"798","DOI":"10.1111\/j.1467-9469.2011.00756.x","volume":"39","author":"JM Cornuet","year":"2012","unstructured":"Cornuet, J.M., Marin, J.M., Mira, A., Robert, C.P.: Adaptive multiple importance sampling. Scand. J. Stat. 39(4), 798\u2013812 (2012)","journal-title":"Scand. J. Stat."},{"key":"1522_CR6","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1051\/ps:2007028","volume":"11","author":"R Douc","year":"2007","unstructured":"Douc, R., Guillin, A., Marin, J.M., Robert, C.P.: Minimum variance importance sampling via population Monte Carlo. ESAIM Probab. Stat. 11, 424\u2013447 (2007)","journal-title":"ESAIM Probab. Stat."},{"issue":"10","key":"1522_CR7","doi-asserted-by":"publisher","first-page":"1757","DOI":"10.1109\/LSP.2015.2432078","volume":"22","author":"V Elvira","year":"2015","unstructured":"Elvira, V., Martino, L., Luengo, D., Bugallo, M.F.: Efficient multiple importance sampling estimators. IEEE Signal Process. Lett. 22(10), 1757\u20131761 (2015). \n                    https:\/\/doi.org\/10.1109\/LSP.2015.2432078","journal-title":"IEEE Signal Process. Lett."},{"key":"1522_CR8","unstructured":"Elvira, V., Martino, L., Luengo, D., Bugallo, M.F.: Generalized multiple importance sampling. ArXiv e-prints (2015). \n                    https:\/\/arxiv.org\/abs\/1511.03095"},{"issue":"10","key":"1522_CR9","doi-asserted-by":"publisher","first-page":"1474","DOI":"10.1109\/LSP.2016.2600678","volume":"23","author":"V Elvira","year":"2016","unstructured":"Elvira, V., Martino, L., Luengo, D., Bugallo, M.F.: Heretical multiple importance sampling. IEEE Signal Process. Lett. 23(10), 1474\u20131478 (2016)","journal-title":"IEEE Signal Process. Lett."},{"key":"1522_CR10","unstructured":"Elvira, V., Martino, L., Luengo, D., Bugallo, M.F.: Multiple importance sampling with overlapping sets of proposals. In: Statistical Signal Processing Workshop (SSP), 2016 IEEE, pp. 1\u20135. IEEE (2016)"},{"issue":"12","key":"1522_CR11","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.sigpro.2016.07.012","volume":"131","author":"V Elvira","year":"2017","unstructured":"Elvira, V., Martino, L., Luengo, D., Bugallo, M.F.: Improving population Monte Carlo: alternative weighting and resampling schemes. Sig. Process. 131(12), 77\u201391 (2017)","journal-title":"Sig. Process."},{"key":"1522_CR12","doi-asserted-by":"publisher","unstructured":"Havran, V., Sbert, M.: Optimal combination of techniques in multiple importance sampling. In: Proceedings of the 13th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry, VRCAI \u201914, pp. 141\u2013150. ACM, New York, NY, USA (2014). \n                    https:\/\/doi.org\/10.1145\/2670473.2670496","DOI":"10.1145\/2670473.2670496"},{"key":"1522_CR13","unstructured":"He, H.Y., Owen, A.B.: Optimal Mixture Weights in Multiple Importance Sampling. ArXiv preprint \n                    arXiv:1411.3954\n                    \n                   (2014)"},{"key":"1522_CR14","doi-asserted-by":"crossref","unstructured":"Kajiya, J.T.: The rendering equation. In: Evans, D.C., Athay, R.J. (eds.) Computer Graphics (SIGGRAPH \u201986 Proceedings), vol. 20, pp. 143\u2013150 (1986)","DOI":"10.1145\/15886.15902"},{"issue":"7","key":"1522_CR15","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1111\/cgf.12220","volume":"32","author":"H Lu","year":"2013","unstructured":"Lu, H., Pacanowski, R., Granier, X.: Second-order approximation for variance reduction in multiple importance sampling. Comput. Graph. Forum 32(7), 131\u2013136 (2013). \n                    https:\/\/doi.org\/10.1111\/cgf.12220","journal-title":"Comput. Graph. Forum"},{"issue":"3","key":"1522_CR16","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1007\/s11222-016-9642-5","volume":"27","author":"L Martino","year":"2017","unstructured":"Martino, L., Elvira, V., Luengo, D., Corander, J.: Layered adaptive importance sampling. Stat. Comput. 27(3), 599\u2013623 (2017)","journal-title":"Stat. Comput."},{"issue":"3","key":"1522_CR17","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1111\/1467-8659.00337","volume":"18","author":"L Neumann","year":"1999","unstructured":"Neumann, L., Neumann, A., Szirmay-Kalos, L.: Compact metallic reflectance models. Comput. Graph. Forum (Eurographics\u201999) 18(3), 161\u2013172 (1999)","journal-title":"Comput. Graph. Forum (Eurographics\u201999)"},{"key":"1522_CR18","unstructured":"Owen, A.B., Maximov, Y., Chertkov, M.: Importance Sampling the Union of Rare Events with an Application to Power Systems Analysis. ArXiv preprint \n                    arXiv:1710.06965\n                    \n                   (2017)"},{"key":"1522_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-017-1398-1","author":"M Sbert","year":"2017","unstructured":"Sbert, M., Havran, V.: Adaptive multiple importance sampling for general functions. Vis. Comput. (2017). \n                    https:\/\/doi.org\/10.1007\/s00371-017-1398-1","journal-title":"Vis. Comput."},{"issue":"7","key":"1522_CR20","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1111\/cgf.13042","volume":"35","author":"M Sbert","year":"2016","unstructured":"Sbert, M., Havran, V., Szirmay-Kalos, L.: Variance analysis of multi-sample and one-sample multiple importance sampling. Comput. Graph. Forum 35(7), 451\u2013460 (2016). \n                    https:\/\/doi.org\/10.1111\/cgf.13042","journal-title":"Comput. Graph. Forum"},{"issue":"1","key":"1522_CR21","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1186\/s13634-018-0531-2","volume":"2018","author":"M Sbert","year":"2018","unstructured":"Sbert, M., Havran, V., Szirmay-Kalos, L.: Multiple importance sampling revisited: breaking the bounds. EURASIP J. Adv. Signal Process. 2018(1), 15 (2018). \n                    https:\/\/doi.org\/10.1186\/s13634-018-0531-2","journal-title":"EURASIP J. Adv. Signal Process."},{"issue":"1","key":"1522_CR22","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1186\/s13660-016-1233-7","volume":"2016","author":"M Sbert","year":"2016","unstructured":"Sbert, M., Poch, J.: A necessary and sufficient condition for the inequality of generalized weighted means. J. Inequal. Appl. 2016(1), 292 (2016). \n                    https:\/\/doi.org\/10.1186\/s13660-016-1233-7","journal-title":"J. Inequal. Appl."},{"key":"1522_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-34675-5","volume-title":"Stochastic Orders","author":"M Shaked","year":"2007","unstructured":"Shaked, M., Shanthikumar, G.: Stochastic Orders. Springer, New York (2007). \n                    https:\/\/doi.org\/10.1007\/978-0-387-34675-5"},{"key":"1522_CR24","unstructured":"Veach, E.: Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. thesis, Stanford University (1997)"},{"key":"1522_CR25","doi-asserted-by":"publisher","unstructured":"Veach, E., Guibas, L.J.: Optimally combining sampling techniques for Monte Carlo rendering. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH \u201995, pp. 419\u2013428. ACM, New York, NY, USA (1995). \n                    https:\/\/doi.org\/10.1145\/218380.218498","DOI":"10.1145\/218380.218498"}],"container-title":["The Visual Computer"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00371-018-1522-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00371-018-1522-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00371-018-1522-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T19:09:20Z","timestamp":1556824160000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00371-018-1522-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,3]]},"references-count":25,"journal-issue":{"issue":"6-8","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["1522"],"URL":"https:\/\/doi.org\/10.1007\/s00371-018-1522-x","relation":{},"ISSN":["0178-2789","1432-2315"],"issn-type":[{"type":"print","value":"0178-2789"},{"type":"electronic","value":"1432-2315"}],"subject":[],"published":{"date-parts":[[2018,5,3]]},"assertion":[{"value":"3 May 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The authors are funded in part by Czech Science Foundation research program GA14-19213S, by Grant TIN2016-75866-C3-3-R from the Spanish Government, by National Natural Science Foundation of China Grants Nos. 61471261 and 61771335, and by Grant OTKA K-124124 and VKSZ-14 PET\/MRI 7T. V.E. acknowledges support from the Agence Nationale de la Recherche of France under PISCES project (ANR-17-CE40-0031-01), the Fulbright program, and the Marie Curie Fellowship (FP7\/2007-2013) under REA grant agreement n. PCOFUND-GA-2013-609102, through the PRESTIGE program.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Research grants from funding agencies"}}]}}