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These last are generally based on Gaussian assumptions. The main advantage of the probabilistic approach is that it provides a measure of uncertainty associated with the surrogate model in the whole space. This uncertainty is an efficient tool to construct strategies for various problems such as prediction enhancement, optimization, or inversion. In this paper, we propose a universal method to define a measure of uncertainty suitable for any surrogate model either deterministic or probabilistic. It relies on cross-validation submodel predictions. This empirical distribution may be computed in much more general frames than the Gaussian one; thus it is called the universal prediction distribution ( UP distribution). It allows the definition of many sampling criteria. We give and study adaptive sampling techniques for global refinement and an extension of the so-called efficient global optimization algorithm. We also discuss the use of the UP distribution for inversion problems. The performances of these new algorithms are studied both on toy models and on an engineering design problem.<\/jats:p>","DOI":"10.1137\/15m1053529","type":"journal-article","created":{"date-parts":[[2017,11,14]],"date-time":"2017-11-14T13:29:26Z","timestamp":1510666166000},"page":"1086-1109","source":"Crossref","is-referenced-by-count":37,"title":["Universal Prediction Distribution for Surrogate Models"],"prefix":"10.1137","volume":"5","author":[{"given":"Malek","family":"Ben Salem","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olivier","family":"Roustant","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabrice","family":"Gamboa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lionel","family":"Tomaso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,11,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1214\/09-SS054"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-013-0918-5"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-011-9241-4"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.2514\/1.34321"},{"key":"atypb5","unstructured":"G. E. P. Box, W. G. Hunter, and J. S. Hunter,\n                      Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building\n                      , Wiley, New York, 1978."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/050639983"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2013.03.008"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1979.1056087"},{"key":"atypb9","unstructured":"L. C. W. Dixon and G. P. Szego\u0308,\n                      Towards Global Optimisation\n                      2, North-Holland, Amsterdam, 1978."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2007.915111"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1975.10479865"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"A. A. Giunta, S. F. Wojtkiewicz, and M. S. Eldred,\n                      Overview of modern design of experiments methods for computational simulations\n                      , in 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA, Reston, VA, AIAA-2003-0649, 2003.","DOI":"10.2514\/6.2003-649"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-006-0051-9"},{"key":"atypb14","first-page":"2039","volume":"10","author":"Gorissen D.","year":"2009","journal-title":"J. Mach. Learn. 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Azarm,\n                      Maximum accumulative error sampling strategy for approximation of deterministic engineering simulations\n                      , in Proceedings of the AIAA-ISSMO Multidisciplinary Analysis and Optimization Conference, 2006, AIAA, Reston, VA, AIAA-2006-7051.","DOI":"10.2514\/6.2006-7051"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-005-0574-5"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"Y. Lin, F. Mistree, J. K. Allen, K. L Tsui, and V. Chen,\n                      Sequential metamodeling in engineering design\n                      , in Proceedings of AIAA-ISSMO Multidisciplinary Analysis and Optimization Conference, Reston, VA, 2004, AIAA-2004-4304.","DOI":"10.2514\/6.2004-4304"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1198\/TECH.2009.08040"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.2113\/gsecongeo.58.8.1246"},{"key":"atypb28","first-page":"239","volume":"21","author":"McKay M. 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Goovaerts,\n                      Metamodeling sampling criteria in a global optimization framework\n                      , in Proceedings of the 8th Symposium Multidisciplinary Analysis and Optimization, American Institute of Aeronautics and Astronautics, Reston, VA, 2000, AIAA-2000-4921.","DOI":"10.2514\/6.2000-4921"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1115\/1.2838329"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1080\/02664768700000020"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1023\/B:STCO.0000035301.49549.88"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.04.018"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-008-0338-0"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-012-9892-5"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1115\/1.2429697"},{"key":"atypb41","unstructured":"G. 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