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Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables are dependent. Our main goal here is to show that Shapley value removes the conceptual problems. We do this with some simple examples where Shapley value leads to intuitively reasonable nearly closed form answers.<\/jats:p>","DOI":"10.1137\/16m1097717","type":"journal-article","created":{"date-parts":[[2017,9,19]],"date-time":"2017-09-19T11:35:32Z","timestamp":1505820932000},"page":"986-1002","source":"Crossref","is-referenced-by-count":114,"title":["On Shapley Value for Measuring Importance of Dependent Inputs"],"prefix":"10.1137","volume":"5","author":[{"given":"Art B.","family":"Owen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cl\u00e9mentine","family":"Prieur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2008.04.004"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1214\/12-EJS749"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2014.960415"},{"key":"atypb4","first-page":"1","author":"Colini-Baldeschi R.","year":"2016","journal-title":"Methodol. 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Shah (2016),\n                      Sobol' indices for problems defined in non-rectangular domains\n                      , Technical report,arXiv:1605.05069.","DOI":"10.1016\/j.ress.2017.06.001"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(78)90178-6"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2014.03.006"},{"key":"atypb14","unstructured":"R. H. Lindeman, P. F. Merenda, and R. Z. Gold (1980),\n                      Introduction to Bivariate and Multivariate Analysis\n                      , Scott Foresman and Company, Glenview, IL."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/120876782"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/130936233"},{"key":"atypb17","unstructured":"L. S. Shapley (1953),\n                      A value for n-person games\n                      , in Contribution to the Theory of Games II, Ann. Math. Stud. 28, H. W. Kuhn and A. W. Tucker, eds., Princeton University Press, Princeton, NJ, pp. 307-317."},{"key":"atypb18","first-page":"112","volume":"2","author":"Sobol I. M.","year":"1990","journal-title":"Matematicheskoe Modelirovanie"},{"key":"atypb19","first-page":"407","volume":"1","author":"Sobol I. M.","year":"1993","journal-title":"Math. Model. Comput. Experiment"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/15M1048070"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325361"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"E. Winter (2002),\n                      The Shapley value\n                      , Handbook of game theory with economic applications, 3, pp. 2025-2054.","DOI":"10.1016\/S1574-0005(02)03016-3"},{"key":"atypb23","unstructured":"C. F. J. Wu and M. S. Hamada (2011),\n                      Experiments: Planning, Analysis, and Optimization\n                      , John Wiley & Sons., New York."}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1097717","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:20Z","timestamp":1787336840000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1097717"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1097717"],"URL":"https:\/\/doi.org\/10.1137\/16m1097717","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}