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Particular improvements over previous nonhierarchical methods are mainly concerning the construction of new evaluation points at run time. In this construction process, referred to as experimental design, a flexible two\u2010stage method is employed, where adaptive domain refinement is combined with sequential experimental design. The hierarchical method is applied to statistical data analysis, where the data is generated by a very complex and computationally expensive computer model, called a simulator. In this application, a fast and accurate statistical approximation, called an emulator, is required as a cheap surrogate of the expensive simulator. The construction of the emulator relies on computer experiments using a very small set of carefully selected input configurations for the simulator runs. The hierarchical method proposed in this paper is, for various analyzed models from reservoir forecasting, more efficient than existing standard methods. This is supported by numerical results, which show that our hierarchical method is, at comparable computational costs, up to ten times more accurate than traditional nonhierarchical methods, as utilized in commercial software relying on the response surface methodology (RSM).<\/jats:p>","DOI":"10.1137\/050639983","type":"journal-article","created":{"date-parts":[[2007,1,8]],"date-time":"2007-01-08T18:00:23Z","timestamp":1168279223000},"page":"49-69","source":"Crossref","is-referenced-by-count":54,"title":["Hierarchical Nonlinear Approximation for Experimental Design and Statistical Data Fitting"],"prefix":"10.1137","volume":"29","author":[{"given":"Daniel","family":"Busby","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chris L.","family":"Farmer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Armin","family":"Iske","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,1,8]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"M. 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