{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Monotonicity Properties of Stochastic Kriging Metamodels and Related Applications","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76371"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"Stochastic kriging (SK) and stochastic kriging with gradient estimators (SKG) are popular approaches to approximate complex simulation models because of their ability to replace the expensive simulation outputs by metamodel values. Obtaining an accurate SK/SKG metamodel is highly desirable in practice. This dissertation studies the monotonicity properties of the mean squared error (MSE) of optimal SK and SKG predictors. In particular, we show that in both SK and SKG, the MSEs of the corresponding optimal predictors are non-increasing functions of the numbers of design points. Based on these findings, we design an adaptive sequential sampling approach to obtain SK/SKG predictors with a pre-defined level of accuracy. In each step, our approach selects the point that achieves the maximum reduction in the current integrated MSE (IMSE) and adaptively allocates the number of simulation replications. Theoretical analysis is also provided to guarantee that a desired performance can be achieved. We run numerical examples to justify the monotonicity properties of the predictors under both SK and SKG frameworks, and illustrate the effectiveness of the proposed approach by comparing its performance with two other existing methods. The comparison results indicate that our approach can be more efficient both in terms of the number of design points used and the simulation efforts expended."},{"label":"dcterms.available","value":"2017-09-20T16:50:07Z"},{"label":"dcterms.contributor","value":"Wu, Song"},{"label":"dcterms.creator","value":"Wang, Bing"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:07Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:07Z"},{"label":"dcterms.description","value":"Department of Applied Mathematics and Statistics."},{"label":"dcterms.extent","value":"119 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76371"},{"label":"dcterms.issued","value":"2016-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:07Z (GMT). No. of bitstreams: 1\nWang_grad.sunysb_0771E_12694.pdf: 703954 bytes, checksum: 2d5f231e0e8eac2239f521529f242d3b (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Operations research"},{"label":"dcterms.title","value":"Monotonicity Properties of Stochastic Kriging Metamodels and Related Applications"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/16%2F35%2F45%2F163545284734263590390565296366348753269/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/16%2F35%2F45%2F163545284734263590390565296366348753269","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}