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...f Y tend to be highly inaccurate and may lead to significant underestimation of the variability. Since the variability of the random vector V may be substantial, sensitivity and perturbation methods (=-=Ghanem and Spanos 1991-=-, Kleiber et al. 1992) applied near the mean of V may be highly inaccurate as well. Polynomial chaos expansion, stochastic Galerkin, and stochastic collocation methods are frequently used for UQ in an...

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...inaccurate as well. Polynomial chaos expansion, stochastic Galerkin, and stochastic collocation methods are frequently used for UQ in an effort to overcome these difficulties (Ghanem and Spanos 1991, =-=Xiu and Karniadakis 2002-=-, Babuska et al. 2004, Ganapathysubramanian and Zabaras 2007, Nobile et al. 2008, Eldredet al. 2011). These methods build a model of g using polynomial functions and then estimate moments of Y using ...

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...mial chaos expansion, stochastic Galerkin, and stochastic collocation methods are frequently used for UQ in an effort to overcome these difficulties (Ghanem and Spanos 1991, Xiu and Karniadakis 2002, =-=Babuska et al. 2004-=-, Ganapathysubramanian and Zabaras 2007, Nobile et al. 2008, Eldredet al. 2011). These methods build a model of g using polynomial functions and then estimate moments of Y using that model and the (a...

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... 2001). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in an ad-hoc manner. Desirable density estimators can be achieved by means of penalties (=-=Good and Gaskin 1971-=-, de Montricher et al. 1975, Leonard 1978, Klonias 1982, Silverman 1982). While in principle many types of constraints in the estimation problem can be represented by penalty terms, the equivalence of...

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...llocation methods are frequently used for UQ in an effort to overcome these difficulties (Ghanem and Spanos 1991, Xiu and Karniadakis 2002, Babuska et al. 2004, Ganapathysubramanian and Zabaras 2007, =-=Nobile et al. 2008-=-, Eldredet al. 2011). These methods build a model of g using polynomial functions and then estimate moments of Y using that model and the (assumed) knowledge of the distribution of V. Under certain a...

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...timates based on their experience in an ad-hoc manner. Desirable density estimators can be achieved by means of penalties (Good and Gaskin 1971, de Montricher et al. 1975, Leonard 1978, Klonias 1982, =-=Silverman 1982-=-). While in principle many types of constraints in the estimation problem can be represented by penalty terms, the equivalence of such reformulations depends on the successful selection of multiplier ...

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...rior soft information extensively, but results extend much beyond that premise (Wahba 1981, Van de Geer 1987, Thompson and Tapia 1990, Wets 1991, Dupacova 1992, Samaniego and Reneau 1994, Geyer 1994, =-=Groenenboom et al. 2001-=-). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in an ad-hoc manner. Desirable density estimators can be achieved by means of penalties (Good ...

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... stochastic Galerkin, and stochastic collocation methods are frequently used for UQ in an effort to overcome these difficulties (Ghanem and Spanos 1991, Xiu and Karniadakis 2002, Babuska et al. 2004, =-=Ganapathysubramanian and Zabaras 2007-=-, Nobile et al. 2008, Eldredet al. 2011). These methods build a model of g using polynomial functions and then estimate moments of Y using that model and the (assumed) knowledge of the distribution o...

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...titioners may also adjust estimates based on their experience in an ad-hoc manner. Desirable density estimators can be achieved by means of penalties (Good and Gaskin 1971, de Montricher et al. 1975, =-=Leonard 1978-=-, Klonias 1982, Silverman 1982). While in principle many types of constraints in the estimation problem can be represented by penalty terms, the equivalence of such reformulations depends on the succe...

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...accurate and may lead to significant underestimation of the variability. Since the variability of the random vector V may be substantial, sensitivity and perturbation methods (Ghanem and Spanos 1991, =-=Kleiber et al. 1992-=-) applied near the mean of V may be highly inaccurate as well. Polynomial chaos expansion, stochastic Galerkin, and stochastic collocation methods are frequently used for UQ in an effort to overcome t...

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... and determines the ‘best’ estimate within that family. Bayesian estimation makes use of prior soft information extensively, but results extend much beyond that premise (Wahba 1981, Van de Geer 1987, =-=Thompson and Tapia 1990-=-, Wets 1991, Dupacova 1992, Samaniego and Reneau 1994, Geyer 1994, Groenenboom et al. 2001). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in a...

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...olyak sparsegrid approaches (Xiu and Hesthaven 2005, Ganapathysubramanian and Zabaras 2007, Nobile et al. 2008), separated representations based on alternating least-squares approximation techniques (=-=Doostan and Iaccarino 2009-=-), and related approaches are steps in the direction towards handling moderate dimensions of V, but still significant challenges remain when handling high-dimensional cases. We refer to Helton and Pil...

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...ily. Bayesian estimation makes use of prior soft information extensively, but results extend much beyond that premise (Wahba 1981, Van de Geer 1987, Thompson and Tapia 1990, Wets 1991, Dupacova 1992, =-=Samaniego and Reneau 1994-=-, Geyer 1994, Groenenboom et al. 2001). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in an ad-hoc manner. Desirable density estimators can be ...

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...bly based on soft information, and determines the ‘best’ estimate within that family. Bayesian estimation makes use of prior soft information extensively, but results extend much beyond that premise (=-=Wahba 1981-=-, Van de Geer 1987, Thompson and Tapia 1990, Wets 1991, Dupacova 1992, Samaniego and Reneau 1994, Geyer 1994, Groenenboom et al. 2001). In nonparametric density estimation, practitioners may also adju...

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...kes use of prior soft information extensively, but results extend much beyond that premise (Wahba 1981, Van de Geer 1987, Thompson and Tapia 1990, Wets 1991, Dupacova 1992, Samaniego and Reneau 1994, =-=Geyer 1994-=-, Groenenboom et al. 2001). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in an ad-hoc manner. Desirable density estimators can be achieved by ...

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...nt. Each evaluation of the finite-element model takes about 2 hours and few values of E and ν can be examined. We consider a data set of 10 frequencies corresponding to various values of E and ν (see =-=Swiler et al. 2009-=-) and aim to estimate the density of the frequency. Figure 6 shows the estimated density (solid curve) given unimodality and support bounds [813, 2884] deduced from experience with the system. We use ...

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...also adjust estimates based on their experience in an ad-hoc manner. Desirable density estimators can be achieved by means of penalties (Good and Gaskin 1971, de Montricher et al. 1975, Leonard 1978, =-=Klonias 1982-=-, Silverman 1982). While in principle many types of constraints in the estimation problem can be represented by penalty terms, the equivalence of such reformulations depends on the successful selectio...

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...’ estimate within that family. Bayesian estimation makes use of prior soft information extensively, but results extend much beyond that premise (Wahba 1981, Van de Geer 1987, Thompson and Tapia 1990, =-=Wets 1991-=-, Dupacova 1992, Samaniego and Reneau 1994, Geyer 1994, Groenenboom et al. 2001). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in an ad-hoc ma...

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...within that family. Bayesian estimation makes use of prior soft information extensively, but results extend much beyond that premise (Wahba 1981, Van de Geer 1987, Thompson and Tapia 1990, Wets 1991, =-=Dupacova 1992-=-, Samaniego and Reneau 1994, Geyer 1994, Groenenboom et al. 2001). In nonparametric density estimation, practitioners may also adjust estimates based on their experience in an ad-hoc manner. Desirable...