### Citations

791 |
Stochastic Finite Elements: A Spectral Approach
- Ghanem, Spanos
- 1991
(Show Context)
Citation Context ...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... |

398 | The Wiener-Askey polynomial chaos for stochastic differential equations
- Xiu, Karniadakis
(Show Context)
Citation Context ...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 ... |

318 | Dynamics of structures : theory and applications to earthquake engineering, 2nd edition, - Chopra - 2001 |

193 | Galerkin finite element approximations of stochastic elliptic differential equations
- Babus̆ka, Tempone, et al.
(Show Context)
Citation Context ...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... |

117 |
Nonparametric Roughness Penalties for Probability Density
- Good, Gaskins
- 1971
(Show Context)
Citation Context ... 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... |

106 | A sparse grid stochastic collocation method for partial differential equations with random input data.
- Nobile, Tempone, et al.
- 2008
(Show Context)
Citation Context ...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... |

88 |
On the estimation of a probability density function by the maximum penalized likelihood method
- Silverman
- 1982
(Show Context)
Citation Context ...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 ... |

73 | Estimation of convex functions: characterizations and asymptotic
- Groeneboom, Jongbloed, et al.
- 2001
(Show Context)
Citation Context ...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 ... |

46 |
Sparse grid collocation schemes for stochastic natural convection problems,
- Ganapathysubramanian, Zabaras
- 2007
(Show Context)
Citation Context ... 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... |

43 |
Density estimation, stochastic processes and prior information.
- Leonard
- 1978
(Show Context)
Citation Context ...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... |

36 |
The stochastic finite element method: basic perturbation technique and computational implementation.
- Kleiber, TD
- 1992
(Show Context)
Citation Context ...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... |

36 |
Nonparametric Function Estimation, Modeling, and Simulation
- Thompson, Tapia
- 1990
(Show Context)
Citation Context ... 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... |

30 |
A least-squares approximation of partial differential equations with high-dimensional random inputs.
- Doostan, Iaccarino
- 2009
(Show Context)
Citation Context ...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... |

17 |
Toward a reconciliation of the Bayesian and frequentist approaches to point estimation
- SAMANIEGO, RENEAU
- 1994
(Show Context)
Citation Context ...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 ... |

15 |
Data-based optimal smoothing of orthogonal series density estimates
- Wahba
- 1981
(Show Context)
Citation Context ...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... |

13 | Nonparametric maximum likelihood estimation of probability densities by penalty function methods,” Ann. - Montricher, Tapia, et al. - 1975 |

11 |
On the asymptotics of constrained M-estimation. The Annals of Statistics 22
- Geyer
- 1994
(Show Context)
Citation Context ...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 ... |

9 | Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation - Eldred, Swiler, et al. |

7 | Epistemic Uncertainty Quantification Tutorial
- Swiler, Paez, et al.
- 2009
(Show Context)
Citation Context ...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 ... |

5 |
Consistency of two nonparametric maximum penalized likelihood estimators of the probability density function” Annals of Statistics 10
- Klonias
- 1982
(Show Context)
Citation Context ...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... |

5 |
Constrained estimation: Consistency and asymptotics, Applied Stochastic Models and Data Analysis 7
- Wets
- 1991
(Show Context)
Citation Context ...’ 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... |

2 |
Epi-consistency in restricted regression models - the case of a general convex fitting function
- Dupacova
- 1992
(Show Context)
Citation Context ...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... |

2 | Quantification of margins and uncertainties - Helton |

2 | Wets 2013. “Nonparametric Density Estimation with Soft Information Using Exponential Epi-Splines”. Under Review - Royset, J-B |

1 | Wets (2013). Density estimation: exploiting non-data information. Working paper - Casey, J-B |

1 | Wets (2007). Estimating density functions: a constrained maximum likelihood approach - Dong, J-B |

1 | A new approach to least squares estimation - Geer - 1987 |