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144
Bayesian Experimental Design: A Review
 Statistical Science
, 1995
"... This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models. A unified view of the topic is presented by putting experimental design in a decision theoretic framework. This framework justifies many optimality criteria, and opens new possibilities. Various ..."
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Cited by 291 (1 self)
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This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models. A unified view of the topic is presented by putting experimental design in a decision theoretic framework. This framework justifies many optimality criteria, and opens new possibilities. Various design criteria become part of a single, coherent approach.
Bayesian Calibration of Computer Models
 Journal of the Royal Statistical Society, Series B, Methodological
, 2000
"... this paper a Bayesian approach to the calibration of computer models. We represent the unknown inputs as a parameter vector `. Using the observed data we derive the posterior distribution of `, which in particular quantifies the `residual uncertainty' about ..."
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Cited by 166 (3 self)
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this paper a Bayesian approach to the calibration of computer models. We represent the unknown inputs as a parameter vector `. Using the observed data we derive the posterior distribution of `, which in particular quantifies the `residual uncertainty' about
Probabilistic sensitivity analysis of complex models: a Bayesian approach
 Journal of the Royal Statistical Society, Series B
, 2004
"... Summary. In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent ..."
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Cited by 110 (4 self)
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Summary. In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs.This may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application. A broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model’s output to variation in its inputs. In practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs, an approach which is known as probabilistic sensitivity analysis. We present a Bayesian framework which unifies the various tools of probabilistic sensitivity analysis. The Bayesian approach is computationally highly efficient. It allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard Monte Carlo methods. Furthermore, all measures of interest may be computed from a single set of runs.
Computer Experiments
, 1996
"... Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, a ..."
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Cited by 107 (6 self)
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Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the
Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering and System Safety
, 2003
"... ..."
A framework for validation of computer models
, 2002
"... In this paper, we present a framework that enables computer model evaluation oriented towards answering the question: Does the computer model adequately represent reality? The proposed validation framework is a sixstep procedure based upon Bayesian statistical methodology. The Bayesian methodology ..."
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Cited by 78 (17 self)
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In this paper, we present a framework that enables computer model evaluation oriented towards answering the question: Does the computer model adequately represent reality? The proposed validation framework is a sixstep procedure based upon Bayesian statistical methodology. The Bayesian methodology is particularly suited to treating the major issues associated with the validation process: quantifying multiple sources of error and uncertainty in computer models; combining multiple sources of information; and updating validation assessments as new information is acquired. Moreover, it allows inferential statements to be made about predictive error associated with model predictions in untested situations. The framework is implemented in two test bed models (a vehicle crash model and a resistance
Bayesian Treed Gaussian Process Models with an Application to Computer Modeling
 Journal of the American Statistical Association
, 2007
"... This paper explores nonparametric and semiparametric nonstationary modeling methodologies that couple stationary Gaussian processes and (limiting) linear models with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. Mixing between full Gaussian proce ..."
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Cited by 78 (18 self)
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This paper explores nonparametric and semiparametric nonstationary modeling methodologies that couple stationary Gaussian processes and (limiting) linear models with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. Mixing between full Gaussian processes and simple linear models can yield a more parsimonious spatial model while significantly reducing computational effort. The methodological developments and statistical computing details which make this approach efficient are described in detail. Illustrations of our model are given for both synthetic and real datasets. Key words: recursive partitioning, nonstationary spatial model, nonparametric regression, Bayesian model averaging 1
Nonseparable, stationary covariance functions for spacetime data
 Journal of the Americal Statistical Association
, 2002
"... Environmental Protection Agency which provides the Center’s primary funding. ..."
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Cited by 75 (4 self)
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Environmental Protection Agency which provides the Center’s primary funding.
Use of Kriging Models to Approximate Deterministic Computer Models
 AIAA Journal
, 2005
"... 1 Address all correspondences to this author. Phone/fax: (814) 8655930/8634128. The use of kriging models for approximation and global optimization has been steadily on the rise in the past decade. The standard approach used in the Design and Analysis of Computer Experiments (DACE) is to use an Or ..."
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Cited by 70 (0 self)
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1 Address all correspondences to this author. Phone/fax: (814) 8655930/8634128. The use of kriging models for approximation and global optimization has been steadily on the rise in the past decade. The standard approach used in the Design and Analysis of Computer Experiments (DACE) is to use an Ordinary kriging model to approximate a deterministic computer model. Universal and Detrended kriging are two alternative types of kriging models. In this paper, a description on the basics of kriging is given, highlighting the similarities and differences between these three different types of kriging models and the underlying assumptions behind each. A comparative study on the use of three different types of kriging models is then presented using six test problems. The methods of Maximum Likelihood Estimation (MLE) and CrossValidation (CV) for model parameter estimation are compared for the three kriging model types. A onedimension problem is first used to visualize the differences between the different models. In order to show applications in higher dimensions, four twodimension and a 5dimension problem are also given.
Predicting the Output from a Complex Computer Code when Fast Approximations are Available
 Biometrika
, 1998
"... this paper. ..."