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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 171 (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.
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 67 (5 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
Some New Three Level Designs for the Study of Quantitative Variables
, 1960
"... This article describes some methods which enable us to construct small designs for quantitative factors, while maintaining as much orthogonality of the design as possible. To calculate the D ..."
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Cited by 41 (0 self)
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This article describes some methods which enable us to construct small designs for quantitative factors, while maintaining as much orthogonality of the design as possible. To calculate the D
Exploring estimator biasvariance tradeoffs using the uniform CR bound
 IEEE Trans. on Sig. Proc
, 1996
"... We introduce a plane, which we call the deltasigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a un ..."
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Cited by 40 (15 self)
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We introduce a plane, which we call the deltasigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform CramerRao (CR) bound on estimator variance a deltasigma tradeoff curve is specied which denes an "unachievable region" of the deltasigma plane for a specified statistical model. In order to place an estimator on this plane for comparison to the deltasigma tradeoff curve, the estimator variance, bias gradient, and bias gradient norm must be evaluated. We present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the loglikelihood. We demonstrate the methods developed in this paper for linear Gaussian and nonlinear Poisson inverse problems.
A new approach to the construction of optimal designs
 J. Statistical Planning and Inference
, 1993
"... By combining a modified version of Hooke and Jeeves ’ pattern search with exact or Monte Carlo moment calculations, it is possible to find I, D and Aoptimal (or nearly optimal) designs for a wide range of responsesurface problems. The algorithm routinely handles problems involving the minimizati ..."
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Cited by 31 (10 self)
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By combining a modified version of Hooke and Jeeves ’ pattern search with exact or Monte Carlo moment calculations, it is possible to find I, D and Aoptimal (or nearly optimal) designs for a wide range of responsesurface problems. The algorithm routinely handles problems involving the minimization of functions of 1000 variables, and so for example can construct designs for a full quadratic responsesurface depending on 12 continuous process variables. The algorithm handles continuous or discrete variables, linear equality or inequality constraints, and a response surface that is any low degree polynomial. The design may be required to include a specified set of points, so a sequence of designs can be obtained, each optimal given that the earlier runs have been made. The modeling region need not coincide with the measurement region. The algorithm has been implemented in a program called gosset, which has been used to compute extensive tables of designs. Many of these are more efficient than the best designs previously known.
Robust Designs For Fitting Linear Models With Misspecification
, 1998
"... : This paper considers linear models with misspecification of the form f(x) = E(yjx) = P p j=1 ` j g j (x) + h(x), where h(x) is an unknown function. We assume that the true response function f comes from a reproducing kernel Hilbert space and the estimates of the parameters ` j are obtained by th ..."
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Cited by 8 (0 self)
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: This paper considers linear models with misspecification of the form f(x) = E(yjx) = P p j=1 ` j g j (x) + h(x), where h(x) is an unknown function. We assume that the true response function f comes from a reproducing kernel Hilbert space and the estimates of the parameters ` j are obtained by the standard least squares method. A sharp upper bound for the mean squared error is found in terms of the norm of h. This upper bound is used to choose a design that is robust against the model bias. It is shown that the continuous uniform design on the experimental region is the allbias design. The numerical results of several examples show that allbias designs perform well when some model bias is present for low dimensional cases. AMS 1991 subject classification: 62K05, 64A20 Key words and phrases: linear models with misspecification, reproducing kernel Hilbert spaces, modelrobust designs. Abbreviated title: ModelRobust Designs 1. Introduction This paper considers the design problem f...
ComputerGenerated Minimal (and Larger) ResponseSurface Designs: (II) The Cube
 I) The Sphere, Statistics Research Report, AT&T Bell Laboratories
, 1991
"... Computergenerated designs in the cube are described which have the minimal (or larger) number of runs for a full quadratic responsesurface design. Examples of 2factor designs are included with 6 to 20 runs, 3factor designs with 10 to 20 runs, 4factor designs with 15 to 20 runs, 5factor designs ..."
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Cited by 5 (3 self)
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Computergenerated designs in the cube are described which have the minimal (or larger) number of runs for a full quadratic responsesurface design. Examples of 2factor designs are included with 6 to 20 runs, 3factor designs with 10 to 20 runs, 4factor designs with 15 to 20 runs, 5factor designs with 21 to 25 runs, 6factor designs with 28 to 31 runs, and 7factor designs with 36 and 39 runs. The designs were constructed by minimizing the average prediction variance, and without imposing any prior constraints  such as a central composite structure  on the locations of the points. Key Words. Minimal designs; cube designs; quadratic response surface; computergenerated designs; minimal variance designs. 1 Present address: AT&T Shannon Labs, Florham Park, NJ 079320971 1
Restricted Minimax Robust Designs for Misspecified Regression Models
, 2000
"... The authors propose and explore new regression designs. Within a particular parametric class, these designs are minimax robust against bias caused by model misspecification while attaining reasonable levels of e#ciency as well. The introduction of this restricted class of designs is motivated by a d ..."
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Cited by 4 (2 self)
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The authors propose and explore new regression designs. Within a particular parametric class, these designs are minimax robust against bias caused by model misspecification while attaining reasonable levels of e#ciency as well. The introduction of this restricted class of designs is motivated by a desire to avoid the mathematical and numerical intractability found in the unrestricted minimax theory. Robustness is provided against a family of model departures su#ciently broad that the minimax design measures are necessarily absolutely continuous. Examples of implementation involve approximate polynomial and second order multiple regression. R ESUM E Les auteurs proposent et explorent de nouveaux plans experimentaux pour la regression. Ces plans sont minimax par rapport a une classe parametrique restreinte et s'averent a la fois robustes au biais dua un mauvais choix de modele et raisonnablement e#caces. L'introduction de cette classe restreinte de plans est motivee par le desir d'evit...
Operating manual for Gosset: A general purpose program for constructing experimental designs
 AT&T Bell Laboratories
, 1994
"... This is the second edition of the operating manual for gosset, a flexible and powerful computer program for constructing experimental designs. Variables may be discrete or continuous (or both), discrete variables may be numeric or symbolic (or both), and continuous variables may range over a cube or ..."
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Cited by 3 (0 self)
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This is the second edition of the operating manual for gosset, a flexible and powerful computer program for constructing experimental designs. Variables may be discrete or continuous (or both), discrete variables may be numeric or symbolic (or both), and continuous variables may range over a cube or a ball (or both). The variables may be required to satisfy linear equalities or inequalities, and the model to be fitted may be any low degree polynomial (e.g. a quadratic). The number of observations is specified by the user. The design may be required to include a specified set of points (so a sequence of designs can be found, each of which is optimal given that the earlier measurements have been made). The region where the model is to be fitted need not be the same as the region where measurements are to be made (so the designs can be used for interpolation or extrapolation). The following types of designs can be requested: I, A, D or Eoptimal; the same but with protection against the loss of one run; or packings (when no model is available). Block designs, and designs with correlated errors can also be constructed. The algorithm is powerful enough to routinely minimize functions of 1000 variables (e.g. can find optimal or nearly optimal designs for a quadratic model involving 12 variables). An extensive library of precomputed optimal designs is included for linear and quadratic designs in the cube, ball and simplex. The user does not have to specify starting points for the search. The user also has control over how much effort is expended by the algorithm, and can monitor the progress of the search. Applications so far include VLSI production, conductivity of diamond films, growth of protein crystals, flow through a catalytic converter, laser welding, etc.
THE CORRELATED KNOWLEDGE GRADIENT FOR SIMULATION OPTIMIZATION OF CONTINUOUS PARAMETERS USING GAUSSIAN PROCESS REGRESSION
"... Abstract. We extend the concept of the correlated knowledgegradient policy for ranking and selection of a finite set of alternatives to the case of continuous decision variables. We propose an approximate knowledge gradient for problems with continuous decision variables in the context of a Gaussia ..."
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Cited by 3 (1 self)
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Abstract. We extend the concept of the correlated knowledgegradient policy for ranking and selection of a finite set of alternatives to the case of continuous decision variables. We propose an approximate knowledge gradient for problems with continuous decision variables in the context of a Gaussian process regression model in a Bayesian setting, along with an algorithm to maximize the approximate knowledge gradient. In the problem class considered, we use the knowledge gradient for continuous parameters to sequentially choose where to sample an expensive noisy function in order to find the maximum quickly. We show that the knowledge gradient for continuous decisions is a generalization of the efficient global optimization algorithm proposed by Jones, Schonlau, and Welch.