THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.

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Efficient Global Optimization of Expensive Black-Box Functions

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.

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MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example

/pdf/the-design-and-analysis-of-computer-experiments-1kfo89lyf2.pdf

The design and analysis of computer experiments

Statistics for Spatial Data.

A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function of inputs that, when evaluated, produces outputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observed elementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or ad...

Factorial sampling plans for preliminary computational experiments

Exploratory designs for computational experiments

This article is concerned with prediction of a function y(t) over a (multidimensional) domain T, given the function values at a set of “sites” {t (1), t (2), …, t (n)} in T, and with the design, that is, with the selection of those sites. The motivating application is the design and analysis of computer experiments, where t determines the input to a computer model of a physical or behavioral system, and y(t) is a response that is part of the output or is calculated from it. Following a Bayesian formulation, prior uncertainty about the function y is expressed by means of a random function Y, which is taken here to be a Gaussian stochastic process. The mean of the posterior process can be used as the prediction function ŷ(t), and the variance can be used as a measure of uncertainty. This kind of approach has been used previously in Bayesian interpolation and is strongly related to the kriging methods used in geostatistics. Here emphasis is placed on product linear and product cubic correlation func...

Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments

Many scientific phenomena are now investigated by complex computer models or codes. Given the input values, the code produces one or more outputs via a complex mathematical model. Often the code is expensive to run, and it may be necessary to build a computationally cheaper predictor to enable, for example, optimization of the inputs. If there are many input factors, an initial step in building a predictor is identifying (screening) the active factors. We model the output of the computer code as the realization of a stochastic process. This model has a number of advantages. First, it provides a statistical basis, via the likelihood, for a stepwise algorithm to determine the important factors. Second, it is very flexible, allowing nonlinear and interaction effects to emerge without explicitly modeling such effects. Third, the same data are used for screening and building the predictor, so expensive runs are efficiently used. We illustrate the methodology with two examples, both having 20 input variables. I...

Max D. Morris

Papers

Factorial sampling plans for preliminary computational experiments

Factorial sampling plans for preliminary computational experiments

Exploratory designs for computational experiments

Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments

Screening, predicting, and computer experiments