Theory Of Optimal Experiments Research Articles

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This cocktail algorithm extends the well-known vertex direction method (VDM; Fedorov in Theory of Optimal Experiments, 1972) and the multiplicative algorithm (Silvey et al. in Commun. Stat. Theory Methods 14:1379–1389, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.

Comparison of adaptive psychometric procedures motivated by the Theory of Optimal Experiments: Simulated and experimental results

The wide use of psychometric assessments and the time necessary to conduct comprehensive psychometric tests has motivated significant research into the development of psychometric testing procedures that will provide accurate and efficient estimates of the parameters of interest. One potential framework for developing adaptive psychometric procedures is the Theory of Optimal Experiments. The Theory of Optimal Experiments provides several metrics for determining informative stimulus values based on a model of the psychometric function to be provided by the investigator. In this study, two methods based on a previous implementation of the Theory of Optimal Experiments are presented for comparison to two fixed step size staircase methods and also an existing adaptive method that utilizes a Bayesian framework. The psychometric procedures were used to measure detection thresholds and discrimination limens on two separate psychoacoustic tasks with normal-hearing subjects. Computer simulations were performed based on the outcomes of the experimental psychoacoustic detection task to analyze performance over a large sample size in the case of known truth. Results suggest that the proposed stimulus selection rules motivated by the Theory of Optimal Experiments perform better than previous techniques and also extend estimation to multiple parameters.

Optimal Maneuvering of Seismic Sensors for Localization of Subsurface Targets

We consider the problem of detecting and locating subsurface objects by using a maneuvering array that receives scattered seismic surface waves. We demonstrate an adaptive system that moves an array of receivers according to an optimal positioning algorithm that is based on the theory of optimal experiments. The goal is to minimize the number of distinct measurements (array movements) needed to localize objects such as buried landmines. The adaptive localization algorithm has been tested using data collected in a laboratory facility. The performance of the algorithm is exhibited for cases with one or two targets and in the presence of common types of clutter such as rocks in the soil. Results are also shown for a case where the propagation properties of the medium vary spatially. In these tests, the landmines were located using three or four array movements. It is envisioned that future systems could incorporate this new method into a portable mobile mine-location system

A comparison of adaptive psychometric procedures based on the theory of optimal experiments and Bayesian techniques: Implications for cochlear implant testing

Numerous previous studies have focused on the development of quick and efficient adaptive psychometric procedures. In psychophysics, there is often a model of the psychometric function supported by previous studies for the task of interest. The theory of optimal experiments provides a framework for utilizing a model of the process to develop quick and efficient sequential-testing strategies for estimating model parameters, making it appropriate for developing adaptive psychophysical-testing methods. In this study, we investigated the application of sequential parameter search strategies based on the theory of optimal experiments and Bayesian adaptive procedures for measuring psychophysical variables. The results presented in this article suggest that more sophisticated psychometric procedures can expedite the measurement of psychophysical variables. Such techniques for quickly collecting psychophysical data may be particularly useful in cochlear implant research, where a large set of psychophysical variables are useful for characterizing the performance of an implanted device. It is to be hoped that further development of these techniques will make psychophysical measurements available to clinicians for tuning and optimizing the speech processors of individual cochlear implant patients.

On Minimally-supported D-optimal Designs for Polynomial Regression with Log-concave Weight Function

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. For example, $$(1-x)^{\alpha+1}(1+x)^{\beta+1}(-1\le x\le 1,\alpha\ge -1,\beta\ge -1),x^{\alpha+1}\exp(-x) (x\ge 0,\alpha\ge -1)$$ and exp(−x 2) in Theorem 2.3.2 of Fedorov (Theory of optimal experiments, 1972) are all log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be constructed efficiently by cyclic exchange algorithm.

Adaptive multiaspect target classification and detection with hidden Markov models

Target detection and classification are considered based on backscattered signals observed from a sequence of target-sensor orientations, with the measurements performed as a function of orientation (angle) at a fixed range. The theory of optimal experiments is applied to adaptively optimize the sequence of target-sensor orientations considered. This is motivated by the fact that if fewer, better-chosen measurements are used then targets can be recognized more accurately with less time and expense. Specifically, based on the previous sequence of observations O/sub t/={O/sub 1/,...,O/sub t/}, the technique determines what change in relative target-sensor orientation /spl Delta//spl theta//sub t+1/ is optimal for performing measurement t+1, to yield observation O/sub t+1/. The target is assumed distant or hidden, and, therefore, the absolute target-sensor orientation is unknown. We detail the adaptive-sensing algorithm, employing a hidden Markov model representation of the multiaspect scattered fields, and example classification and detection results are presented for underwater targets using acoustic scattering data.

Optimum experimental designs for multinomial logistic models.

Multinomial responses frequently occur in dose level experiments. For example, in a study of the influence of gamma radiation on the emergence of house flies (Musca domestica L., 1758), three disjoint outcomes occurred: death before the pupae opened, death during emergence, and life after emergence. Although the flies are easy to breed, this sort of bioassay is, in general, very expensive since it requires the use of a gamma radiation source. Experiments therefore need to be designed to involve the minimum number of different doses. Here the theory of optimum experimental design is applied to provide efficient experiments to estimate the parameters of those multinomial logistic models that are a special case of the multivariate logistic models of Glonek and McCullagh (1995, Journal of the Royal Statistical Society, Series B 57, 533-546). The purpose is to reduce the overall experimental cost. The general equivalence theorem (Fedorov, 1972, Theory of Optimal Experiments) is adapted to this class of models, providing an effective method of generating and checking the optimality of designs. One example on flies demonstrates the method, which can be easily implemented.

Neural Network Exploration Using Optimal Experiment Design

I consider the question “How should one act when the only goal is to learn as much as possible?”. Building on the theoretical results of Fedorov (1972, Theory of Optimal Experiments, Academic Press) and MacKay (1992, Neural Computation, 4, 590–604), I apply techniques from optimal experiment design (OED) to guide the query/action selection of a neural network learner. I demonstrate that these techniques allow the learner to minimize its generalization error by exploring its domain efficiently and completely. I conclude that, while not a panacea, OED-based query/action selection has much to offer, especially in domains where its high computational costs can be tolerated. Copyright © 1996 Elsevier Science Ltd

Discussion of the Papers by Atkinson, and Bates et al.

Discussion of the Papers by Atkinson, and Bates <i>et al.</i>

New filtering method for linear weakly coupled stochastic systems

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Some Properties of Multiresponse D-Optimal Designs

The properties of D-optimal designs for multiresponse models are explored using the Equivalence Theorem by Fedorov ["Theory of Optimal Experiments," Academic Press, New York, 1972]. For some classes of multiresponse linear models, the results can be applied to simplify complicated multiresponse experimental design problems or to reduce multiresponse experimental design problems to single-response experimental design problems using the D-optimal design criterion.

Sequential generation ofD-optimal input designs for linear dynamic systems

This paper considers the problem of sequentially generating test signals for parameter estimation in linear, single-input, single-output, discrete-time systems using a frequency-domain approach based on the theory of optimal experiments in regression analysis. The input signals are power constrained and are optimal in the sense that system information is maximized, where the criterion employed is the determinant of the Fisher information matrix (D-optimality). A class of algorithms is investigated, each member of which generates a sequence of input designs converging to aD-optimum. A number of these algorithms are compared computationally.

On Tests of Optimality of Experimental Designs for a Regression Model with Random Variables

Previous article Next article On Tests of Optimality of Experimental Designs for a Regression Model with Random VariablesA. V. TsukanovA. V. Tsukanovhttps://doi.org/10.1137/1126018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] C. Radhakrishna Rao, Linear statistical inference and its applications, John Wiley & Sons Inc., New York, 1965xviii+522 36:4668 0137.36203 Google Scholar[2] V. V. Fedorov, Theory of optimal experiments, Academic Press, New York, 1972xi+292 53:6916 Google Scholar[3] F. R. Gantmacher, Theory of Matrices, Nauka, Moscow, 1967, [In Russian.] Google Scholar[4] T. W. Anderson, The non-central Wishart distribution and certain problems of multivariate statistics, Ann. Math. Statistics, 17 (1946), 409–431 8,394c 0063.00085 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Augmenting a Factorial Experiment When One Factor Is an Uncontrollable Random Variable: A Case StudyTechnometrics, Vol. 37, No. 1 | 1 Feb 1995 Cross Ref Testing optimality of experimental designs for a regression model with random variablesJournal of Statistical Planning and Inference, Vol. 11, No. 1 | 1 Jan 1985 Cross Ref Volume 26, Issue 1| 1981Theory of Probability & Its Applications1-217 History Submitted:13 March 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1126018Article page range:pp. 173-177ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Sequences Converging to $D$-Optimal Designs of Experiments

Fedorov (Theory of Optimal Experiments (1972)) gives a sequence of designs converging to a $D$-optimal design. Several modifications of that sequence are given to improve the speed of convergence. The analogous sequence for estimating some of the parameters is shown to converge to a $D$-optimal design, whether or not all the parameters are estimable under the limiting design. We prove the result $d(x, \xi)\xi(x) \leqq 1$, and several related results.

Theory of Optimal Experiments.

Theory of Optimal Experiments.