A-optimal designs for optimum mixture in an additive quadratic mixture model
TL;DR: In the analysis of experiments with mixtures, quadratic models have been widely used as mentioned in this paper, and the optimum designs for the estimation of optimum mixing proportions in a Quadratic mixture model have been proposed.
Abstract: In the analysis of experiments with mixtures, quadratic models have been widely used. The optimum designs for the estimation of optimum mixing proportions in a quadratic mixture model have ...
Citations
More filters
TL;DR: This research provides a methodology for expanding Principal Component Analysis (PCA) by including category moment estimations in low-dimensional projections and shows that LOLR projections and its extensions enhance representations of data for future classifications while retaining computing flexibility and reliability using both experimental and simulated data benchmark.
Abstract: Experimenters today frequently quantify millions or even billions of characteristics (measurements) each sample to address critical biological issues, in the hopes that machine learning tools would be able to make correct data-driven judgments. An efficient analysis requires a low-dimensional representation that preserves the differentiating features in data whose size and complexity are orders of magnitude apart (e.g., if a certain ailment is present in the person's body). While there are several systems that can handle millions of variables and yet have strong empirical and conceptual guarantees, there are few that can be clearly understood. This research presents an evaluation of supervised dimensionality reduction for large scale data. We provide a methodology for expanding Principal Component Analysis (PCA) by including category moment estimations in low-dimensional projections. Linear Optimum Low-Rank (LOLR) projection, the cheapest variant, includes the class-conditional means. We show that LOLR projections and its extensions enhance representations of data for future classifications while retaining computing flexibility and reliability using both experimental and simulated data benchmark. When it comes to accuracy, LOLR prediction outperforms other modular linear dimension reduction methods that require much longer computation times on conventional computers. LOLR uses more than 150 million attributes in brain image processing datasets, and many genome sequencing datasets have more than half a million attributes.
1 citations
TL;DR: In this article , a finite element analysis (FEA) model of an inserted tooth-type slip assembly under bear setting load and axial load was established, and the difference between the inserted teeth of the sidetracking packer slip-formed furrow shapes on the casing face was analyzed.
Abstract: This work established a finite element analysis (FEA) model of an inserted tooth-type slip assembly under bear setting load and axial load, calculated the differences between the inserted teeth of the sidetracking packer slip-formed furrow shapes on the casing face, and analyzed the setting reliability of the inserted tooth slip sidetracking packer. The orthogonal optimization analysis of the structural parameters of the sidetracking packer was carried out on the basis of the furrow effect. Finally, the setting experiment was conducted with the inserted tooth slip sidetracking packer developed to verify correctness of the FEA model and the simulation results. The results show that in the FEA and calculation of the setting process of the inserted tooth-type slip, it is not only necessary to consider the furrow friction coefficient, but also the effect of the ridge on the furrow friction coefficient. The corresponding furrow friction coefficient varies according to the different furrow effects occurring on the casing surface caused by the various types of teeth inserted on the packer slips. The furrow effect is related to the sharpness of the tooth tips of the slips. The sharper the tooth tips, the more obvious the furrow effect is. Under the dual effects of the furrow effect and the adhesion effect, the carbide teeth of the slip feed into the casing wall to produce a uniform and distinct indentation on the premise of meeting the inserted tooth strength to ensure a reliable setting and hanging the inserted tooth slip sidetracking packer. The optimal combination of slip parameters was obtained by taking the optimal bite depth uniformity as the objective function: slip tooth installation spacing L = 10 mm, slip tooth installation angle α = 80°, slip tooth diameter d = 10 mm, and slip wedge angle β = 6°. The standard deviation of bite depth uniformity of the optimized slip teeth is 74.45% lower than that before optimization. The research results of this paper basically meet the requirements of engineering applications.
References
More filters
TL;DR: This paper reviews the literature on Bayesian experimental design, both for linear and nonlinear models, and presents a uniied view of the topic by putting experimental design in a decision theoretic framework.
Abstract: This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.
1,903 citations
"A-optimal designs for optimum mixtu..." refers methods in this paper
...Chaloner andVerdinelli [23] gave a review of the Bayesian experimental designs....
[...]
TL;DR: This book is well intentioned for science majors, but it seems to miss the mark by being overly complicated with the unnecessary use of calculus on one hand and the recommendation of some poor statistical techniques on the other hand.
Abstract: There are some nice examples and datasets to cover the points. The section on “fitting a scatterplot by eye” has to be a first for a book claiming to be a serious statistics text for students. With all of the software available to do regression, this approach is inexcusable. Chapters 16 and 17 cover the analysis of categorical data and resampling methods. This book is well intentioned for science majors, but it seems to miss the mark by being overly complicated with the unnecessary use of calculus on one hand and the recommendation of some poor statistical techniques on the other hand. Starting out science majors on their careers with a useful basis in statistics will serve them well, so care should be taken to avoid techniques that complicate or underwhelm. The authors have the makings of an excellent text, but they need to pare it back a little before I can recommend it.
783 citations
TL;DR: For general optimality criteria, this article obtained criteria equivalent to $\Phi$-optimality under various conditions on ''Phi'' and showed that such equivalent criteria are useful for analytic or machine computation of ''phi''-optimum designs.
Abstract: For general optimality criteria $\Phi$, criteria equivalent to $\Phi$-optimality are obtained under various conditions on $\Phi$. Such equivalent criteria are useful for analytic or machine computation of $\Phi$-optimum designs. The theory includes that previously developed in the case of $D$-optimality (Kiefer-Wolfowitz) and $L$-optimality (Karlin-Studden-Fedorov), as well as $E$-optimality and criteria arising in response surface fitting and minimax extrapolation. Multiresponse settings and models with variable covariance and cost structure are included. Methods for verifying the conditions required on $\Phi$, and for computing the equivalent criteria, are illustrated.
736 citations
"A-optimal designs for optimum mixtu..." refers background in this paper
...Most of the literature on mixture experiments is concerned with finding optimum designs for estimation of model parameters, see, for example, Kiefer [5], Atwood [6], Galil and Kiefer [7], Chan et al. [8], Draper and Pukelsheim [9]....
[...]
...A-optimal designs for q=3, 4 and 5 Kiefer [24] established the general equivalence theoremwhich gives a necessary and sufficient condition for a design to be optimum in the entire class of competitive designs....
[...]
TL;DR: Experiments with Mixtures as discussed by the authors is a collection of experiments with mixtures written by J. A. Cornell and published by Wiley, Chichester, 1990. 632 pp.
Abstract: Experiments with Mixtures. By J. A. Cornell. ISBN 0 471 52221 X. Wiley, Chichester, 1990. 632 pp. £47.50.
376 citations
TL;DR: In this article, the problem of multilinear regression on the simplex has been studied and a sufficient condition for optimality is given, and a corrected version is given to the condition which Karlin and Studden (1966a) state as equivalent to optimality.
Abstract: This paper consists of new results continuing the series of papers on optimal design theory by Kiefer (1959), (1960), (1961), Kiefer and Wolfowitz (1959), (1960), Farrell, Kiefer and Walbran (1965) and Karlin and Studden (1966a). After disposing of the necessary preliminaries in Section 1, we show in Section 2 that in several classes of problems an optimal design for estimating all the parameters is supported only on certain points of symmetry. This is applied to the problem (introduced by Scheffe (1958)) of multilinear regression on the simplex. In Section 3 we consider optimality when nuisance parameters are present. A new sufficient condition for optimality is given. A corrected version is given to the condition which Karlin and Studden (1966a) state as equivalent to optimality, and we prove the natural invariance theorem involving this condition. These results are applied to the problem of multilinear regression on the simplex when estimating only some of the parameters. Section 4 consists primarily of a number of bounds on the efficiency of designs; these are summarized at the beginning of that section.
186 citations
Additional excerpts
...Most of the literature on mixture experiments is concerned with finding optimum designs for estimation of model parameters, see, for example, Kiefer [5], Atwood [6], Galil and Kiefer [7], Chan et al. [8], Draper and Pukelsheim [9]....
[...]
...Most of the literature on mixture experiments is concerned with finding optimum designs for estimation of model parameters, see, for example, Kiefer [5], Atwood [6], Galil and Kiefer [7], Chan et al....
[...]