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

Statistics for Spatial Data.

http://ee.sharif.edu/~miap/Files/A%20Survey%20of%20Medical%20Image%20Registration.pdf

A survey of medical image registration.

The successful application of a conceptual rainfall-runoff (CRR) model depends on how well it is calibrated. Despite the popularity of CRR models, reports in the literature indicate that it is typically difficult, if not impossible, to obtain unique optimal values for their parameters using automatic calibration methods. Unless the best set of parameters associated with a given calibration data set can be found, it is difficult to determine how sensitive the parameter estimates (and hence the model forecasts) are to factors such as input and output data error, model error, quantity and quality of data, objective function used, and so on. Results are presented that establish clearly the nature of the multiple optima problem for the research CRR model SIXPAR. These results suggest that the CRR model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets. Next, the performance of three existing global search procedures are evaluated on the model SIXPAR. Finally, a powerful new global optimization procedure is presented, entitled the shuffled complex evolution (SCE-UA) method, which was able to consistently locate the global optimum of the SIXPAR model, and appears to be capable of efficiently and effectively solving the CRR model optimization problem.

Effective and efficient global optimization for conceptual rainfall‐runoff models

We present an automatic subpixel registration algorithm that minimizes the mean square intensity difference between a reference and a test data set, which can be either images (two-dimensional) or volumes (three-dimensional). It uses an explicit spline representation of the images in conjunction with spline processing, and is based on a coarse-to-fine iterative strategy (pyramid approach). The minimization is performed according to a new variation (ML*) of the Marquardt-Levenberg algorithm for nonlinear least-square optimization. The geometric deformation model is a global three-dimensional (3-D) affine transformation that can be optionally restricted to rigid-body motion (rotation and translation), combined with isometric scaling. It also includes an optional adjustment of image contrast differences. We obtain excellent results for the registration of intramodality positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) data. We conclude that the multiresolution refinement strategy is more robust than a comparable single-stage method, being less likely to be trapped into a false local optimum. In addition, our improved version of the Marquardt-Levenberg algorithm is faster.

/pdf/a-pyramid-approach-to-subpixel-registration-based-on-41xhw0es6x.pdf

A pyramid approach to subpixel registration based on intensity

A design method is proposed that sequentially generates observation sites for the construction of a kriging predictive model. The objective of the construction is to allow a precise inversion of the system in the following sense: with any reachable target point T in the output space one wishes to be able to associate an input vector x_T such that the system response at x_T will be close to T (which requires that the model ensures a precise prediction of the response at x_T ). Intuitively, the observation sites should not be spread over the admissible input space, but should rather concentrate in areas such that, when mapped by the system, they cover the reachable output space. Two approaches are proposed that are shown on examples (one with five input and two outputs, derived from a problem in oil industry) to give satisfactory results. They are based on the maximization of a measure of dispersion of the observations in the output space and can cope with the presence of observation errors, a rather typical situation for experimentation with real physical systems.

https://hal.archives-ouvertes.fr/hal-00290418/document

Design of experiments for response diversity

The paper is a continuation of earlier work (Pronzato and Thierry, Proc. 20th Int. Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, p.169-80, 2001; Proc. ICASSP, 2001): we estimate parameters in a regression model, linear or not, by minimizing (an estimate of) the entropy of the symmetrized residuals, obtained by a kernel estimation of their distribution. The objective is to obtain efficiency in the absence of knowledge of the density, f, of the observation errors, which is called adaptive estimation (Stein, C., 1956; Stone, C.J., 1975; Bickel, P.J., 1982;. Manski, C.F, 1984). Connections and differences with previous work are indicated. Numerical results illustrate that asymptotic efficiency is not necessarily in conflict with robustness.

/pdf/minimum-entropy-estimation-in-semi-parametric-models-43ks8bal0x.pdf

Minimum entropy estimation in semi parametric models

This edited volume, dedicated to Henry P. Wynn, reflects his broad range of research interests, focusing in particular on the applications of optimal design theory in optimization and statistics. It covers algorithms for constructing optimal experimental designs, general gradient-type algorithms for convex optimization, majorization and stochastic ordering, algebraic statistics, Bayesian networks and nonlinear regression. Written by leading specialists in the field, each chapter contains a survey of the existing literature along with substantial new material. This work will appeal to both the specialist and the non-expert in the areas covered. By attracting the attention of experts in optimization to important interconnected areas, it should help stimulate further research with a potential impact on applications.

Optimal Design and Related Areas in Optimization and Statistics

The paper extends the result of Harman and Pronzato [Stat. & Prob. Lett., 77:90--94, 2007], which corresponds to $p=0$, to all strictly concave criteria in Kiefer's $\phi_p$-class. Let $\xi$ be any design on a compact set $X\subset\mathbb{R}^m$ with a nonsingular information matrix $\Mb(\xi)$, and let $\delta$ be the maximum of the directional derivative $F_{\phi_p}(\xi,x)$ over all $x\in X$. We show that any support point $x_*$ of a $\phi_p$-optimal design satisfies the inequality $F_{\phi_p}(\xi,x_*) \geq h_p[\Mb(\xi),\delta]$, where the bound $h_p[\Mb(\xi),\delta]$ is easily computed: it requires the determination of the unique root of a simple univariate equation (polynomial when $p$ is integer) in a given interval. The construction can be used to accelerate algorithms for $\phi_p$-optimal design and is illustrated on an example with $A$-optimal design.

A delimitation of the support of optimal designs for Kiefer's $\phi_p$-class of criteria

A deterministic model-based approach to quality improvement is proposed, along Taguchi’s ideas for off-line quality control. This new approach takes into account fluctuations in the factors; these fluctuations are characterized in terms of tolerance intervals.

Luc Pronzato

Papers

Design of experiments for response diversity

Minimum entropy estimation in semi parametric models

Optimal Design and Related Areas in Optimization and Statistics

A delimitation of the support of optimal designs for Kiefer's $\phi_p$-class of criteria

Quality Improvement via Optimization of Tolerance Intervals During the Design Stage