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

We extend the results in (L. F. Kozachenko, N. N. Leonenko: On statistical estimation of entropy of random vector, Problems Inform. Transmission 23 (1987), 95-101; Translated from Problemy Peredachi Informatsii 23 (1987), 9-16 (in Russian)) and (M. N. Goria, N. N. Leonenko, V. V. Mergel, P. L. Novi Inverardi: A new class of random vector entropy estimators and its applications in testing statistical hypotheses, J. Nonparametr. Statist. 17 (2005), 277-297) and show how kth nearest-neighbor distances in a sample of N i.i.d. vectors distributed with the probability density f can be used to estimate consistently Reny and Tsallis entropies of the unknown f under minimal assumptions. The method is extended to the estimation of statistical distances between two distributions in the case when one i.i.d. sample from each is available.

https://hal.archives-ouvertes.fr/hal-00322783/document

Estimation of entropies and divergences via nearest neighbors

https://hal.archives-ouvertes.fr/hal-01246483/document

Convex relaxation for IMSE optimal design in random-field models

We consider the situation where the parameters /spl theta/ of a linear regression model have to be estimated from observations corrupted by an additive noise with unknown distribution f. Since maximum likelihood estimation cannot be used, we estimate /spl theta/ by minimizing the entropy of a kernel estimate of f, constructed from the residuals. An example of parameter estimation in the presence of interference with random binary signals is presented.

Entropy minimization for parameter estimation problems with unknown distribution of the output noise

Experiment design for bounded-error models

For heterogeneous catalysis, ordinary differential equations in time can be used to interpret transient tracer data obtained in a continuous stirred tank reactor or gradientless reactor in which a steady-state reaction is occurring. The same procedure is often used for plug-flow reactor modeling. However, for transient tracing data obtained with a plug-flow reactor operating under differential conversion, it is necessary to use a set of partial differential equations involving distance through the reactor as well as time. In this paper, the authors present a case study of methanation on a nickel catalyst to illustrate the modeling procedure needed to estimate the desired parameters.

Luc Pronzato

Papers

Estimation of entropies and divergences via nearest neighbors

Convex relaxation for IMSE optimal design in random-field models

Entropy minimization for parameter estimation problems with unknown distribution of the output noise

Experiment design for bounded-error models

Modeling transient tracing in plug-flow reactors : a case study