Design and Analysis of Experiments

Hinkelmann, Klaus; Kempthorne, Oscar

doi:10.1002/0471709948

Cited by 215 publications

(198 citation statements)

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“…For the results presented in this dissertation, the above understanding of the statistical analysis of linear models is su cient. For more detail, however, the reader is referred to the many comprehensive texts on the subject (for example, [53]). …”

Section: Linear Models and Regressionmentioning

confidence: 99%

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

137

224

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Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from three-dimensional images and surface descriptions. While computationally-derived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address.In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the state-of-the-art by overcoming many of the limitations of existing methods. The framework uses a particle-system representation of shape, with a fast correspondence-point optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy metrics and no free parameters. The idea is to maximize both the geometric accuracy and the statistical simplicity of the shape model, in accordance with the principle of parsimony in model selection. The nonparametric representation allows the method to be applied to a larger class of problems than existing methods, including nonspherical surfaces, open surfaces, and sets of multiple surfaces.The relative simplicity of the surface representation and the low number of free parameters results in a framework that is easy to use and can operate directly on image segmentations. In collaboration with scientists from several important areas of biomedicine, I have demonstrated that the proposed method is indeed an e↵ective tool for scientific research.The specific research contributions of this dissertation are as follows. First, I describe a mathematical framework and a robust numerical algorithm for computing optimized correspondence-point shape models using an entropy-based optimization and particle-system technology. Second, I develop a series of extensions of the framework to more general classes of shape analysis problems, including the analysis of multiple-object complexes, the generalization to correspondence based on generic functions of position, an extension to handle surfaces with open boundaries, and shape modeling with simple regression. Third, I describe the application of statistical hypothesis testing, regression analysis, and multiple-analysis of covariance to the proposed shape models. I also introduce new techniques for visualization and interpretation of these statistics. Finally, in cooperation with biomedical researchers, I present validation of the above research contributions by their successful application to real-world research problems.

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Section: Linear Models and Regressionmentioning

confidence: 99%

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

137

224

View full text Add to dashboard Cite

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“…In this work we examine statistical properties of designs under a randomization-derived linear model of observations (random block effects describing the structure of units) with treatment (combination) effects being fixed (cf. Caliński and Kageyama, 2000, 2003, Hinkelmann and Kempthorne, 2005, Hinkelmann, 2012. The experimenter usually makes a ranking of factors as well as linear functions of level effects (contrasts) with respect to the scientific interest and aim of the experiment.…”

Section: Applicationsmentioning

confidence: 99%

Use of α-resolvable designs in the construction of two-factor experiments of split-plot type

Ozawa

Kuriki

Mejza

2016

Biometrical Letters

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“…For the present problem industry is the blocking variable [23]. We can test the first problem with the help of a different industry result and to check whether results are varied across the industry or not.…”

Section: Problem Identified and Hypothesis Developedmentioning

confidence: 99%