Model selection in rheology: Providing a practical framework, surveying the field, and assessing the uses and limitations of BIC
The selection of which model or models to use when studying a complex fluid is of constant relevance in rheology, though often too little attention is paid to framing this problem of selection such as to yield consistent, credible, and meaningful results. In this thesis I provide a novel framework for identifying the purpose of rheological models along with background on model selection techniques and criteria, assess the state of and need for model selection in rheological literature, and perform several case studies investigating how model selection techniques may be applied in rheology and note their advantages and limitations. While there remains no single, straightforward technique for selecting a model in all cases, the rheological literature so rarely acknowledges this crucial step in analysis and often fails to sufficiently report methodology relating to model fits, let alone selection, that even preliminary consideration of this problem and the application of simple criteria such as the Bayesian Information Criterion (BIC) may add significant value and validity to these analyses. There remains even greater opportunity in the application of more sophisticated methods such as the calculation of Bayes Factors and the formulation of priors for rheological models. The background, review, case studies, and examples presented in this thesis provide a jumping-off point for an ongoing discussion regarding the place of these theories and techniques in rheology while offering clear examples of their use and conclusions that may be drawn from them.
rheology, model selection, yield stress, thixotropy, model fit, bayesian, least-squares fitting
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign