Abstract:
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In classical problems, e.g., comparing two populations, fitting a regression surface, etc., variability is a nuisance parameter. The term "nuisance parameter" is meant here in both the technical and the practical sense. In my career, however, I have encountered many problems where understanding the structure of variability is just as central as understanding the mean structure. I will review a few of these problems, among which are the following list: a.) determining the validity of an immunoassay; b.) managing the Atlantic menhaden fishery; c.) understanding whether food frequency questionnaires have ability to detect meaningful fat intake/breast cancer relationships; and d.) radiation dose-response in the presence of dose uncertainty. In these and other problems, treating variance structure as a nuisance. instead of a central part of the modeling effort, not only leads to inefficient estimation of means, but also to misleading conclusions.
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