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Published online by Cambridge University Press: 07 September 2011
Detailed consideration is required to ensure that the most appropriate parameters of interest are chosen for a particular research question. It is also important to ensure the appropriate treatment of nonspecific effects, which correspond to systematic differences that are not of direct concern. Thus in the present chapter we discuss aspects relating to the choice of models for a particular application, first the choice between distinct model families and then the choice of a specific model within the selected family.
Criteria for parameters
Preliminaries
In some applications analysis and interpretation may be based on nonparametric formulations, for example the use of smooth curves or surfaces summarizing complex dependencies not easily captured in a simple formula. The reporting of estimated spectral densities of time series or line spectra representing complex mixtures of molecules are examples. Mostly, however, we aim to summarize the aspects of interest by parameters, preferably small in number and formally defined as properties of the probability model. In the cases on which we concentrate, the distribution specified by the model is determined by a finite number of such unknown parameters.
For a specific research question, parameters may be classified as parameters of interest, that is, directly addressing the questions of concern, or as nuisance parameters necessary to complete the statistical specification. Often the variation studied is a mixture of systematic and haphazard components, with attention focused on the former.
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