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Published in:
2022 | OriginalPaper | Chapter
12. Principles
Author : Peter McCullagh
Published in: Ten Projects in Applied Statistics
Publisher: Springer International Publishing
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Abstract
This chapter discusses a number of principles of statistical modelling. Foremost is the principle of consistency of stochastic formulations under sub-sampling. It is this principle that allows the statistician to make statements about population values on the basis of values observed on a sample. This principle is ordinarily satisfied in the great majority of areas of application, but there are exceptions. The text discusses problems that arise from formulations that are not sampling consistent.
Adequacy of the model for the application is the second principle. Chapters 1–10 provide numerous examples of models that are adequate to varying degrees. Every model is proposed tentatively in the knowledge that it is inadequate to some degree. Depending on the application, some infelicities such as unaccommodated interaction or correlation may produce misleading conclusions; others such as non-normality or non-constancy of variance may be benign. It is necessary to understand the effect of various inadequacies on a range of conclusions.
The likelihood principle is included in third place because it is entirely subsidiary to the first two.
Finally, attitudes to statistics and applied mathematics are discussed, with particular reference to Richard Courant and George Box.