What is a statistical model

@article{McCullagh2002WhatIA,
  title={What is a statistical model},
  author={Peter McCullagh},
  journal={Annals of Statistics},
  year={2002},
  volume={30},
  pages={1225-1310}
}
  • P. McCullagh
  • Published 1 October 2002
  • Philosophy
  • Annals of Statistics
This paper addresses two closely related questions, What is a statistical model? and What is a parameter? The notions that a model must make sense, and that a parameter must have a well-defined meaning are deeply ingrained in applied statistical work, reasonably well understood at an instinctive level, but absent from most formal theories of modelling and inference. In this paper, these concepts are defined in algebraic terms, using morphisms, functors and natural transformations. It is argued… 
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