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Chapter 1 A MODEL SELECTION TALE Jean-Jacques Droesbeke, Gilbert Saporta and Christine Thomas-Agnan

1.1

Introduction

Modeling holds an important place in statistics, which is borne out in numerous articles, books and encyclopedias. Nevertheless, models simplify reality, and as George Box (1919-2013) liked to say, “Essentially, all models are wrong, but some are useful ”. What is certain is that a large number of leaps forward in statistics have rested on the use of models, and in particular the selection of relevant ones. This has also been true in the history of other scientific subjects. In this chapter1 we are going to describe a key model selection tale from history whose consequences for statistics turned out to be quite important.

1.2

Elements of the history of words and ideas

We know that from an etymological point of view, the term “model” comes from the Italian modello, which at the beginning of the 16th century meant an “illustration to be reproduced” 2 . This word is itself derived from the Late Latin modellus, and the earlier Latin modulus (diminutive of modus: measure) with the original meaning: “arbitrary measure used to determine the proportional relationships between parts of a work of architecture” 3 . 1 This paragraph and the two following it are principally based on the work of Droesbeke and Saporta [2010] as well as Lacombe and Costabel [1988] and Chapter 4 of the doctoral thesis of Armatte [1995]. 2 The same is true for the French modèle and the German modell. 3 See Bachelard [1979], p. 15.

Model Choice and Model Aggregation, F. Bertrand - Editions Techip  

For over fourty years, choosing a statistical model thanks to data consisted in optimizing a criterion based on penalized likelihood (H. Aka...

Model Choice and Model Aggregation, F. Bertrand - Editions Techip  

For over fourty years, choosing a statistical model thanks to data consisted in optimizing a criterion based on penalized likelihood (H. Aka...

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