Model choice

and model aggregation

For over fourty years, choosing a statistical model thanks to data

consisted in optimizing a criterion based on penalized likelihood

(H. Akaike, 1973) or penalized least squares (C. Mallows, 1973). These

methods are valid for predictive model choice (regression, classification)

and for descriptive models (clustering, mixtures). Most of their

properties are asymptotic, but a non asymptotic theory has emerged at

the end of the last century (Birgé-Massart, 1997). Instead of choosing the

best model among several candidates, model aggregation combines

different models, often linearly, allowing better predictions. Bayesian

statistics provide a useful framework for model choice and model

aggregation with Bayesian Model Averaging.

In a purely predictive context and with very few assumptions,

ensemble methods or meta-algorithms, such as boosting and random

forests, have proven their efficiency.

This volume originates from the collaboration of high-level specialists :

Christophe Biernacki (Université de Lille I), Jean-Michel Marin (Université

de Montpellier), Pascal Massart (Université de Paris-Sud), Cathy

Maugis-Rabusseau (INSA de Toulouse), Mathilde Mougeot (Université

Paris Diderot), and Nicolas Vayatis (École Normale Supérieure de Cachan)

who were all speakers at the 16th biennal workshop on advanced

statistics organized by the French Statistical Society . In this book, the

reader will find a synthesis of the methodologies' foundations and of

recent work and applications in various fields.

The French Statistical Society (SFdS) is a non-profit organization that

promotes the development of statistics, as well as a professional body for all

kinds of statisticians working in public and private sectors. Founded in

1997, SFdS is the heir of the Société de Statistique de Paris , established in

1860. SFdS is a corporate member of the International Statistical Institute and

a founding member of FENStatS - the Federation of European National

Statistical Societies .