Méthodes Quantitatives Avancées en Environnement Marin.
Ce cours est une introduction aux méthodes classiques de traitement de tableaux de données croisant  un grand nombre d'individus sur lesquels sont mesurées des variables quantitatives ou qualitatives. Différents rappels d'algèbre matricielle y sont présentés avant d'aborder les notions d'inertie d'un nuage de points et les relations avec des quantités statistiques usuelles (moyenne, variance, etc...).

Introduction (document pdf)
Introduction et motivation de ce cours au travers de différents exemples pris en océanographie

Exo corrigés
Lien vers deux exercices interessants du poly de J. F. Durand. Ces exercices sont corrigés.

TDs informatiques corrigés :

1) Functional data analysis of a set of profiles of temperature (T, °C), salinity (S, SI) and dissolved oxygen (DO, %).
An observation of the following dataset is constitued with 30 values : 10 measures of T, 10 measures of S and 10 measures of DO sampled every 1m from 0m to 9m in the Berre lagoon. An observation can then be seen as a multivariate sampled profile of 3 variables.
We dispose of a collection of such observations from 1994 to 2010 with about 24 observations a year. The objective of this work is to study the variability of this dataset using PCA. However, some constraints must be added to the PCA analysis because the data are functional and multivariate. We propose a PCA version which takes into account the functional structure of tha dataset as well as the covariance structure between profiles of T, S and DO. Before solving the eigenvalue problem provided by PCA, data are weighted by dividing each block of variables (T, S and DO) by the square root of the trace of the variance-covariance matrix of each block. This allows to compare profiles composed with varaibles which don't have the same unity.  
    - Link towards the R program
    - Link toward the datasets :
            bers.txt : contains salinity profiles
            bert.txt : contains temperature profiles
            bero.txt : contains dissolved oxygen profiles

Liens utiles