Méthodes Quantitatives Avancées en Environnement Marin.
Multivariate Statistical Methods in Marine Environment.
This course is an introduction to multivariate statistical methods for quantitative data. We remind some basics in matrix algebra before introducing the notion of inertia in a dataset and relations with usual statistical descriptors (mean, variance, etc...).

Rprojection.r
This Rfile illustrates the notion of projections and dimension reduction on simple examples.


Introduction (pdf file)
Introduction et motivation of the course through numerous examples in oceanography.

Introduction to functional data analysis
This is a pdf beamer file on data that arrive as curves in oceanography. Fitted methods and basis functional pca is presented.

Corrected exercises
Link toward interesting corrected exercises of J. F. Durand manuscript (link below)..

Correction of TD1.
Find some simple exercises assisted with R code in order to understand inertia and variance-covariance notions.
 - Link towards R program

Correction of TD1B.
Find some simple exercices assisted with basic R codes in order to understand variance-covariance notions and the link with correlation.
 - Link towards statement + R program

Correction of TD2.
Some basic examples of PCA construction..
 - Link towards statement + corrections.

Correction of TD4.
Some basic examples of PCA construction again.
 - Link towards statement + corrections.

Corrected R program :

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 constituted 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 associated with PCA, data are weighted by dividing each block of variables (T, S and DO respectively) by the square root of the trace of the variance-covariance matrix of each block. This allows to compare profiles composed with variables which do not 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

2) PCA of metal contaminants.
We dispose of several stations on the Berre lagoon where dosages of heavy metal contamination and organic carbon have been carried out. We propose a PCA of the data in order to construct a pollution index and to construct a spatial map of the contamination.
    - access to contamination data
    - access to main R file
    - access to Lat. location and Long. location
    - access to bathymetry file
    - access to coast line

3) PCA R script.
A complete source code in R for PCA and interpretation tools
acpxqd.r

Useful links