Objectifs :
Starting from the formal description of stochastic processes, this lectures will present several methods to analyse time-series and random fields emerging in physical sciences including astronomy and astrophysics, biophysics, condensed matter, nano and neurosciences, particle physics, plasma physics (Brownian-like trajectories, astronomical transients, spectra, digital images, spatial maps...).

Programme :
Time-series, random fields, point processes. Folding; peaks detection, Savitzky-Golay filtering, matched filtering. Spectral analysis of stationary and non-stationary digital signals (DFT, FFT, WFT, STFT, wavelets). Two-point correlation functions and estimators (natural, Landay-Szalay; classical, Bartlett Lomb-Scargle); Minkowski functionals; covariance (jack-knife, bootstrap, MonteCarlo), tapering. Sampling: MCMC, HMC, Gibbs, OLH. Inverse problem: pseudo-inverse and Wiener filters, Richardson-Lucy deconvolution, Tikhonov regularization. Multivariate analysis: PCA, kernel PCA, functional PCA, SVM.

Pré-requis :
Basics of probability and statistics

Equipe pédagogique :
Carlo Schimd

Méthode pédagogique :
Frontal lectures and hands-on sessions using real or simulated data proposed by students.

Compétences acquises à l'issue de la formation :
Ability to identify the more appropriate data analysis technique, use of appropriate libraries and routines in C/C++, Python or Mathematica®, data modeling and estimation of errors.

La formation participe à l'objectif suivant :conforter la culture scientifique des doctorants dans leur champ disciplinaire ou en interdisciplinaire