ED352 - course 'Advanced statistical methods for data analysis' - SCHIMD / VEROPALUMBO

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 astrophysics, biophysics, plasma physics, and condensed matter (Brownian-like trajectories, astronomical transients, spectra, digital images, spatial maps...).

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

Basics of probability and statistics

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.