Course information

Course description

The course is aimed to provide an advanced theoretical and practical background that goes beyond the probability theory and statistics knowledge acquirable in the undergraduate physics program. The introduced topics are unavoidable for the efficient evaluation of modern experimental and simulation data, as well as for the analysis of data using computer models and machine learning. The course also gives an outlook into the deterministic and stochastic modelling of chaotic and discrete time processes. By visiting the lectures, student get acquainted with building complex hy-potheses and statistical models and the practical methods of evaluation thereof.

Topics

  • Distributions, hypothesis tests, discrete and continuous variable, statistical models, regression, confidence, p-value
  • Rare events, exact tests
  • Statistics of extemes, universality
  • Post-hoc analysis, robust statistics
  • Linear models, hierarchical models
  • Correlation analysis, tests of independence, measures of information
  • Bayesian analysis
  • MCMC methods
  • Dynamical systems, stability, attractor
  • Modelling discrete time processes, difference equations, generator functions
  • Growth phenomena, scale-independence, stability of distributions
  • Fractal measures
  • Stochastic processes

Recommended readings

  • Larry Wasserman: All of Statistics (Springer 2004)
  • Alfred Renyi: Probability Theory (Dover Publications 2007, ISBN:978-0486458670)

Course material