TEACHING


Statistical Methods for Astrophysics and Cosmology

 PART ONE

 

Probability

Theory

 

 

  • Probability and probability distributions
  • Multivariate and conditional distributions
  • Binomial, negative binomial and geometric distributions
  • Gamma, exponential and chi-squared distributions
  • Power-law (Pareto) distribution
  • Gaussian distribution
  • Multivariate Gaussian distribution
  • t- and F-distributions, Student's theorem
  • Stochastic convergence, central limit theorem

 


Download lecture notes: part one

PART TWO

 

Statistical

Inference

 

 

  • Samples, statistics and estimators
  • Point estimation and Fisher information
  • Interval estimation
  • Resampling techniques
  • Hypothesis testing
  • Information, entropy and priors
  • Kolmogorov-Smirnov nonparametric testing
  • Regression and correlation
  • Sufficiency and completeness

 

 

 


Download lecture notes: part two

PART THREE

 

Advanced

Topics

 

 

  • Fourier analysis of time series
  • Markov Chain Montecarlo (MCMC) and Hamiltonian Montecarlo (HMC)
  • Machine and statistical learning (Intro)
  • Neural networks and deep learning (Intro)
  • Astronomical applications: detection, completeness and reliability; luminosity functions and counts; Malquist and Eddington bias; 1/Vmax method; survival analysis; confusion noise and P(D) technique; data smoothing; clustering.

 


Download lecture notes: part three

(new version in prep. for A.Y. 2019/2020)