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
  • Gaussian distributions
  • Multivariate Gaussian distributions
  • t- and F-distributions
  • Convergence and limiting distributions, central limit theorem

 


Download lecture notes: part one

PART TWO

 

Statistical

Inference

 

 

  • Samples, statistics and estimators
  • Point estimation and Fisher information
  • Interval estimation
  • Resampling
  • Hypothesis testing
  • Kolmogorov-Smirnov nonparametric testing
  • Regression and correlation
  • Sufficiency
  • Information, entropy and priors
  • Astronomical aside: luminosity functions, counts and biases

 


Download lecture notes: part two

PART THREE

 

Mathematical Tools

 

 

  • Euler Gamma and Beta functions
  • Riemann Zeta function
  • Markov-Chain Monte Carlo (MCMC)
  • Time series
  • Spatial point processes and clustering
  • Stochastic processes
  • Stochastic differential equations
  • Cosmological aside: first crossing distributions and halo mass functions

 

 

 


Download lecture notes: part three