Course Dates Credits
Statistical Methods for Astrophysics and Cosmology I 3.5
Lecturers
Andrea Lapi

Program:

  • Part I-Probability Theory: Probability and probability distributions; Multivariate and conditional distributions; Binomial, negative binomial and geometric distributions; Gamma, exponential and chi-squared distributions; Power-law distribution; Gaussian distributions; Multivariate Gaussian distributions; t- and F-distributions, Student's theorem; Stochastic convergence and central limit theorem.
  • Part II-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.
  • Part III-Advanced topics: Fourier analysis of time series; Markov Chain Montecarlo and Hamiltonian Montecarlo; Machine and statistical learning (Intro); Neural Networks and deep learning (Intro); Astronomical applications.

    Prerequisites:

    Basics of mathematical analysis and linear algebra.

    Books:

  • Lecture notes (A. Lapi)
  • Introduction to Mathematical Statistics (R.V. Hoog, J. McKean, A.T. Craig)
  • Bayesian Data Analysis for the Physical Sciences (P. Gregory)
  • Practical Statistics for Astronomers (J.V. Wall & C.R. Jenkins)
  • Modern Statistical Methods for Astronomy (E.D. Feigelson & G. J. Babu)
  • Website: https://lapi.jimdo.com/teaching/

    Online Resources:

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