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



Program:
Part IProbability Theory: Probability and probability
distributions; Multivariate and conditional distributions;
Binomial, negative binomial and geometric distributions; Gamma,
exponential and chisquared distributions; Powerlaw distribution;
Gaussian distributions;
Multivariate Gaussian distributions; t and Fdistributions, Student's theorem;
Stochastic convergence and central limit theorem.
Part IIStatistical inference: Samples, statistics and
estimators; Point estimation and Fisher information; Interval
estimation; Resampling techniques; Hypothesis testing; Information,
entropy and priors; KolmogorovSmirnov nonparametric testing;
Regression and correlation; Sufficiency and completeness.
Part IIIAdvanced 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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