Statistical analysis of experimental data

Faculty of Physics, University of Warsaw winter semester 2024/2025

e-mail:

zarnecki@fuw.edu.pl

Tel:

+48 22 5532801

Office:

Room 4.01, Pasteura 5

Lecture slides

Concept of probability

lecture 03.10.2024: PDF

Introduction to Python

lecture 10.10.2024: PDF

lecture notebook

Probability distributions and their properties

lecture 17.10.2024: PDF

Binomial distribution

Poisson distribution

Gamma distribution

Model of radioactivity

Measurements and their uncertainties

lecture 24.10.2024: PDF

Bessel's correction script

Central Limit Theorem script

Direct generation method script

von Neuman generation method script

General generation method

Monte Carlo methods

lecture 31.10.2024: PDF

2-D Monte Carlo integration example script

3-D numerical integration example script

3-D Monte Carlo integration example script

Parameter Inference

lecture 7.11.2024: PDF

log-likelihood contours script

probability density contours script

probability density Monte-Carlo contours

Gauss probability intervals script

Poisson probability intervals script

Gamma probability intervals script

Parameter Inference (2)

lecture 14.11.2024: PDF

Frequentist central interval construction for Gaussian variable

Comparison of Bayesian and Frequentist limits for Gaussian variable with bound

Unified interval construction for Gaussian variable with bound

Frequentist central interval construction for Poisson variable with background

Unified interval construction for Poisson variable with background

Least-squares method

lecture 21.11.2024: PDF

χ² distribution modelling

t distribution modelling

Critical χ² values plot

Example of linear least-squares fit of Fourier series

Data for homework exercise