# Statistical analysis of experimental data

Faculty of Physics, University of Warsaw
winter semester 2023/2024

Lecturer:
prof. dr hab. Aleksander Filip Żarnecki
Institute of Experimental Physics
e-mail:
zarnecki@fuw.edu.pl
Tel:
+48 22 5532801
Office:
Room 4.01, Pasteura 5
Full description can be found on USOS
Lecture slides and homework tasks are also available on Kampus platform

Python notebooks are available on github and Google Colab platform:

## Make-up exam

Make-up exam problems
Problem description and data file for problem 2.
Solutions to be uploaded by Friday, March 1, 2024.

## Lecture slides

Concept of probability
lecture 05.10.2023: PDF
Introduction to Python
lecture 12.10.2023: PDF
lecture notebook
Probability distributions and their properties
lecture 19.10.2023: PDF
Dice rolling
Exponential distribution
Binomial distribution
Poisson distribution
Gamma distribution
Measurements and their uncertainties
lecture 26.10.2023: 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 09.11.2023: PDF
numerical integration example script
Monte Carlo integration example script
Parameter Inference
lecture 16.11.2023: 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 23.11.2023: 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 30.11.2023: PDF
χ2 distribution modelling
t distribution modelling
Critical χ2 values plot
Example of linear least-squares fit of Fourier series
Data for homework exercise
Least-squares method (2)
lecture 07.12.2023: PDF
General fit example
F-test distribution
Critical F-test values plot
General fit example for model testing
Linear fit with constraints using variable elimination method
Linear fit with constraints using Lagrange multipliers method
Systematic uncertainties
lecture 14.12.2023: PDF
Background fit example
Fit with systematic uncertainties (from example above)
Eigenvector calculation example
Variable distributions
lecture 21.12.2023: PDF
Binned likelihood fit example
Binned likelihood shape fit example
Unbinned likelihood fit example
Example data for the above scripts
Data for homework exercise
Classification
lecture 11.01.2024: PDF
Fisher linear discriminant example
Naive Bayes classifier example
k Nearest Neighbors classifier with Mahalanobis distance measure
Linear discriminant with iterative procedure
Machine learning
lecture 18.01.2024: PDF
Percepton classifier with hidden layer
Artificial Neural Networks example with sklearn
Decision Tree example with sklearn
Classifier boosting example
Boosted Decision Tree example based on sklearn
Data for homework exercise:
Training background sample
Training signal sample
Test sample for actual analysis
Markov Chains
lecture 25.01.2024: PDF
Atom excitation: example of Markov Chain
Atom excitation: evolution of probabilities
Markov Chain Monte Carlo: uniform distribution
Markov Chain Monte Carlo: with probability distribution
Markov Chain Monte Carlo: application to parameter fit

All materials are dedicated to the students of the University of Warsaw only