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.
More information and upload links on
Kampus platform
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
χ
^{2}
distribution
modelling
t distribution
modelling
Critical χ
^{2}
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
See also
Slides and scripts from the past courses:
2022/2023