Statistical methods in physics

Regular enrolement

Probability: definition of probability, rules of multiplication and addition, Bayesian theorem.
Sampling: Principles of sampling, hypergeometric and binomial distribution.
Theory of probability distributions: random variables, discrete and continuous distributions, the distribution function, the density distribution, characteristic function and its derivatives, examples of probability distributions, the central limit theorem.
Monte Carlo (MC) generators of (pseudo) random numbers, the hit-miss method, integration, generation of various distributions, MC method in Markov chains.
Parameter estimation: Bayes theorem, point estimates and interval estimates, consistency of the method, the maximum likelihood method, sufficiency.
The a priori probability: the attribution of a priory probability distributions, robustness.
Hypothesis testing: testing of binary hypotheses, simultaneous test of multiple hypotheses (model selection).

• Christopher M. Bishop: Pattern Recognition and Machine Learning, Springer New York, NY, 2006
• Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Jonathan Taylor: An Introduction to Statistical Learning – with Application in Python, Springer Cham, 2023

Objectives:
Students will learn basic knowledge on probability theory based methods for the analysis data in medical physics applications.

Competences:
Understanding of basic laws of probability and of scienfitic reasoning. Ability to apply probability methods to the analysis of data in medical physics. Ability to critically compare theoretical predictions and measurements on a finite data sample.

Knowledge and understanding:
Obtaining basic knowledge on probability theory based methods for the analysis data in medical physics applications.

Application:
Use of basic probability concepts for solving problems in the analysis of data in medical physics.

Reflection:
Critical evaluation of theoretical predictions in comparison to measurements on a finite data sample.

Transferable skills:
Ability to collect data and explain obtained results.

Regular homework - problem solving, final project.

Regular homeworks (problem solving)
Final project
5 - 10, a student passes the exam if he is graded from 6 to 10

Urban Simončič:

1. STOKELJ, Eva, TOMŠE, Petra, TOMANIČ, Tadej, DHAWAN, Vijay, EIDELBERG, David, TROŠT, Maja, SIMONČIČ, Urban. Effect of the identification group size and image resolution on the diagnostic performance of metabolic Alzheimer’s disease-related pattern. EJNMMI research. 24 May 2023, vol. 13, str. 1-19, ilustr. ISSN 2191-219X.
2. SIMONČIČ, Urban, MILANIČ, Matija. Hyperspectral imaging with active illumination: a theoretical study on the use of incandescent lamp and variable filament temperature. Sensors. Nov. 2023, vol. 23, iss. 23, art no. 9326, 18 str., ilustr. ISSN 1424-8220.
3. SIMONČIČ, Urban, LEIBFARTH, Sara, WELZ, Stefan, SCHWENZER, Nina, SCHMIDT, Holger, REISCHL, Gerald, PFANNENBERG, Christina, LA FOUGÈRE, Christian, NIKOLAU, Konstantin, ZIPS, Daniel, THORWARTH, Daniela. Comparison of DCE-MRI kinetic parameters and FMISO-PET uptake parameters in head and neck cancer patients. Medical physics. [Print ed.]. 2017, vol. 44, no. 6, str. 2358-2368. ISSN 0094-2405.
4. SIMONČIČ, Urban, PERLMAN, S. B., LIU, Glenn, STAAB, Mary Jane, STRAUS, Jane Elizabeth, JERAJ, Robert. Comparison of NaF and FDG PET/CT for assessment of treatment response in castration-resistant prostate cancers with osseous metastases. Clinical genitourinary cancer. 2015, vol. 13, issue 1, str. 7-17. ISSN 1558-7673.