Statistical methods in physics

2021/2022
Programme:
Medical Physics, Second Cycle
Year:
1 in 2 year
Semester:
first or second
Kind:
optional
ECTS:
6
Language:
slovenian
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
0
Tutorial
1
Lab
0
Prerequisites

Regular enrolement

Content (Syllabus outline)

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).

Readings

• D.S.Sivia: Data Analysys – A Bayesian Tutorial, Oxford University Press, 1996
• E.T.Jaynes: Probability Theory – The Logic of Science, Cambridge University Press, 2003.
• H.Frank, S.C.Althoen: Statistics – Concepts and Applications, Cambridge University Press, 1994.

Objectives and competences

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.

Intended learning outcomes

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.

Learning and teaching methods

Regular homework - problem solving, final project.

Assessment

Regular homeworks (problem solving)
Final project
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references
  1. T. Podobnik and T. Živko, On probabilistic parametric inference, Journal of Statistical Planning and Inference 142 (2012) 3152–3166
  2. B. Kerševan, B. Golob, G. Kernel, T. Podobnik, Nucl. Instr. Meth. A462 (2001) 536
  3. DELPHI Collaboration, ABDALLAH, J., BRAČKO, Marko, GOLOB, Boštjan, KERNEL, Gabrijel, KERŠEVAN, Borut Paul, PODOBNIK, Tomaž, ZAVRTANIK, Danilo, et al. Measurements of CP-conserving trilinear gauge boson couplings WWV (V [equivalent] [gamma], Z) in e[sup]+ e[sup]- collisions at LEP2. The European physical journal. C, ISSN 1434-6044, Mar. 2010, vol. 66, issue 1/2, str. 35-56.
  4. DELPHI Collaboration, ABDALLAH, J., BRAČKO, Marko, GOLOB, Boštjan, KERNEL, Gabrijel, KERŠEVAN, Borut Paul, PODOBNIK, Tomaž, ZAVRTANIK, Danilo, et al. Search for single top quark production via contact interactions at LEP2. The European physical journal. C, ISSN 1434-6044, 2011, vol. 71, no. 2, str. 1555-1-1555-13.