Title of the course: **Statistical Methods in
Nuclear Physics: I, II**

Part One: *A specializing course for the Master
Program in Physics* (*Data analysis in Nuclear and High Energy
Physics*).

Part two: *A specializing course for the Master
and Ph.D. Program in Physics* (*Computer Simulations in Statistical
Physics).
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Home institution: The St. Kliment Ohridski University
of Sofia
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This course has been existing and new cases has been
adding to it. Its original structure was based on two parts. The
first part covers selected topics from the statistics and data
analysis necessary to handle experimental data taken by the modern
set-up. It is included in the Master Program at the Faculty of
Physics, the University of Sofia).
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The second part gives the students ideas of how natural
processes can be simulated by using computers. It provides a specializing
education for students enrolled in both the Master and the Ph.D.
programs in Theoretical Physics.
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As a result of the project, the specializing course
Statistical Methods in Nuclear Physics included in the M.
Program at the Faculty of Physics, University of Sofia covers
the same topics as such a course available at the Institute of
Physics, the Catholic University of Louvain.
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Objectives: The course
on Data analysis in Nuclear and High Energy Physics is
intended to cover selected topics from the probabilistic theory
and statistics applied in the specified fields of physics and
thus providing a specializing education for students enrolled
in the Master Program.
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Background: Linear algebra,
calculus, introductory course in the probabilistic theory, calculus
I and II, mathematical methods in physics
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- Independent events. Probability Space.Examples of generated sequences of independent events: Topologies of bubble chamber events
- (*) Example 2: Efficiency of a Cerenkov counter.(*) Example 3: Beam contamination and -rays.
- Marginal probability.(*) Example: Topologies of bubble chamber events (2)
- Special properties of probability distributions: density and characteristic functions.
- Distributions of more than one random variable: the joint density and characteristic functions.Linear functions of random variables. Propagation of errors.
- Special probability distributions: binomial, multinomial, Poisson, exponential, gamma, Gaussian, Lorentz. Random number generators - interrelations between the precision of the computed results and the generator quality. Tests for random number generators. Special random distributions based on the uniform generator. Inverse function method. Rejection method.
- Parceval's theorem - convolution of distributions. Application of the Fourier transformation for solving ill-posed problems in the nuclear spectroscopy. Sampling distributions: chi-square, Student's, F-distribution.
- The Maximum- Likelihood method: properties of the estimators.(*) Examples: Estimate of Mean Life Time; polarization. (*) Application of the Maximum- Likelihood method to classified data. The least-square method : linear model; general polynomial fitting. Example: Fitting of a straight line - linear; polynomial. Application of the least-square method to classified data: construction of. (*) Examples: Polarization of antiprotons; angular momentum analysis (1).
- The method of moments: one-parameter and multi-parameter case. (*) Examples: Density matrix elements; angular momentum analysis (2). Minimization procedures: step methods (grid and random search).
- Gradient Methods: numerical calculation of derivatives; steepest descent method
- Minimization with constraints.
- Hypothesis testing: simple and composite hypothesis. (*) Neuman - Pearson test on mean lifetime.Tests of consistency and randomness. (*) Consistency test for two sets of measurements of the lifetime.