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FPF:UFDF021 Statistics for Physicists - Course Information

## UFDF021 Statistics for Physicists

**Faculty of Philosophy and Science in Opava**

Summer 2022

**Extent and Intensity**- 0/0/0. 0 credit(s). Type of Completion: dzk.
**Guaranteed by**- doc. RNDr. Stanislav Hledík, Ph.D.

Institute of Physics - Faculty of Philosophy and Science in Opava **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Theoretical Physics and Astrophysics (programme FPF, P1703 Fyz4) (2)
- Theoretical Physics and Astrophysics (programme FPF, P1703 Fyz4) (2)

**Course objectives**- The aim is to familiarize students with the fundamentals of probability, the basics of descriptive and inductive statistically including the presentation of statistical data, and the basics of data modeling. The lectures are supplemented by interactive computer demonstrations based on real data and cases.
**Syllabus**- 1. Basic concepts of probability theory. Repetition, combinatorics. The concept of probability, random experiment, random event, the definition and properties of probability. Independence of events, conditional probability. Random variable discrete and continuous, the probability distribution function ( probability density function, PDF) and (cumulative ) distribution function (CDF ).

2. Characteristics of probability distributions. Moments, mean, variance, standard deviation, skewness, kurtosita, another rate variability. Median, percentiles, modus. Transformation of random variables.

3. The one-dimensional distribution function. Discrete distribution function (alternative, binomial, Poisson, hypergeometric, geometric, negative binomial ). Continuous distribution function ( uniform, exponential, normal, log- normal, chi -square, Weibull, Erlang ).

4. random vector. Distribution and probability density function of multivariate distributions. Marginal distributions, correlation ( contingency ) table. Moments division, covariance, linear correlation coefficient, uncorrelated and independent variables. Multinomial distribution, a two-dimensional normal distribution.

5. Limit theorems of probability. Bernoulli's theorem, law of large numbers ( Chebyshev theorem), the central limit theorem.

6. Statistics - Introduction and statistical investigation. Basic concepts. Qualitative and quantitative variables and their statistical characteristics. The sampling methods and types of errors. Sample distributions and their characteristics - population vs. selective frequency. Distribution statistics in selections from a normal distribution.

7. Introduction to estimation theory. Point and interval estimation, impartial and unbiased best estimate. Asymptotic properties of estimates, consistent estimation. Construction of point estimation ( method of moments, maximum likelihood method ). Construction of interval estimation.

8. Testing statistical hypotheses. Methodology for testing hypotheses, statistical hypothesis, null and alternative hypothesis, test statistic, the level of statistical significance, p- value, degrees of freedom, the error of the first and second kind.

9. Selected parametric tests. Testing arithmetic mean and variance ( Student's t -test and F - test), goodness of fit tests (chi square, Kolmogorov- Smirnov test). Analysis of relationships ( pivot tables and association, Pearson coefficient). Analysis of variance (ANOVA), post-hoc analysis.

10. Selected nonparametric tests. Mann-Whitney test, Kruskal - Wallis test, Spearman coefficient Kendall tau. Tests for dependent samples ( Friedman test).

11. Regression and correlation analysis. Model, the coefficients of the model. Linear regression model. Point estimates ( point estimates of the parameters of the regression line, the meaning of point estimates ), model verification, model stability, residue testing. Generalized linear regression (structural matrix, the normal equation, multicollinearity ). Index Determination, partial correlation coefficients.

12. Examples of case studies and applications of statistics and data modeling.

- 1. Basic concepts of probability theory. Repetition, combinatorics. The concept of probability, random experiment, random event, the definition and properties of probability. Independence of events, conditional probability. Random variable discrete and continuous, the probability distribution function ( probability density function, PDF) and (cumulative ) distribution function (CDF ).
**Literature**- P. Gregory.
*Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica? Support*. Cambridge University Press; 1 edition (June 28,. ISBN 978-0521150125. info - E.T. Jaynes.
*Probability Theory: The Logic of Science*. Cambridge University Press (June 9, 2003). ISBN 978-0521592710. info - RICE, John A.
*Mathematical Statistics and Data Analysis (with CD Data Sets)*. 3 edition. Belmont, CA: Thomson/Brooks/Cole, 2007. ISBN 0-534-39942-8. info

*recommended literature*- P. Gregory.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- The attendance at lectures is recommended. It can be substituted by the self-study of recommended literature and individual consultations.

- Enrolment Statistics (recent)

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