## 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
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.
Literature
recommended 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
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.
The course is also listed under the following terms Winter 2000, Summer 2001, Winter 2001, Summer 2002, Winter 2002, Summer 2003, Winter 2003, Summer 2004, Winter 2004, Summer 2005, Winter 2006, Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Winter 2013, Summer 2014, Winter 2014, Summer 2015, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Winter 2019, Summer 2020, Winter 2020, Summer 2021, Winter 2021.
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