Course detail
Probability, Statistics and Data Analysis: Introductive Course
FSI-S1D-A Acad. year: 2024/2025 Winter semester
Summary and expansion of elementary concepts from probability theory and mathematical statistics. Parameter estimate methods and their properties. Scattering analysis including post-hoc analysis. Distribution tests, tests of good compliance, regression analysis, regression model diagnostics, non-parametric methods and categorical data analysis.
Language of instruction
English
Number of ECTS credits
6
Supervisor
Department
Entry knowledge
Foundations of differential and integral calculus.
Foundations of descriptive statistics, probability theory and mathematical statistics.
Rules for evaluation and completion of the course
Two tests will be written during the semester – 5th and 10th week. The exact term will be specified by the lecturer. The test duration is 60 minutes. The evaluation of each test is 0-10 points.
Project evaluation: 0-10 points.
Examination: written and oral. Exam, questions are selected from a list of 4 set areas (25+25+25+25 points). At least a basic knowledge of the terms and their properties is required in each of the areas. Evaluation by points: excellent (90 – 100 points), very good (80 – 89 points), good (70 – 79 points), satisfactory (60 – 69 points), sufficient (50 – 59 points), failed (0 – 49 points).
Participation in lectures in this subject is not controlled.
Participation in the exercises is compulsory. During the semester two abstentions are tolerated. Replacement of missed lessons is determined by the leading exercises.
Aims
Introduction of further concepts, methods and algorithms of probability theory, descriptive and mathematical statistics. Development of probability and statistical topics from previous courses. Formation of a stochastic way of thinking leading to formulation of mathematical models with an emphasis on applicability to data.
Students will extend their knowledge of probability and statistics, especially in the following areas:
- parameter estimates for a specific distribution
- simultaneous testing of multiple parameters
- hypothesis testing on distributions
- correlation analysis
- regression analysis including regression modeling
- nonparametric methods
- creation of parameter estimates
- Bayesian statistics
The study programmes with the given course
Programme N-LAN-A: Logistics Analytics, Master's, compulsory-optional
Programme C-AKR-P: , Lifelong learning
specialization CZS: , elective
Type of course unit
Lecture
26 hours, optionally
Syllabus
- Summarizing and recalling the knowledge and methods used in previous courses – probability, random variable.
- Summarizing and recalling the knowledge and methods used in previous courses – random vector, mathematical statistics. An outline of other areas of probability and statistics that will be covered.
- Extension of hypothesis tests for binomial and normal distributions.
- Analysis of variance (simple sorting, ANOVA), post-hoc analysis.
- Correlation analysis
- Regression analysis – part 1.:linear regression model. Comparison of regression models.
- Regression analysis – part 2.:non-linear regression model. Diagnostics.
- Distribution tests.
- Estimation of parameters using the method of moments and the maximum likelihood method.
- Bayesian approach and construction of Bayesian estimates.
- Nonparametric methods of testing statistical hypotheses – part 1.
- Nonparametric methods of testing statistical hypotheses – part 2
- Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.
Computer-assisted exercise
26 hours, compulsory
Syllabus
- A reminder of the examples discussed in previous courses – probability, random variable.
- A reminder of the examples discussed in previous courses – random vector, mathematical statistics.
- Hypothesis tests for binomial and normal distributions.
- Project assignment, analysis of variance, post-hoc analysis.
- Correlation analysis
- Regression analysis – linear models.
- Regression analysis – non-linear models.
- Distribution tests
- The method of moments and the maximum likelihood method.
- Bayesian estimates.
- Nonparametric methods of testing statistical hypotheses – part 1.
- Nonparametric methods of testing statistical hypotheses – part 2.
- Analysis of categorical data. Contingency table. Four-field tables.