Course detail

Probability, Statistics and Data Analysis: Advanced Course

FSI-S2D-AAcad. year: 2024/2025

This course is concerned with the following topics: theory of estimation, maximum likelihood, method of moments, Bayesian methods of estimation, testing statistical hypotheses, nonparametric methods, exponential family of distribution, asymptotic tests, generalized linear models.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Zuzana Hübnerová, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Rudiments of probability theory and mathematical statistics, linear models.

Rules for evaluation and completion of the course

Course-unit credit requirements: active participation in seminars, mastering the subject matter, demonstration of gaines skills in practical data analysis on PC in a project, and succesfull solution of possible written tests.

Examination: oral exam, questions are selected from a list of 3 set areas (30+30+40 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 the exercise is mandatory and the teacher decides on the compensation for absences.

Aims

The course objective is to make students of the international course Logistics analytics acquainted with methods of estimation theory, an asymptotic approach to statistical hypotheses testing resulting in the generalized linear models modeling and prepare students for independent applications of these methods for statistical analysis of real data.


Students acquire needed knowledge from important parts of mathematical statistics, which will enable them to evaluate and develop stochastic models of technical phenomena and processes based on these methods and realize them on PC.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Hogg, V.R., McKean J.W., and Craig A.T. Introduction to Mathematical Statistics. 7th ed., 2013. New York: Pearson. ISBN: 978-0-321-79543-4. (EN)
Casella, G., Berger, R.L. Statistical Inference. 2nd ed., 2001. ISBN: 978-0534243128 (EN)
Dobson, A.J., Barnett, A.G. An Introduction to Generalized Linear Models. 4th ed. 2018. Chapman & Hall. ISBN: 978-1138741515 (EN)

Recommended reading

Lehmann, E.L., Romano, J.P. Testing Statistical Hypotheses, 2010. New York: Springer. ISBN 978-1-4419-3178-8

(EN)

McCullagh, P., Nelder, J.A. Generalized Linear Models, 2nd ed., 1989. CRC Press. ISBN 978-1584889502

(EN)

Classification of course in study plans

  • Programme N-LAN-A Master's, 1. year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Zuzana Hübnerová, Ph.D.

Syllabus

1. Unbiased and consistent estimates
2. Regular family of distributions, Rao - Cramér theorem, efficient estimates
3. Fisher information and Fisher information matrix
4. Exponential family of distribution
5. Sufficient statistics, Neyman factorization criterion
6. Rao - Blackwell theorem and its applications
7. Method of moments, maximum likelihood method
8. Bayesian approach
9. Testing statistical hypotheses
10. Principles of nonparametric methods
11. Asymptotic tests based on likelihood function
12. Tests with nuisance parameters, examples
13. Generalized linear models – logistic regression, log-linear models

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

doc. Mgr. Zuzana Hübnerová, Ph.D.

Syllabus

1. Survey of probability distributions, graphs of densities
2. Unbiased and consistent estimates - examples of estimates and verification of their properties
3. Computation of the lower bound for variance of unbiased estimates
4. Determination of Fisher information and Fisher information matrix for given distributions
5. Examples of distributions from exponential family
6. Applications of Neyman factorization criterion
7. Findings estimates by Rao - Blackwell theorem
8. Estimator’s determination by method of moments and by maximum likelihood method
9. Estimator’s determination by Bayes method
10. Application of asymptotic tests based on likelihood function
11. Tests with nuisance parameters, estimates of parameters for Weibull and gamma distribution
12. Tests of hypotheses on parameters of generalized linear model
13. Logistic regression, loglinear models