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# Course detail

## Probability and Statistics III

Course unit code: FSI-SP3
Type of course unit: compulsory
Level of course unit: Master's (2nd cycle)
Year of study: 1
Semester: summer
Number of ECTS credits:
 Learning outcomes of the course unit: 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.
 Mode of delivery: 90 % face-to-face, 10 % distance learning
 Prerequisites: Rudiments of probability theory and mathematical statistics, linear models.
 Co-requisites: Not applicable.
 Recommended optional programme components: Not applicable.
 Course contents (annotation): 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.
 Recommended or required reading: Anděl, J. Základy matematické statistiky. Matfyzpress. Praha 2005Lehmann, E.L., Casella G.: Theory of Point Estimation. New York: Springer. 2003 (EN)Hogg, V.R., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics. Seventh Edition, 2012. Macmillan Publishing Co., INC. New York. ISBN-13: 978-0321795434Militký, J.: Statistické techniky v řízení jakosti. Pardubice : TriloByte, 1996.
 Planned learning activities and teaching methods: The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
 Assesment methods and criteria linked to learning outcomes: Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing both written exams and semester assignment acceptance. Preparing and defending a project. Evaluation according to the number of points from the project: 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).
 Language of instruction: Czech
 Work placements: Not applicable.
 Course curriculum: Not applicable.
 Aims: The course objective is to make students majoring in Mathematical Engineering acquainted with methods of estimation theory, asymptotic approach to statistical hypotheses testing and prepare students for independent applications of these methods for statistical analyse of real data
 Specification of controlled education, way of implementation and compensation for absences: Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Type of course unit:

Lecture: 26 hours, optionally doc. RNDr. Libor Žák, Ph.D. Unbiased and consistent estimates Regular family of distributions, Rao - Cramér theorem, efficient estimates Fisher information and Fisher information matrix Sufficient statistics, Neuman factorization criterion Rao - Blackwell theorem and its applications Method of moments, maximum likelihood method Bayes approach Testing statistical hypotheses Principles of nonparametric methods Exponential family of distribution Asymptotic tests based on likelihood function Tests with nuisance parameters, examples Tests of hypotheses on parameters 13 hours, compulsory doc. RNDr. Libor Žák, Ph.D. Survey of probability distributions, graphs of densities in MATLAB Unbiased and consistent estimates - examples of estimates and verification of their properties Computation of the lower bound for variance of unbiased estimates Determination of Fisher information and Fisher information matrix for given distributions Applications of Neuman factorization criterion Findings estimates by Rao - Blackwell theorem Estimator’s determination by method of moments and by maximum likelihood method Estimator’s determination by Bayes method Project setting - finding parameters estimates for given distribution - application at least two approaches, verification properties of the estimates and their numerical computation Verification of exponential family for given distribution Application of asymptotic tests based on likelihood function Tests with nuisance parameters, estimates of parameters for Weibull and gamma distribution Tests of hypotheses on parameters of generalized linear model

The study programmes with the given course