Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Mathematical Statistics

    A tantárgy neve magyarul / Name of the subject in Hungarian: Matematikai statisztika

    Last updated: 2024. február 17.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Course ID Semester Assessment Credit Tantárgyfélév
    VISZMA11   3/0/1/v 5  
    3. Course coordinator and department Dr. Pintér Márta,
    4. Instructors
    Dr. Márta Pintér, associate professor, Department of Computer Science and Information Theory

    Máté Vizer, teaching assitant, Department of Computer Science and Information Theory
    5. Required knowledge Probability, mathematical analysis, linear algebra
    7. Objectives, learning outcomes and obtained knowledge The objective of the course is to introduce the basic principles and methods of mathematical statistics and their applications in a series of introductory lectures and laboratories. In the second half of the semester, laboratory exercises will be used to illustrate the applications of the methods using a statistical software package (e.g. R). Besides learning how to use the software system, students will be confronted with the usefulness of the material through complex statistical analysis of data matrices.
    8. Synopsis
    1. Review of concepts in probability   

    2. Basic concepts of mathematical statistics: population, sample, sampling, sample number determination, statistics, parameter. 

    3. Parameter estimation 1 - point estimation, properties of estimation (unbiasedness, consistency, strong consistency, efficiency), specific estimation procedures (maximum likelihood method, method of moments) and their properties 

    4. Parameter estimation 2 - Student distribution, interval estimation, confidence interval 
    Hypothesis testing 1 - new distributions (chi-square distribution, Fisher distribution), introduction to hypothesis testing, basic concepts 

    5. Hypothesis testing 2 - parametric tests: one- and two-sample, one- and two-sided u- and t-tests. The F-test and the Welch test. 

    6. Hypothesis testing 3/non-parametric tests 1 - Kolmogorov-Szmirnov tests. Kruskal-Wallis, Wilcoxon, Friedman, sign and Mann-Whitney tests. 

    7. Hypothesis testing 4./ Non-parametric tests 2. - Chi-square tests, analysis of variance, Friedman test, exact tests

    8. Regression analysis 1 - introduction, theoretical, bivariate linear, least squares, regressions back to linear 

    9. Regression Analysis 2 - Multivariate Linear 1 - task definition, coefficient estimates, coefficients and model testing 

    10. Regression Analysis 3 - Multivariate Linear 2 - Model building, coefficients of correlation, partial and multiple correlation. 

    11. Principal component analysis, multivariate scaling, cluster analysis 

    12. Stochastic processes - Markov chains, Poisson process 

    13. Time series 1 - Deterministic methods, trend analysis. Exponential filtering.

    14. Time series 2 - Box-Jenkins time series models (AR, MA, ARMA models)
    9. Method of instruction 3 lectures per week and 1 labratory exercise per week.
    10. Assessment
    A successful midterm test (at least 40%) and homework assigngment to be handed in by the end of the semester  are required for a signature. The homework is a complex statistical analysis on a data matrix. In addition to the evaluation of the resulting tables and graphs, the homework must include a mathematical description of the method used.

    The examination is oral and based on a given set of topics. In addition to the oral answer (50%), the mark will include the midterm result (30%) and the homework result (20%).
    11. Recaps
    During the semester, there is a retake for the midterm, which may be used to complete the missed midterm or to improve the result of an unsuccessful midterm or to improve the result of a successfully completed midterm. If someone retakes an already  written midterm, the new mark will be valid - even if it is worse than the previous one. If a person attends a retake, they are considered to have attempted to write the test. If someone attempts to correct a successful midterm but scores less than 40% on the retake, they will only lose the points above 40% of their original midterm score (i.e. they will carry forward 40%). At least 70% of the labs, i.e. at least 5 out of 7 sessions, must be attended, no make-ups are possible.

    The homework may be submitted late during the  make-up week for a special procedure fee.
    12. Consultations By appointment.
    14. Required learning hours and assignment
    In class56
    Preparation for lectures20
    Preparation for midterms14
    Homework20
    Preparation for the final40
    Total150
    15. Syllabus prepared by
    Dr. Márta Pintér, associate professor, Department of Computer Science and Information Theory

    Máté Vizer, teaching assitant, Department of Computer Science and Information Theory