JEB035 - Advanced Statistics
| Credit: | 6 |
|---|---|
| Credit ETCS: | 6 |
| Hours weekly: | 2/2 |
| Status: | Bachelors - All Bachelors - elective BEF - elective English Semester - winter |
| Obligatory courses: | JEB105 - Statistics |
| Recommended courses: | |
| Course supervisors: | prof. RNDr. Jan Ámos Víšek CSc. |
| Teachers: | prof. RNDr. Jan Ámos Víšek CSc. |
| Assistants: | Mgr. Josef Stráský |
| Schedule: | |
| Announcements: | Homework 3 is now posted. |
| Literature: | J. Á. Víšek : Selected Topics from Statistics. Carolinum. Anděl, J.: Matematická statistika, SNTL & ALFA, Praha, Bratislava, 1978. Anděl, J. (1993): Statistické metody, MATFYZPRESS, Praha,1993. Antoch, J.- Vorlíčková, D.: Vybrané metody statistické analýzy dat. Academia, Praha, 1992. Rao, C., R.: Lineární metody statistické indukce a jejich aplikace. Academia, Praha, 1978. See also syllabus. |
| Description: | The course is a continuation of the courses Probability and mathematical statistics I and II and enlarges knowledge from there about the new topics, namely frequently used ones. Firstly, the attention is paid to the bayesian statistics, i.e. to the possibility to utilize the a priori obtained knowledge in the statistical inference. It is an approach which is altyernative to the classical Fisher statistics. Then we shall turn to the tests of good fit, processing of contingency tables and finally we will study theory of selection from finite populations. |
| Content: | 1. Repetition Repetition of principal concepts, definitions and theorems form courses Probability and Statstics I and II. 2. Bayesian statistics Basic idea of bayesian statistics, Bayes´ theorem, systems of apriori- distributions, uncertainty principal, Jeffrey´s theorem and corresponding system of apriori-distributions. Predictive density. Types of estimates. 3. Tests of good fit Chi-squre test of good fit with known and unknown parameters. Kolmogorov-Smirnovov´s tests. Tests of good fit for some special distributions. 4. Contingency tables Test of independence and of symmetry, Fisher´s and McNemara´s tests. Stuart´s test. Simpson paradox. 5. Sampling from finite populations Basic idea, support of selection, probabilities of drawing and inclusion in the sample and their relations. Types of sampling (simple random, Poisson´s, rejecting, Sampford´s, successive, stratified, more stages sampling), estimation of total. Representativeness, unbiasedness. Basic ideas of questionnaries. |
| Seminar: | |
| Examination dates: | The schedule of exams will be given before the end of term. |
| Course requirements: | 3 homeworks (posted on this page throughout semester) + exam test |
| Downloadable: | AS_evaluation_hw1 AS_evaluation_hw2 AS_evaluation_hw3 goodness_of_fit_tests_websources HW1 HW2 HW3 stat_tables_testsofgoodfit |