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