Probability Theory and Statistics III - JEB035

• Title: Pravděpodobnost a matematická statistika III
• Guaranteed by: Institute of Economic Studies (23-IES)
• Faculty: Faculty of Social Sciences
• Actual: from 2007 to 2009
• Semester: winter
• E-Credits: 7
• Examination process: winter s.:
• Hours per week, examination: winter s.:2/2, C+Ex [HT]
• Capacity: unknown / unknown (unknown)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: Czech
• Teaching methods: full-time
• Teaching methods: full-time
• Note: course can be enrolled in outside the study plan; enabled for web enrollment
• Guarantor: prof. RNDr. Jan Ámos Víšek, CSc.; Ing. Monika Hollmannová
• Pre-requisite : JEB012

Annotation

Last update: VISEK (01.10.2012)

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.

Aim of the course

Last update: VISEK (01.10.2012)

To enlarge knowledge in statistics about some selected topics. To help in this way to the understanding of basic statistical ideas.

Literature

Last update: VISEK (01.10.2012)

Breiman, L. (1968): Probability, Addison-Wesley Publishing Company, London 1968.

Lehmann, E. L. (1998): Theory of Point Estimation (Springer Texts in Statistics)

Lehmann, E. L. (1998): Testing Statistical Hypotheses, (Springer Texts in Statistics).

Rao, R. C. (1973): Linear Statistical Inference and Its Applications. New York: J.Wiley and Sons.

Víšek, J. Á. : Selected Topics from Statistics. Carolinum.

Teaching methods

Last update: VISEK (01.10.2012)

Lectures with seminars.

Requirements to the exam

Last update: VISEK (01.10.2012)

Writing reports - homeworks from seminars and passing tests for credits.

Syllabus

English

Last update: VISEK (01.10.2012)

I. 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.

II. 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.

III. Contingency tables

Test of independence and of symmetry, Fisher´s and McNemara´s tests. Stuart´s test. Simpson paradox.

IV. 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.

Czech

Last update: VISEK (01.10.2012)

1. Opakování
Opakování základních pojmů a tvrzení ze Statistics I.

2. Bayesovská statistika

Základní idea, bayesova věta, třídy apriorních rozdělení, bodové odhady, prediktivní hustota.
2. Testy dobré shody
Multinomické rozdělení, testy chi-kvadrát při známých parametrech, testy chi-kvadrát při neznámých parametrech, testy normality, testy Poissonova rozdělení, Kolmogorovovy--Smirnovovy testy
3. Kontingenční tabulky.
Test nezávislosti, test homogenity multinomických rozdělení, některé další testy.
4. Výběrová šetření
Prostý náhodný výběr, odhad průměru, odhad rozptylu, intervaly spolehlivosti pro průměr, odhady poměrné četnosti, poměrový odhad, některé další typy výběru

Entry requirements

Last update: VISEK (01.10.2012)

Passing mathematics (JEB005, 006, 028 a 029) a statistics (JEB011 a 012).