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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Statistical Decision Theory

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Code Completion Credits Range Language
01STR ZK 2 2+0 Czech
Lecturer:
Václav Kůs (guarantor)
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The subject is devoted to the statistical techniques for general decision procedures based on optimization of suitable stochastic criterion, their mutual comparisons with respect to their properties and applicability.

Requirements:

01MAS or 01PRST, recommended 01MIP.

Syllabus of lectures:

1. General principles of classical statistics.

2. Loss and risk functions, decision functions, optimal strategies.

3. Bayes and minimax solutions, admissibility principle and its consequences within classical statistics.

4. Convex loss functions, properties of Bayes estimates.

5. Unbiasedness, sufficiency, Rao-Blackwell theorem and its applications, UMVUE estimators.

6. Minimum distance estimates.

7. Computational aspects for Bayesian methods, numerical procedures, approximative calculations.

8. Examples from the survival data analysis under random censoring experimental scheme.

Syllabus of tutorials:
Study Objective:

Knowledge:

Extension of the decision makinng principles with random effects and their application in optimization tasks.

Skills:

Orientation in various stochastical approaches and their properties. Practical task solvations within risk models and numerical treatment.

Study materials:

Key references:

[1] Berger J.O., Statistical Decision Theory and Bayesian Analysis, Springer, N.Y., 1985.

Recommended refernces:

[2] Fishman G.S., Monte Carlo, Springer, 1996.

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-10-18
For updated information see http://bilakniha.cvut.cz/en/predmet24173405.html