Statistical Decision Theory

Garant předmětu:

Lecturer:

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (elective course)
• BS Matematické inženýrství - Matematická fyzika (elective course)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (elective course)
• BS Informatická fyzika (elective course)
• BS Aplikace softwarového inženýrství (elective course)
• BS Aplikovaná informatika (elective course)
• BS jaderné inženýrství B (elective course)
• BS Jaderné inženýrství C (elective course)
• BS Dozimetrie a aplikace ionizujícího záření (elective course)
• BS Experimentální jaderná a částicová fyzika (elective course)
• BS Inženýrství pevných látek (elective course)
• BS Diagnostika materiálů (elective course)
• BS Fyzika a technika termojaderné fúze (elective course)
• BS Fyzikální elektronika (elective course)
• BS Jaderná chemie (elective course)