Statistical Decision Theory

Course guarantor:

Václav Kůs

Lecturer:

Václav Kůs

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:

01MIP (Measure and Probability) + 01MAS (Matehmatical Statistics), or 01PRST (Probability and Mathematical Statistics)

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 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: