Statistical decision theory
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 01STR | ZK | 2 | 2+0 | Czech |
- Lecturer:
- Václav Kůs (gar.)
- Tutor:
- Václav Kůs (gar.)
- 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:
-
Basic course of Calculus and Probability (in the extent of the courses 01MAA3-4 or 01MAB3-4, 01PRA1 nebo 01PRST held at the FNSPE CTU in Prague).
- Syllabus of lectures:
-
General principles of classical statistics, loss and risk functions, decision functions, optimal strategies, Bayes and minimax solutions, admissibility principle and its consequences within classical statistics. Convex loss functions, properties of Bayes estimates, unbiasedness, sufficiency, Rao-Blackwell theorem, UMVUE estimators. Minimum distance estimates. Computational aspects for Bayesian methods, numerical procedures, approximative calculations, 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.
Abilities: Orientation in various stochastical approaches and their properties.
- Study materials:
-
[1] Berger J.O., Statistical Decision Theory and Bayesian Analysis, Springer, N.Y., 1985.
[2] Fishman G.S., Monte Carlo, Springer, 1996.
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans: