Description:

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.

Contents:

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.

Recommended literature:

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.

Keywords:

Loss functions, optimal strategies, Bayesian risk, minimax solution, admissibility, aproximative calculation.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar