Theory of Statistical Decision 1000-135TDS

The aim of the course is to present basics of the theory of statistical decisions. This theory interprets statistics as a game between a "statistician" and "nature". This allows for a unified treatment of such problems as estimation, testing hypotheses, prediction and other. Decision-theoretic notions are now widely accepted as foundations of mathematical statistics.
The course is particularly focused on bayesian statistics, because of its increasing importance and numerous applications. It covers estimation, discussion of different loss functions, classification, testing hypotheses and introduction to model choice from the bayesian perspective. Selected applications of the bayesian theory will be presented in detail, e.g. "credibility theory" in insurance mathematics, simple models of pattern recognition and image reconstruction, etc.