Course description
Statistics teaches us how to behave in the face of uncertainties, according to the famous mathematician Abraham Wald. Roughly speaking, we will learn strategies of treating chances in everyday life. The main concept is that our inference is based on a randomly selected sample from a large population, and hence, our observations are treated as random variables. Applications are also discussed, mainly on a theoretical basis, but we make the students capable of solving numerical exercises by choosing the most convenient method for a given real-life problem.

Topics:

1. Short introduction (refreshment) to probability theory (random variables, laws of large numbers, Central Limit Theorem).
2. Descriptive study of data. Statistical sample, basic statistics.
3. Basic concepts of testing hypotheses and point estimation.
4. Inferences about a population.
5. Comparing two treatments.
6. Regression analysis (linear regression, model fitting).
7. Analysis of variance.
8. Analysis of categorized data (contingency tables).
9. If time permits, we will cover the following topics too: sufficiency, efficiency and consistency of estimators, Neyman-Fisher factorization, Cramer-Rao inequality, Neyman-Pearson theorem.