Overview

Nowadays there exist several branches of so-called statistical inferences that are common for the mathematical statistics, data mining, and machine learning.

While the statistics and probability are traditionally studied in mathematical departments, the data mining and machine learning are specified to computer science education. What can be lost during the process of such divergence is the basic common knowledge that may help to avoid confusion and mistakes.

The novel contributions are mostly informal and linked usually to the Bayesian point of view. Moreover, the probability theory itself is more than Kolmogorov's axiomatic approach: until now the frequentist approach of R. von Mises coexists with novel contributions from quantum probabilities.

This course tries to show the existing diversity of approaches while staying within classical Kolmogorov's probability theory. The necessary classical theoretical material would be explained as well. We aim to consider several paradoxical situations that arise in practice.

Most examples belong to natural sciences and simple situations in the data analysis, the outcome is expected to be the practical training in data processing together with the ability to critically read a professional text. A standard undergraduate course in calculus is required, some basic experience in MATLAB or PYTHON programming would be appreciated. As an option, all the exercises and the numerical tests can be solved using OCTAVE --- the freeware clone of the MATLAB.