PROBABILITY ANDSTATISTICS: THEORYAND IMPLEMENTATION

ANDREYKHOKHLOV

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.

After getting his Ph.D. in Algebraic Topology in 1983 Andrey worked in several scientific and/or teaching organisations, among them are the Russian Academy of Sciences, Moscow State University, and Baumann Technology University. The Scientific advising of the graduate and thesis students was part of his activities, not only in Russia, but also in France.

Andrey’s main results in science are linked with geophysical data processing, so naturally his teaching interests are now concentrated in the applied methods of Statistics and their algorithmic implementations. He currently helps his students avoid some common errors within the probabilistic inferences and support their attempts to study Probability and Statistics theory in general.

This course tries to show the existing diversity of approaches while staying within the classical Kolmogorov's probability theory. The necessary classical theoretical material would be explained as well.

First of all, we aim to improve practical skills in probabilistic methods of data analysis: technical details nowadays are well implemented as parts of computational packages, however, there are still many chances to confuse the logic of the method design.

There exists also several similar vocabularies that are used for the significantly different approaches --- they also should be studied to avoid misinterpretations and erroneous results. The training in reading the modern and classical texts in Probability and Statistics is also an important goal of the course.

**SKILLS:**

-Mathematical Statistics

-Probability

-Python

-C++

-OpenGL

-LATEX

-MS Visual Studio

ABOUT ANDREY

**HARBOUR.SPACE **

WHAT YOUWILL LEARN

**DATE:** 25 Nov - 13 Dec, 2019

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

**LOCATION: **__Barcelona, Harbour.Space Campus__

**COURSE TYPE: **Offline

HARBOUR.SPACEUNIVERSITY

**DATE: **25 Nov - 13 Dec, 2019

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

**LOCATION: **Barcelona, Harbour.Space Campus

**COURSE TYPE: **Offline

All rights reserved. 2017

COURSE OUTLINE

**Session 1**

Classical finite models and the need of the rigid theory. Paradoxes and Natural Sciences

**Session 4**

Heuristic non-finite models derived by means of the symmetry arguments. Algebra of events and the corresponding mathematical theory. Probabilities in discrete sample spaces and axiomatic approach

**Session 3**

Conditional probabilities, the independence of events and its formal properties. Bayesian approach for finite and infinite discrete cases

**Session 2**

Combinatorics, cases of distinguishable and indistinguishable objects. Generation functions and other computational tools

PROBABILITYAND STATISTICS:THEORY ANDIMPLEMENTATION

REQUIRED READING

Numerical Recipes 3rd Edition:The Art of Scientific Computing byWilliam H. Press, Saul A. Teukolsky,William T. Vetterling& Brian P. Flannery(Cambridge University Press,2007)

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.

This course tries to show the existing diversity of approaches while staying within the classical Kolmogorov's probability theory. The necessary classical theoretical material would be explained as well.

First of all, we aim to improve practical skills in probabilistic methods of data analysis: technical details nowadays are well implemented as parts of computational packages, however, there are still many chances to confuse the logic of the method design.

There exists also several similar vocabularies that are used for the significantly different approaches --- they also should be studied to avoid misinterpretations and erroneous results. The training in reading the modern and classical texts in Probability and Statistics is also an important goal of the course.

Andrey’s main results in science are linked with geophysical data processing, so naturally his teaching interests are now concentrated in the applied methods of Statistics and their algorithmic implementations. He currently helps his students avoid some common errors within the probabilistic inferences and support their attempts to study Probability and Statistics theory in general.