Delivered at:: Big Data and Information Retrieval School

Course type:: Compulsory course

When:: 2 year, 1-4 module

Instructors

Goryainov, Alexander

Zhukov, Pavel

Lukianchenko, Peter

Full Syllabus

Abstract

This course is designed to introduce students to the basic ideas and methods of statistics as well as the application of statistical methods in econometrics, data science and the social sciences. This course provides some of the analytical tools that are required by advanced courses of data science and machine learning. This course provides students with experience in the methods and applications of statistics to a wide range of theoretical and practical situations. The course is taught in English. Prerequisites are Calculus (functions of several variables, partial derivatives, integrals, maximum of functions), and elements of Linear algebra (vectors, matrices, linear equations).

Learning Objectives

This course introduces some of the basic ideas of theoretical statistics, emphasizing the applications of these methods and the interpretation of tables and results.
We will introduce concepts and methods that provide the foundation for more specialised courses in statistics.

Expected Learning Outcomes

Students will be able to apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments.
Students will be able to choose appropriate methods of inference to tackle real problems.
Students will be able to explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform hypothesis tests in a number of different settings.
Students will be able to explain the principles of data reduction.
Students will be able to perform inference to test the significance of common measures such as means and proportions and conduct chi-squared tests of contingency tables.
Students will be able to recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions.
Students will be able to routinely apply a variety of methods for explaining, summarising and presenting data and interpreting results clearly using appropriate diagrams, titles, and labels when required.
Students will be able to summarise the ideas of randomness and variability and the way in which these link to probability theory to allow the systematic and logical collection of statistical techniques of great practical importance in many applied areas.
Students will be able to use simple linear regression and correlation analysis and know when it is appropriate to do so.
Students will demonstrate an understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems.
Students will have a grounding in probability theory and some grasp of the most common statistical methods.

Course Contents

Data presentation.
Elements of probability theory.
Discrete random variables.
Continuous random variables.
Multivariate random variables.
Conditional distributions.
Limit theorems.
The normal distribution and ideas of sampling.
Populations and samples.
Point estimation of parameters.
Confidence intervals.
Testing of statistical hypotheses.
Linear regression.
ANOVA.
Experiment design.

Assessment Elements

Spring Midterm
Homework
The number of score points for the tasks will be determined individually for each paper and announced by the teacher. The total grade will be calculated by combining the score points. The grading system may be specified in the paper. A partial score may be given for an incomplete answer if the criteria are formulated in advance. Homework submitted after the general deadline will not be accepted. Any fact of cheating or breach of academic integrity will result in receiving a "0" (zero) for this work.
Fall midterm
At the end of the module the students sit a written exam.
December Exam

Interim Assessment

2024/2025 3rd module
Grade=45% * Fall Midterm + 35% * December Exam + 20% * HW
2024/2025 4th module
Final Grade = 20% * Fall Midterm + 15% * December Exam + 10% * HW (m1+m2) + 25%* Spring Midterm + 10%* HW (m3) + 20%* HW(m4).

Bibliography

Recommended Core Bibliography

Statistics for business and economics, Newbold, P., 2007

Recommended Additional Bibliography

Bartoszyński, R., & Niewiadomska-Bugaj, M. (2008). Probability and Statistical Inference (Vol. 2nd ed). Hoboken, N.J.: Wiley-Interscience. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=219782
Freund, J. E., Miller, I., & Miller, M. (2014). John E. Freund’s Mathematical Statistics with Applications: Pearson New International Edition (Vol. Eighth edition, Pearson new international edition). Essex, England: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418305
Hogg, R. V., McKean, J. W., & Craig, A. T. (2014). Introduction to Mathematical Statistics: Pearson New International Edition. Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1418145
Hogg, R. V., Zimmerman, D. L., & Tanis, E. A. (2015). Probability and Statistical Inference, Global Edition (Vol. Ninth edition. Global edition). Boston: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419274
Larsen, R. J., & Marx, M. L. (2015). An introduction to mathematical statistics and its applications. Slovenia, Europe: Prentice Hall. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.19D77756
Lindgren, B. W. (1993). Statistical Theory (Vol. Fourth edition). Boca Raton, Florida: Routledge. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1683924

Authors

LUKYANCHENKO PETR PAVLOVICH

Bachelor’s Programme 'Data Science and Business Analytics'

Probability Theory and Mathematical Statistics