2023/2024
Probability Theory, Statistics and Exploratory Data Analysis
Type:
Mago-Lego
Delivered by:
Big Data and Information Retrieval School
When:
2 module
Online hours:
20
Open to:
students of one campus
Instructors:
Yana Khassan
Language:
English
ECTS credits:
3
Contact hours:
12
Course Syllabus
Abstract
The core concept of the course is random variable — i.e. variable whose values are determined by random experiment. Random variables are used as a model for data generation processes we want to study. Properties of the data are deeply linked to the corresponding properties of random variables, such as expected value, variance and correlations. Dependencies between random variables are crucial factor that allows us to predict unknown quantities based on known values, which forms the basis of supervised machine learning. We begin with the notion of independent events and conditional probability, then introduce two main classes of random variables: discrete and continuous and study their properties. Finally, we learn different types of data and their connection with random variables.
While introducing you to the theory, we'll pay special attention to practical aspects for working with probabilities, sampling, data analysis, and data visualization in Python.
Learning Objectives
- моделировать и изучать случайные величины с помощью Python
- понимать различные способы определения случайной величины; - изучать связи между случайными величинами
- анализировать дискретные и непрерывные случайные величины
- использовать закон полной вероятности и правило Байеса
- выражать проблемы реальной жизни в терминах событий, вероятностей, случайных величин
Expected Learning Outcomes
- use the law of total probability and the Bayes rule; analyze discrete and continuous random variables; understand different ways of determining a random variable; - study the relationships between random variables; simulate and study random variables using Python.
- express real-life problems in terms of events, probabilities, random variables; use the law of total probability and the Bayes rule; analyze discrete and continuous random variables; understand different ways of determining a random variable; - study the relationships between random variables; simulate and study random variables using Python.
Course Contents
- Conditional probability and independence of events. Definitions and applications. Mutual and pairwise independence. Bernoulli scheme. The law of total probability. Bayes rule.
- Random variables; Properties of random variables; Continuous random variables; The law of large numbers and the central limit theoremPractical project: building a Bayesian classifier Multidimensional distribution
Bibliography
Recommended Core Bibliography
- An introduction to mathematical statistics and its applications : student solution manual, Larsen, R. J., 2012
- Basics of modern mathematical statistics : exercises and solutions, , 2014
- Elements of mathematical statistics, Alexander, H. W., 1961
- 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
- Introduction to mathematical statistics and its applications, Larsen, R. J., 2014
- Introduction to mathematical statistics, Hogg, R. V., 2005
- Introduction to mathematical statistics, Hogg, R. V., 2014
- 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
- Mathematical statistics and data analysis, Rice, J. A., 2007
- Mathematical statistics with applications, Wackerly, D. D., 2008
- Modern mathematical statistics with applications, Devore, J. L., 2007
Recommended Additional Bibliography
- An introduction to mathematical statistics and its applications, Larsen, R. J., 2012
- 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
- Mathematical statistics : Asymptotic minimax theory, Korostelev, A., 2011
- Mathematical statistics and data analysis, Rice, J., 2007
- Mathematical statistics with applications in R, Ramachandran, K. M., 2015
- Mathematical statistics with applications, Wackerly, D. D., 2002