Магистратура
2024/2025
Стохастические модели
Статус:
Курс по выбору (Аналитика данных и прикладная статистика / Data Analytics and Social Statistics)
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет социальных наук
Когда читается:
2-й курс, 3 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Прогр. обучения:
Прикладная статистика с методами сетевого анализа
Язык:
английский
Кредиты:
3
Course Syllabus
Abstract
Mathematical models based on probability theory prove to be extremely useful in describing and analyzing complex systems that exhibit random components. The goal of this course is to introduce several classes of stochastic processes, analyze their behavior over a finite or infinite time horizon, and help students enhance their problem solving skills. The course combines classic topics such as martingales, Markov chains, renewal processes, and queuing systems with approaches based on Stein’s method and on concentration inequalities. The course focuses mostly on discrete-time models and explores a number of applications in operations research, finance, and engineering. This is an elective course, offered to MASNA students, and examples used in class may differ depending on students’ interests.
Learning Objectives
- The course gives students an important foundation to develop and conduct their own research as well as to evaluate research of others.
Expected Learning Outcomes
- Have the skill to meaningfully develop an appropriate model for the research question
- Have the skill to work with statistical software, required to analyze the data.
- Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods.
- Be able to criticize constructively and determine existing issues with applied linear models in published work .
- Be able to explore the advantages and disadvantages of stochasticity in the models and demonstrate how it contributes to the analysis.
- Be able to work with major linear modeling programs, especially R, so that they can use them and interpret their output.
- Have an understanding of the basic principles of stochastic models and lay the foundation for future learning in the area.
- Know modern extensions to stochastic modeling.
- Know the basic principles behind working with all types of data for using stochastic components in models.
- Know the theoretical foundation of stochastic processes.
Course Contents
- Understanding randomness
- Stein’s method and central limit theorems
- Conditional expectation and martingales
- Probability inequalities
- Discrete-time Markov chains
- Renewal theory
- Queueing theory (multiple class meetings)
Interim Assessment
- 2024/2025 3rd module0.5 * Final In-Class or Take-home exam + 0.2 * Homework Assignments + 0.2 * In-Class Labs + 0.1 * Quizzes
Bibliography
Recommended Core Bibliography
- Medhi, J. (2003). Stochastic Models in Queueing Theory (Vol. 2nd ed). Amsterdam: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=205403
- Meerschaert, M. M., & Sikorskii, A. (2011). Stochastic Models for Fractional Calculus. Berlin: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=430094
- Ruggeri, F., Ríos Insua, D., & Wiper, M. M. (2012). Bayesian Analysis of Stochastic Process Models. Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=443018
Recommended Additional Bibliography
- Li, Q.-L. (2010). Constructive Computation in Stochastic Models with Applications : The RG-Factorizations. Beijing: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=374057