Магистратура
2025/2026
Стохастические модели
ID 947848
Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус:
Курс по выбору (Аналитика данных и прикладная статистика / Data Analytics and Social Statistics)
Когда читается:
2-й курс, 3 модуль
Охват аудитории:
для своего кампуса
Преподаватели:
Петров Илья Владимирович
Язык:
английский
Кредиты:
3
Контактные часы:
40
Course Syllabus
Abstract
This course guides students through practical stochastic methods to model, simulate, and analyze complex systems where uncertainty, interaction, and non-analytic behavior dominate. It connects probability paradigms with computational modeling to support understanding, research, and decision-making through simulation. The goal of the course is to enable students to design and implement Monte Carlo and agent-based models and to assess the usability and value of such models. Students will be able to identify when simulation is appropriate and to set up reproducible numerical experiments.
Learning Objectives
- To provide students with a solid theoretical foundation in stochastic paradigms (randomness and chaos), key probabilistic approaches (frequentist and Bayesian), processes (e.g., Markov), methods (analytical versus Monte Carlo and agent-based), and the mathematical principles underlying randomness, uncertainty, evolution, and emergence.
- The course involves mastering a broad range of methodologies, selected and applied depending on the given problem. The main part of the course is based on the application of numerical methods, but it also covers relevant analytical, statistical, and various hybrid approaches. These include Bayesian methods and updates, Markov chains, numerical vs. analytical solutions, and more. The choice and applicability evaluation of these approaches are based on the system’s properties, available data, and specific task.
- We will cover a wide range of problems, from simulating random processes to the stochastic modeling of games, including Bayesian approaches. We will also explore numerical methods for analyzing complex systems and emergence, and, among other things, test data analysis methods using numerical examples. This will foster a deep understanding of how numerical techniques allow us to tailor our methods to a specific task, test hypotheses, and determine the properties of complex systems.
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
- 2025/2026 3rd module0.2 * Homework Assignments + 0.5 * Final In-Class or Take-home exam + 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
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