Магистратура
2026/2027
Стохастические модели
Статус:
Курс по выбору (Аналитика данных и прикладная статистика / Data Analytics and Social Statistics)
Где читается:
Факультет социальных наук
Когда читается:
2-й курс, 3 модуль
Охват аудитории:
для своего кампуса
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
- Be able to develop and/or foster critical reviewing skills of published empirical research using applied statistical methods
- 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 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.
- Know the theoretical foundation of stochastic processes.
- Be able to work with major linear modeling programs, especially Python, so that they can use them and interpret their output.
- Know the theoretical foundation of stochastic processes.
- Havet he skill to meaningfully develop an appropriate model for the research question.
Course Contents
- Introduction to Stochastic Paradigms
- Modeling Stochastic Systems
- Random Walks, the Wiener Process, and Martingales
- Agent-Based Modeling
- Noise and Representativeness
- Evaluating the Significance and Utility of Numerical Simulations
- Analyzing Complex Non-analytic Systems
- Numerical Modeling on Graphs and Networks
- State-of-the-Art Topics
- Applications Examples
Assessment Elements
- In-class activity
- Homework with explanations
- Presentation
- Student case report peer review
- Solving seminar exercises after the seminar using a non-presented approach
Interim Assessment
- 2026/2027 3rd moduleFinal grade = 0.2 × In-class activity (seminar exercises solving) + 0.4 × Homework with explanations (8 blocks of exercisers - 20% from the maximum for each week of late homework submission) + 0.4 × Presentation (student case report) + Extra [0.1 for student case report peer review + 0.1 for solving seminar exercises after the seminar using a non-presented approach with in-person online explanations]
Bibliography
Recommended Core Bibliography
- A first look at stochastic processes, Rosenthal, J. S., 2020
- Chandra, T. K., & Gangopadhyay, S. (2018). Introduction to Stochastic Processes. New Delhi: Narosa Publishing House Pvt. Ltd. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2023979
- Ghahramani, S. (2018). Fundamentals of Probability : With Stochastic Processes (Vol. Fourth edition). Boca Raton, FL: Chapman and Hall/CRC. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1875108
Recommended Additional Bibliography
- Charu C. Aggarwal. (n.d.). Chapter 1 AN INTRODUCTION TO SOCIAL NETWORK DATA ANALYTICS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.A1C03FD0
- Ibe, O. C. (2013). Markov Processes for Stochastic Modeling (Vol. 2nd edition). Chennai: Elsevier. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=516132
- Paul Embrechts, Chapter In P. Embrechts, R. Frey, & A. Mcneil. (2004). Stochastic Methods for Quantitative Risk Management. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.E3A771C1
- Quantal response equilibrium : a stochastic theory of games, Goeree, J. K., 2016
- Stochastic programming in supply chain risk management : resilience, viability, and cybersecurity, Sawik, T., 2024