Стохастические модели

2024/2025

Статус: Маго-лего

Кто читает: Международная лаборатория прикладного сетевого анализа

Когда читается: 3 модуль

Охват аудитории: для своего кампуса

Язык: русский

Кредиты: 3

Полная версия программы учебной дисциплины

Аннотация

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.

Цель освоения дисциплины

The course gives students an important foundation to develop and conduct their own research as well as to evaluate research of others.

Планируемые результаты обучения

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.