VBA 224E - Stochastic Models in Data Science

Course Objectives

I. Gain a thorough understanding of probability theory, stochastic processes, and Markov chains, including their discrete and continuous-time variants.
II. Learn to apply Markov chain models for transient and stationary analysis, and explore applications of exponential and Poisson distributions in real-world scenarios.
III. Analyze queueing systems such as M/M/1, M/M/k, M/M/k/N, and G/M/1 through birth and death processes, understanding their dynamics and performance metrics.
IV. Develop proficiency in Monte Carlo simulation techniques, including generating random numbers, variance reduction methods, and analyzing simulation results for accuracy and efficiency.
V. Explore heuristic optimization methods like simulated annealing, tabu search, and genetic algorithms, and apply multi-criteria optimization techniques to solve complex decision-making problems effectively.

Course Description

This course covers foundational and advanced topics in probability, stochastic processes, simulation, and optimization techniques essential for modeling and analysis in various domains. Topics include Markov chains, Poisson processes, queueing systems, Monte Carlo simulation, agent-based modeling, and heuristic optimization methods like simulated annealing and genetic algorithms. Gain practical skills in analyzing complex systems and optimizing decision-making processes through hands-on simulations and multi-criteria optimization approaches.