Markov Chains - From Probability Transition Matrix to Ergodic Properties and Algorithms - L24

Explore the mathematical foundations and computational methods of Markov chains in this comprehensive lecture covering probability transition matrices, ergodic properties, and practical algorithms. Learn how transition matrices relate to column-L1-normalized adjacency matrices of graphs and understand key concepts including non-transient, non-absorbing, acyclic, and connected states. Discover the importance of limiting states and delicate balance principles in Markov chain analysis. Master four essential algorithms for working with Markov chains: eigenvalue methods, power method iterations, random walk simulations, and gain exposure to Metropolis algorithms for advanced applications in data science and probability theory.