Markov Chains and Algorithm Applications

This lecture covers the concept of Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling. The instructor explains the goal of sampling from the stationary distribution of a Markov chain, emphasizing the importance of convergence rate and mixing time. The lecture delves into the Metropolis-Hastings algorithm, detailing the process of constructing a Markov chain with a desired limiting distribution. It also discusses the design of acceptance probabilities and the criteria for aperiodicity and irreducibility. The lecture concludes by highlighting the significance of detailed balance in sampling 'hard' distributions.