Markov Chain Monte Carlo: Sampling High-Dimensional Distributions

This lecture introduces the concept of Markov Chain Monte Carlo (MCMC) as a powerful algorithm for sampling high-dimensional probability distributions. It covers the Metropolis-Hastings algorithm, detailed balance equations, and practical implementation strategies. The lecture discusses the challenges of sampling from high-dimensional distributions, the advantages of MCMC methods, and their applications in solving optimization problems like the Knapsack Problem and cryptography. Examples include the Ising model and decoding ciphers using MCMC. The instructor emphasizes the importance of understanding the power and pitfalls of MCMC algorithms.