Demystifying Markov Chain Monte Carlo: A Simple Explanation

This post provides a clear and accessible explanation of Markov Chain Monte Carlo (MCMC), a powerful technique for sampling from complex probability distributions. Using an analogy of estimating probabilities of baby names, the author illustrates the core problem MCMC solves. The explanation cleverly relates MCMC to a random walk on a graph, leveraging the stationary distribution theorem to show how to construct a Markov chain whose stationary distribution matches the target distribution. The Metropolis-Hastings algorithm, a common MCMC method, is introduced and its effectiveness is demonstrated.