Introduction to Markov Chain Monte Carlo (MCMC)

This is a presentation I made and presented at an MIT class on Bayesian Learning. The presentation introduces the foundational concepts of Markov Chain Monte Carlo (MCMC) to students with prior knowledge of simpler statistical methods, such as rejection sampling and importance sampling. The session explores how MCMC improves parameter estimation in posterior distributions, addressing the limitations of basic techniques. After walking through the theoretical insights of MCMC and some practical demonstrations, the presentation ends with an application of MCMC in a Bayesian learning framework for a model built using Gen. The model detects linear regression parameters for a dataset while simultaneously assigning probabilities for outlier detection.