This lecture covers the rejection sampling method used to generate sample values from a target distribution X with an arbitrary probability density function, by using a proposal distribution Y. The process involves generating samples from Y and accepting them based on a certain probability. The lecture also delves into the implementation of a function to generate samples from X using rejection sampling, along with practical examples and applications. Additionally, it explores the concept of Bayesian inference using MCMC, emphasizing the importance of understanding transition probabilities and invariant distributions in Markov chains.