Markov chain Monte Carlo (MCMC) algorithms have played a significant role in Statistics, Physics and Computing science over the last two decades. Among the large class of these sampling algorithms, the Metropolis algorithm is found among the ten algorithms which have the greatest influence on the development of science and engineering in the 20th century (Beichl and Sullivan, 2000). We first present some of the applications of MCMC for graphs and networks sampling where mathematical proofs and simulations will be introduced. Following, we link MCMC to Machine Learning and Data Science by presenting a method to estimate the kernel bandwidth in supervised learning.


Beichl and F. Sullivan. The Metropolis algorithm. Computing in Science & Engineering, 2:1,pp: 65-69. 2000.