“Introduction To Monte Carlo Algorithms”

Introduction To Monte Carlo Algorithms” by Werner Krauth (1998) is a cute, simple introduction to Monte Carlo algorithms with both amusing hand drawn images and informative graphics.  He starts with a simple game from Monaco for estimating $\pi$ (not Buffon’s Needle) and revises it to introduce the concepts of Markov Chain Monte Carlo (MCMC), ergodicity, rejection, and Detailed Balance (see also Haystings-Metropolis).  He then introduces the hard sphere MCMC example, Random Sequential Absorption, the 8-puzzle, and ends with some accelerated algorithms for sampling.