Recently I was reading articles and books about MCMC, and realized that many materials were not taught in my graduate study. To this end, I decide to make a summary of such content, to assist readers and myself to gain deeper understanding of MCMC in the future. I hope to make this topic a series, although I cannot guarantee its completion. This article is the first one in this hypothetical series, and we are going to introduce an important concept, the geometric ergodicity.
