Just for friendly argument’s sake, allow me to disagree a little bit, and explain why. It’s a shame if we can’t allow people to learn and share mathematical int

Just for friendly argument’s sake, allow me to disagree a little bit, and explain why. It’s a shame if we can’t allow people to learn and share mathematical intuition in small pieces. I like that the author saw the boundary behavior and thought about it, questioned why it actually works. The intuitive argument presented does take one step in the direction of detailed balance, it just doesn’t cover the continuous case. (And I’m not sure - does detailed balance actually apply to the boundary? The process doesn’t run in reverse for areas where your probability field goes to zero, right?) I don’t necessarily think that an article on math should cover everything that is known about a subject. It’s okay to write for an audience that doesn’t know anything about autocorrelation and multi-chain methods. The need to elaborate so thoroughly on every possible prerequisite and/or application, and cover every corner case you might have is one of the reasons so many people dislike reading math on Wikipedia ... it’s unapproachable unless you already know everything about it. It’s becoming a reference only for experts not very usable for learning by a student. Anyway, what’s the true danger of a simple or incomplete understanding? It’s not that likely to lead to people putting the wrong thing into nuclear reactors; isn’t it more likely to lead to someone getting the wrong answer in a weekend project software and then spending Sunday learning a little more about MCMC methods?