User:IssaRice/Metropolis–Hastings algorithm

without exception, every single explanation i have seen so far of this absolutely sucks. like, not just "most really suck, and some suck a little". literally everything just sucks really bad. this might be my best guess for the most horribly-explained thing ever.

in my opinion, the things a good explanation must cover are:

• what the heck is sampling, even? once we have a fair coin, use that to generate samples for:
  • arbitrary biased coin
  • a discrete uniform distribution over 1,...,n
  • a continuous uniform(0,1) distribution
  • use a continuous uniform to sample from an arbitrary distribution using inverse transform sampling
  • bonus: go from a biased coin (with unknown bias) to a fair coin
• why doesn't inverse transform sampling work in situations where we have to use metropolis-hastings?
• an actually convincing example of MCMC. the stuff i've seen so far are so boring i just don't even care if we can sample from it.
• where the heck does the accept/reject rule come from? why this division thing to get the threshold?
• why do we need a transition matrix, can this matrix be literally anything, and why do we care if it's symmetric?