When MCMC fails: The advice we’re giving is wrong. Here’s what we you should be doing instead. (Hint: it’s all about the folk theorem.)

In applied Bayesian statistics we often use Markov chain Monte Carlo: a family of iterative algorithms that yield approximate draws from the posterior distribution. For example, Stan uses Hamiltonian Monte Carlo. One annoying thing about these iterative algorithms is that they can take awhile, but on the plus side this spins off all sorts of …