Abstract: Markov chain simulation methods are a mainstay of
computational statistics. Do they really work? It’s harder to answer
than one might think! I’ll review some real scandals and delineate some
standard ways of approaching the question–From proving theorems through
convergence diagnostics, along with their strengths and weaknesses. One
highlight will be a little known method of making inferences when you
can’t prove your chain has converged or even if it’s connected. This is
the approach of Besag-Clifford along with many more modern bells and
whistles. Of course, it has strengths and weaknesses too. There is a lot
to think about, but many people HAVE been thinking.