- Come up with a model.
- Write MCMC code to sample parameters of the model.
- Run MCMC code with available data.
- Notice that it doesn't work.
- Spend several months getting the MCMC to work.
I recently came across an old discussion in The American Statistician (found here, it might be behind a paywall depending on where you are), where three experienced practitioners discuss best MCMC practices. I wish I had read this discussion a few years ago, for two reasons: 1) It contains a lot of useful tips that I had to learn the hard way. 2) It makes it clear that MCMC vary a lot, depending on your personal preference, domain of application, degree of complexity of your model and so on.
What I take away from this discussion is that in order to be successful at sampling with MCMC, you need to be tenacious, resourceful, and rigorous. Whenever I have failed at an attempt, it was usually because I took a "choose two out of three" approach to these qualities. Here's hoping success will come easier in the future.