I think probably the single most intuitive way of implementing a Bayesian model for a programmer is ABC: https://en.wikipedia.org/wiki/Approximate_Bayesian_computati... because it is generative and inherently algorithmic. I wonder if there is a good tutorial way of starting with ABC and developing into MCMC and other more efficient methods? It's easy to transition from simple Monte Carlo methods to ABC rejection sampling, but I'm not sure how to link up ABC and MCMC (in part because I don't grok MCMC myself well enough to explain it).