I did a PhD in statistics, and spent a lot of that time doing applied modeling.
My perspective is that MCMC is one of the great scientific discoveries of the 20th century. There are pros and cons to different samplers, lots of caveats, concerns over convergence—all valid. Still, MCMC opens up a whole new world of model building, letting you easily try a whole slew of models. It provides flexibility, even creativity. As a concept it’s clever. As a technical achievement it’s amazing.
My perspective is that MCMC is one of the great scientific discoveries of the 20th century. There are pros and cons to different samplers, lots of caveats, concerns over convergence—all valid. Still, MCMC opens up a whole new world of model building, letting you easily try a whole slew of models. It provides flexibility, even creativity. As a concept it’s clever. As a technical achievement it’s amazing.