Fastest Fitting for Bayesian Models?

Right now, I’m focused on computational efficiency (and thereby speed) of fitting Bayesian models. For my dissertation I used R-INLA, so in this “lab notebook” of a blog I need to jot down my thoughts around some current methodological hangups. Right now, even though it seems to be the fastest thing available, it’s honestly still not quite fast or  efficient enough for the full analysis I want to run. It’s taking too long for a re-analysis. I’m exploring whether or not it’s still the best thing available.

• R-INLA
  • pros…
    • fast, as compared to other fitting algorithms
  • cons…
    • parallel processing (considering how much processing is sometimes required) can easily hog shared server resources: a postdoc I worked with and I talked about this a fair amount
    • crashes without clear indication of what happened: it’s a bit of a black box
    • can’t always estimate some parameters of interest
• Hamiltonian Monte Carlo (Nov. 2016)
  • Stan: faster than BUGS (MCMC)
  • No-U-Turn Sampler
  • faster than INLA?
• Bayesian variable selection regression (2017)