I just ran a 100K standard normal model on my 2012 Mac Pro notebook and it took:
> fit <- sampling(model, data = list(D = 100000), chains = 1)
SAMPLING FOR MODEL 'norm' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.002456 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 24.56 seconds.
Chain 1: Adjust your expectations accordingly!
Chain 1:
Chain 1:
Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
Chain 1: Iteration: 200 / 2000 [ 10%] (Warmup)
Chain 1: Iteration: 400 / 2000 [ 20%] (Warmup)
Chain 1: Iteration: 600 / 2000 [ 30%] (Warmup)
Chain 1: Iteration: 800 / 2000 [ 40%] (Warmup)
Chain 1: Iteration: 1000 / 2000 [ 50%] (Warmup)
Chain 1: Iteration: 1001 / 2000 [ 50%] (Sampling)
Chain 1: Iteration: 1200 / 2000 [ 60%] (Sampling)
Chain 1: Iteration: 1400 / 2000 [ 70%] (Sampling)
Chain 1: Iteration: 1600 / 2000 [ 80%] (Sampling)
Chain 1: Iteration: 1800 / 2000 [ 90%] (Sampling)
Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)
Chain 1:
Chain 1: Elapsed Time: 489.771 seconds (Warm-up)
Chain 1: 365.287 seconds (Sampling)
Chain 1: 855.058 seconds (Total)
That’s 14 minutes to complete sampling. So if you ran four chains one after the other, it’d be about an hour. It’d be faster with a faster CPU and faster memory. I can run four chains in parallel and get this all done in 15 minutes, even on my ancient notebook (assuming I don’t want to do anything else on it).
I’m still waiting for it to return because RStan does a lot of extraneous work creating a stanfit object compared to CmdStan just saving the draws!
Daniel Lee and I fit a hierarchical Bradley-Terry model for baseball batting matchups over all time (15K parameters, 10M observations) in about two days on a regular computer in our office many years ago. I don’t know how long 100K parameters and 100M observations would’ve taken but presumably longer than our patience would’ve lasted. It can be hard to speed this up with map_rect because the computation is so simple per data point and parameter.