  Stata users have access to two easy-to-use implementations of Bayesian
inference: Stata's native {\tt bayesmh} function and StataStan, which calls the
general Bayesian engine Stan. We compare these on two models that are important
for education research: the Rasch model and the hierarchical Rasch model. Stan
(as called from Stata) fits a more general range of models than can be fit by
{\tt bayesmh} and is also more scalable, in that it could easily fit models
with at least ten times more parameters than could be fit using Stata's native
Bayesian implementation. In addition, Stan runs between two and ten times
faster than {\tt bayesmh} as measured in effective sample size per second: that
is, compared to Stan, it takes Stata's built-in Bayesian engine twice to ten
times as long to get inferences with equivalent precision. We attribute Stan's
advantage in flexibility to its general modeling language, and its advantages
in scalability and speed to an efficient sampling algorithm: Hamiltonian Monte
Carlo using the no-U-turn sampler. In order to further investigate scalability,
we also compared to the package Jags, which performed better than Stata's
native Bayesian engine but not as well as StataStan.
  Given its advantages in speed, generality, and scalability, and that Stan is
open-source and can be run directly from Stata using StataStan, we recommend
that Stata users adopt Stan as their Bayesian inference engine of choice.
