It seems the innovation here is that the dependency structure of the model is explicit which allows the algorithms to do interesting things like block updates,

It seems the innovation here is that the dependency structure of the model is explicit which allows the algorithms to do interesting things like block updates, beneficial for correlated variables. They also have Newtonian Monte Carlo, an exotic, new technique. Oddly though, Stan is still faster in their own benchmarks, despite their statements. In other words, while Bean Machine has a lower wall time, Stan produces more effective samples per second than Bean Machine (and this, not wall time alone, is the important metric).