The first thing I do in cases like that is usually to try and find out why it is slow. There are two basic reasons for the slowness. Either the gradient evaluations take a lot of time or we need a lot of gradient evaluations for each sample. If it is the first, the problem is the shape of the posterior, so you need to look into reparametrizations that reduce funnels or correlations. If it is the second, you can use theano’s profiling tools to figure out where the problem is.
You can access the profile using something along those lines:
func = model.logp_dlogp_function(profile=True)
func.set_extra_values({})
x = np.random.randn(func.size)
%timeit func(x)
func.profile.print_summary()
You can access the number of grad evals using trace.tree_size. There are also a couple of other diagnostics that you could look at, there is a list in the doc for pymc3.NUTS.