Dear all,
My apologies if the question is rudimentary. I am following a notebook from @fonnesbeck presented at PyData NYC 2019, shared here on multidimensional GP, I am using the newly released PyMC4, I am not able to do any MCMC sampling or even doing any pm.find_MAP()
. I keep getting an error which I think is related to the specification of sf2
variable. The error reads " **ValueError : Random variables detected in the logp graph: [l]. This can happen when DensityDist logp or Interval transform functions reference nonlocal variables.**"
nd = 15
xu1, xu2 = np.meshgrid(np.linspace(0, 300, nd), np.linspace(0, 300, nd))
Xu = np.concatenate([xu1.reshape(nd*nd, 1), xu2.reshape(nd*nd, 1)], 1)
with pm.Model() as spatial_model:
l = pm.HalfCauchy("l", beta=3, shape=(2,))
sf2 = pm.HalfCauchy("sf2", beta=3)
sn2 = pm.HalfCauchy("sn2", beta=3)
K = pm.gp.cov.ExpQuad(2, l) * sf2**2
gp_spatial = pm.gp.MarginalSparse(cov_func=K, approx="FITC")
obs = gp_spatial.marginal_likelihood("obs", X=X_obs, Xu=Xu, y=y_obs, noise=sn2)
mp = pm.find_MAP()
nd = 30
z1, z2 = np.meshgrid(np.linspace(0, 300, nd), np.linspace(0, 300, nd))
Z = np.concatenate([z1.reshape(nd*nd, 1), z2.reshape(nd*nd, 1)], 1)
with spatial_model:
f_pred = gp_spatial.conditional('f_pred', Z)
samples = pm.sample_posterior_predictive([mp], vars=[f_pred], samples=100)
with sns.axes_style("white"):
plt.figure(figsize=(10,8))
ax = sns.heatmap(samples['f_pred'].mean(0).reshape(nd, nd), cmap='viridis')
ax.invert_yaxis()
ax.set_yticklabels([])
ax.set_xticklabels([])
My questions are:

Is there any thing that I could change in the model so that it could carry on with the sampling given that I am using PyMC4?

Is there anything wrong with
obs = gp_spatial.marginal_likelihood("obs", X=X_obs, Xu=Xu, y=y_obs, noise=sn2)
that has to be updated to PyMC4 syntax? 
How about changes in PyMC4 calling the
sample_posterior_predictive
, specifically do I need to change anything in the lines
f_pred = gp_spatial.conditional('f_pred', Z)
samples = pm.sample_posterior_predictive([mp], vars=[f_pred], samples=100)
Many thanks,
Ali