Thanks again. Here’s what I came up with:
plausible_counts = dict()
fig, axs = plt.subplots(1,2)
for i, (etype, mus) in enumerate(trace.posterior.groupby('Event Types')):
mus_for_type = mus.stack(n=('chain', 'draw'))
num_mus = 100
num_samples = 200
possible_mus = gaussian_kde(mus_for_type['mu']).resample(num_mus)
plausible_counts[etype] = poisson(possible_mus).rvs([num_samples, num_mus]).reshape(num_mus * num_samples)
axs[i].hist(plausible_counts[etype], bins=30, density=True, stacked=True)
axs[i].axvline(plausible_counts[etype].mean(),color='red')
axs[i].set_xlabel(f"Event type: {etype}")
for etype, counts in plausible_counts.items():
print(f"{etype} | Mean: {counts.mean()}, 15%: {np.quantile(counts, 0.15)}, 85%: {np.quantile(counts, 0.85)}")
And the results look alright to me -

Thanks for the help!