How to get a smoother mean posterior predictive plot over long tails?

Questions v5
2

The ppc plot itself looks fine but it is the mean that looks weird:
ppc

ppc mean line plot has been known to act weird, see for instance:

I have had similar issues from time to time so I am assuming this is not fixed but there seems to be some suggestions in the links above (my solution is not to plot it!).

Just to double check, I have also ran this model on simulated data and it does seem to run fine in terms of ppc and posterior but the mean line is still bad:

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Mar  7 10:30:58 2024

@author: avicenna
"""

import numpy as np
import pymc as pm
import arviz as az
seed = 0
rng = np.random.default_rng(seed)
alpha_real = 1.35
N=100


with pm.Model() as sim:
  data_dist = pm.Pareto("data_dist", alpha=alpha_real, m=1)

data = pm.draw(data_dist, N)


with pm.Model() as example:
  x = pm.Data('x', data, mutable=True)

  alpha = pm.LogNormal("a", )
  likelihood = pm.Pareto('likelihood', alpha=alpha, m=x.min(), observed=x)

with example:
  trace = pm.sample(1000, tune=1000, chains=6)

az.plot_posterior(trace)

with example:
  pm.sample_posterior_predictive(trace, extend_inferencedata=True)

ax = az.plot_ppc(trace)#
ax.get_figure().savefig("ppc3.png")

ax = ax.plot_posterior(trace)
ax.get_figure().savefig("post.png")

ppc3

post

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