Unexpected results for PredictionBand

[JorisDeRidder]

• UltraNest version: 3.5.7
• Python version: 3.9.16
• Operating System: OSX

Description

Given its name, I expected UltraNest's PredictionBand to give a band derived from the posterior predictive distribution, but this is not what it seems to compute. The following example illustrates this.

• The dots are a synthetic dataset created with

  rng = np.random.default_rng(14)
  xobs = np.linspace(0, 1, 50)
  yobs = 1 + 2 * xobs + rng.normal(0.0, 0.3, 50)

  and which was modeled with a simple straight line using UltraNest

• The lightblue shaded region is the 95% prediction band computed by UltraNest using the code

  band.shade(q=0.475, color='lightsteelblue', alpha=0.6)            # [0.5-0.475, 0.5+0.475] = [0.025, 0.975] 

• The green dot-dashed lines are the frequentist 95% confidence interval of the responses
• The purple dashed lines are the frequentist 95% prediction interval of the responses. They coincide with the 95% HDI of the posterior predictive distribution computed with PyMC or PyStan.

Am I correct in concluding that PredictionBand does not use the posterior predictive distribution, and if so, could this feature be added to UltraNest?

[JorisDeRidder]

Duplicate of #90 because of a GitHub hickup.