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return posterior_predictive from sample_pro #10

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@eclipse1605

sample_pro returns a DataTree without posterior_predictive group rn. in mcmc you’d call pm.sample_posterior_predictive after sampling. i think for PrO that feels backwards, the whole object is defined through predictive ability.

we currently build ppcs by hand. this should be handled inside pymc-prop and return a proper posterior_predictive group from sample_pro, probably behind an include_posterior_predictive flag (default on or off (open to opinion)).

the open design bits are

  • how to draw from the particle ensemble at each retained step (final cloud only vs thinned trajectory, one particle per predictive draw vs per-obs chain resampling)
  • whether the output should follow standard ArviZ draw/chain layout or a dedicated predictive-sample axis.

either way after dt = sample_pro(...), users shuold be able to go straight to az.plot_ppc_dist(dt) without manual xarray surgery.

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