Honestly, I find the term “posterior predictive checking” and “posterior predictive” to be a bit confusing. When trying to evaluate your model/posterior in the diagnostic mode, the term “posterior predictive checking” makes sense (it’s a form of model checking). But there’s a huge number of things you can use your posterior for and I think of these sorts of exercises as “simulation”. And when you talk about wanting to use your posterior to “simulate” new scenarios, it’s a bit more intuitive that there aren’t really any rules about what you should be simulating.
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