Well, if you’re just checking your prior, then I suppose you don’t need real data at all. Make up some numbers and see what happens. What you’re really checking (if you’re being a Bayesian about it, i.e. not like Gelman and company) is not whether your data could come from a model with that prior, but rather whether the properties of the prior you chose seems to match up with the prior you’re modeling. For example, maybe the prior you chose forces two parameters, a and b, to be independent no matter what the data say. In reality, though, you think it’s perfectly reasonable for there to be some association between those two parameters. If you don’t already know that your prior is deficient in this way, posterior predictive checking can pick it up.
In reality, you’re usually checking both your prior and the other parts of your model at the same time, so you might as well use your data, but I could see using different fake data sets in order to check your prior in different ways.
Well, if you’re just checking your prior, then I suppose you don’t need real data at all. Make up some numbers and see what happens. What you’re really checking (if you’re being a Bayesian about it, i.e. not like Gelman and company) is not whether your data could come from a model with that prior, but rather whether the properties of the prior you chose seems to match up with the prior you’re modeling. For example, maybe the prior you chose forces two parameters, a and b, to be independent no matter what the data say. In reality, though, you think it’s perfectly reasonable for there to be some association between those two parameters. If you don’t already know that your prior is deficient in this way, posterior predictive checking can pick it up.
In reality, you’re usually checking both your prior and the other parts of your model at the same time, so you might as well use your data, but I could see using different fake data sets in order to check your prior in different ways.