I understand the mechanics and math behind prior predictive distributions, but I don't understand its practical uses. Theoretically and application wise, what is its purpose?

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    $\begingroup$ It predicts what the data should look like, a priori, and hence can assess whether or not the actual data is compatible with this Bayesian model. $\endgroup$ – Xi'an Jan 15 at 19:57
  • $\begingroup$ @Xi'an so would standard practice be to compare the prior predictive distribution to the data at hand? Could you expand on assessing compatibility with a Bayesian model by this comparison? $\endgroup$ – Brian Ko Jan 15 at 23:51
  • $\begingroup$ I personally prefer to use the prior predictive distribution to select the prior distribution. Because it's more concrete to have a prior belief on the data rather than a prior belief on the parameters. $\endgroup$ – Stéphane Laurent Jan 30 at 17:36

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