Thanks to Chris Fonnesbeck for arguing on the issue; however, I am not entirely convinced. After all, this is a beta-binomial model where the number Bernoulli draws is supposed to be fixed in advance (n=73). In this case, before entering data, the prior distribution is quickly fixed: what else could it be but a \beta distribution? Then, whether it’s \beta(0.5,0.5) or \beta(5,5) doesn’t change much in my opinion: the prior predictive distribution can only reflect the chosen prior distribution, if I’m not mistaken…
The question of the interest of doing this remains open.
If I then consider only 1 experiment and find a result x=46 successes, it seems to me that I cannot deduce anything from it and that the interest of carrying out a prior predictive distribution is nil, because there must not be, in this case, any possible prior predictive check; am I right?.
If, on the other hand, I realize a large number of experiments and my results revolve around \bar{x}=36 \sim 73/2, I could probably deduce that a prior \beta(5.5) is more suited to the model than a prior \beta(0.5,0.5) (which tends to predict results close to 0 or 73); right?
But doesn’t that mean that I am now outside the scope of a predictive prior? Since I no longer test the “before it sees any data” model?
Finally, for something as simplistic as a beta-binomial model with a single \theta parameter, I still don’t see the point of calculating a prior predictive distribution… But there may be many other techniques that I don’t am not aware?