a ~ distribution(data,stuff);

with

FOO ~ distribution(other stuff)

b <- Function(FOO,data);
to prove that data dependent priors are always equivalent to models with data independent priors and different or additional parameters. But I'll leave this up to the computational linguists in the crowd ðŸ™‚ (@Bob Carpenter?)

consider the two following priors:

s ~ exponential(1/1000.0); /* I ask my knowledge K what the value of s is, and it says "I have no idea maybe up to a couple thousand?"*?

vs

e ~ normal(1,0.75/sqrt(20));

s <- e*sd(data);

/* I ask my knowledge K what is s, and it says I'm not sure, but based on some simulations of sampling, I can tell you what the multiplicative factor e is such that s = e * sd(data) */

vs.

s ~ normal(sd(data),sd(data)*0.75/sqrt(20));

where the last two models are totally equivalent, but the final one has a "data dependent prior".

]]>