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## 20.7 Parameters with zero or multiple priors

A warning is generated when a parameter appears to have greater than or less than one prior distribution factor.

This analysis depends on a factor graph representation of a Stan program. A factor F that depends on a parameter P is called a prior factor for P if there is no path in the factor graph from F to any data variable except through P.

One limitation of this approach is that the compiler cannot distinguish between modeled data variables and other convenient uses of data variables such as data sizes or hyperparameters. This warning assumes that all data variables (except for int variables) are modeled data, which may cause extra warnings.

For example, consider the following program.

data {
real x;
}
parameters {
real a;
real b;
real c;
real d;
}
model
{
a ~ normal(0, 1); // this is a prior
x ~ normal(a, 1); // this is not a prior, since data is involved

b ~ normal(x, 1); // this is also not a prior, since data is involved

// this is not a prior for c, since data is involved through b
// but it is a prior for b, since the data is only involved through b
c ~ normal(b, 1);

//these are multiple priors:
d ~ normal(0, 1);
1 ~ normal(d, 1);
}

One prior is found for a and for b, while c only has a factor that touches a data variable and d has multiple priors.

Pedantic mode produces the following warning.

Warning:
The parameter c has no priors.
Warning:
The parameter d has 2 priors.