Currently the prototype integrated Laplace approximation lets the user specify the prior covariance matrix. Mathematically there are advantages to specifying the model in terms of a precision matrix.

We are nowhere near an implementation which supports a precision matrix but looking into the future, we would want to distinguish the two by indicating in the function’s name whether the user passes the covariance or precision matrix.

```
// current name, uses cov matrix
laplace_marginal_lpdf();
// new names
laplace_marginal_cov_lpdf();
laplace_marginal_precision_lpdf();
```

The question is do we want to rename the existing function in anticipation of an implementation which supports precision matrices? As @avehtari points out, even if such an implementation only arrives in a few years, we may as well change the name now to avoid a refactor in the future.

My inclination is to say no, because I think it’s fine to have the default be covariance, and then have a precision as a special case. As @stevebronder pointed out, we use `multinormal`

and `multinormal_cholesky`

, and we don’t have `multinormal_cov`

.

Posting this to hear some opinions.