# Reparameterizing the cauchy for "likelihood"?

The “reparameterizing the cauchy” section of the manual describes how to more efficiently express that a parameter is cauchy distributed; is there a similar way to more efficiently express that data are cauchy distributed? As in:

``````data{
int n;
vector[n] y;
}
...
parameters{
y ~ cauchy(mu,tau) ;
...
}``````

Yikes am I ever far behind on the forums!

I don’t think you’ll have a problem if you have multiple observations `y` and are just trying to fit a single `mu` and `tau`. The posterior for `mu` can turn out to be large, though, because all three of these are the same:

``````y ~ cauchy(mu, tau);
mu ~ cauchy(y, tau);
y - mu ~ cauchy(0, tau);
``````