# Johann D. Gaebler

## Autodiff for Implicit Functions in Stan

### Fast derivatives for functions you can't write down

One of the things that makes Stan powerful is that—in addition to a large library of standard mathematical functions (e.g., $$\exp(x)$$, $$x^y$$, $$x + y$$, $$\Gamma(x)$$, etc.)—it also supports the use of higher-order functions, such as such as solving a user-specified system of ODEs. This greatly expands the range of Bayesian models Stan can handle.