Automatic Differentiation with custom functions within likelihood function

[Tamas_Papp]

You may find this discussion relevant, has a lot of nice suggestions:

AD step for iterative solution

Sometimes it would be useful to AD through an iterative algorithm, eg solving a parametric problem f(x, a) = 0 which implicitly defines x(a), but in practice uses an iterative rootfinding method. The math is clear (implicit differentiation), I am aware of the nice tricks for the multivariate case (adjoint method), this question is about practical Julia implementation. For simple presentation, let’s work with scalars, and use f(x, a) = x^3 - a which we treat as a black box. We assume deri…