Wishlist : inverse CDF functions (or, failing that, a few common special functions).

[Emmanuel Charpentier]

For meta-analytic purposes, it would be useful to have access to inverse CDF of the densities supported by Stan (e. g. to use a quantile).

Failing that (one can always make a dichotomic search on a bounded function guaranteed to be non-decreasing...), a few secial functions could be useful : we have beta and incomplete beta, whe also have gamma and log(gamma) ; log(incomplete_gamma) would be useful (e. g. joint density of a vector of quantiles...).

"Rolling our own" user-defined functions isn't very easy : I know enough numerical analysis to know that I know almost nothing of the subject...

What do you think ?

--
Emmanuel Charpentier

[Bob Carpenter]

Adding inverse CDFs is on our to-do list. The bottleneck
is that we don't know how to calculate the derivatives. We could
autodiff the numerical algorithms for computing the functions,
but this is often poorly behaved numerically.

We need someone to dive into the numerical analysis specifically
for inverse CDFs to figure out reasonable approximations to
their derivatives.

- Bob

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[Emmanuel Charpentier]

On 20/01/2017 18:54, Bob Carpenter wrote:
> Adding inverse CDFs is on our to-do list. The bottleneck
> is that we don't know how to calculate the derivatives. We could
> autodiff the numerical algorithms for computing the functions,
> but this is often poorly behaved numerically.
>
> We need someone to dive into the numerical analysis specifically
> for inverse CDFs to figure out reasonable approximations to
> their derivatives.

Indeed. I had a look at related functions in DLMF : Aaaarghhh.... For
most of them, a power series would probably have very poor convergence.
You'd need something like a Padé approximant. Coming by to them is
definitely not my usual turf...

Sincerely,

--
Emmanuel Charpentier

[Bob Carpenter]

Us, either, which is why we haven't done it. I
just talked to Michael Betancourt, who said we could
do these using a root finder and the implicit function
theorem. And this is something we want to do, so maybe
we might start adding some of these sooner rather than
later.

- Bob