ForwardDiff extension

EpiAwareADToolsForwardDiffExt loads when ForwardDiff is loaded alongside EpiAwareADTools. ForwardDiff dispatches on the Dual argument type and does not read ChainRules, so this extension adds methods directly rather than lifting the rules the ChainRulesCore extension defines.

What it registers

A tape-strip method:

primal(x::Dual) = primal(value(x))

It recurses, so a nested Dual from a higher-order tag chain still reduces to the scalar value. fixed_draw delegates to primal, so it becomes a genuine stop-gradient on this backend through the same method.

Seven methods each for _gamma_cdf, _gamma_logccdf and _beta_cdf, covering every combination of the three arguments in which at least one is a Dual. All of them route to a shared _impl helper that reads out the values, calls the matching _value_and_partials helper, and rebuilds a Dual from the analytic partials and the incoming ones. Dual <: Real, so the seven methods overlap, and the three double-Dual methods and the all-Dual method are the resolvers for those overlaps. The Dual slots are deliberately left unparametrised. A shared {T, V, N} parametrisation across slots would pin the tags equal, the resolvers would then not dominate the mixed-tag intersections, and detect_ambiguities would flag every partial pair. The tag and partial width are read from the first Dual at run time instead.

Two edge cases are unsupported and error inside the helper rather than through ambiguous dispatch: nested Duals, and mixed tags across arguments. ForwardDiff never asks for either in a single differentiation pass.

Twelve Distributions methods, six for Gamma and six for Beta:

Distributions.logcdf(d::Gamma{<:Dual}, x::Real) = logcdf_ad_safe(d, x)
Distributions.logcdf(d::Gamma, x::Dual) = logcdf_ad_safe(d, x)
Distributions.logcdf(d::Gamma{<:Dual}, x::Dual) = logcdf_ad_safe(d, x)

and the logccdf counterparts, then the same six for Beta. Methods are added only for the Dual arguments StatsFuns cannot handle, so the plain float path is untouched. The Gamma{<:Dual} method catches Dual parameters with a constant evaluation point, the ::Dual evaluation-point method catches a Dual bound, and the both-Dual method resolves their overlap.

using EpiAwareADTools, Distributions, ForwardDiff

ForwardDiff.derivative(k -> logcdf(Gamma(k, 1.5), 3.0), 2.0)

-0.4949622662152675

What fails without it

StatsFuns._gammalogcdf has no Dual method, and neither does the beta_inc path behind logcdf(::Beta). A truncated(Gamma; lower) builds its normaliser eagerly at construction, so constructing one with Dual parameters breaks under ForwardDiff before any density is evaluated. The logcdf/logccdf methods above are what close that gap, by routing through logcdf_ad_safe and logccdf_ad_safe and so through the analytic shape and scale partials.

Without the Dual methods on the CDF primitives, the AD-safe hooks themselves have nothing differentiable to call, since the generic primitives return a plain float and drop the partials.

Without the primal(::Dual) method, primal is the identity on a Dual, so a strip a caller relied on silently does nothing and the gradient flows on through.

Upstream target

The same condition as the rest of the family: a Gamma and Beta CDF differentiable in their parameters upstream, tracked for the gamma side by SpecialFunctions.jl issue #531. The primal(::Dual) method goes with the rest of the tape-strip once a shared cross-backend stop-gradient primitive exists.