David Widmann

An alternative would be to add an API like ```julia inverse_link(::typeof(exp)) = log inverse_link(::typeof(log)) = exp inverse_link(::typeof(log1pexp)) = logexpm1 inverse_link(::typeof(logexpm1)) = log1pexp ``` that would allow us to define ```julia...

I think it would be better to move it to Distributions. Most (all?) of these custom distributions should be moved upstream I guess.

> it's not at all clear to me what the appropriate interface is for approximate inference with MCMC, given that we're working outside of a PPL. Maybe one could make...

An additional argument for removing the type aliases and constructors is https://github.com/JuliaGaussianProcesses/GPLikelihoods.jl/pull/51: It shows that (it seems) one could remove `Link` (and also `AbstractLink`) completely, as suggested by @st-- in...

I think I'd prefer the second approach, it feels natural to me to only state the likelihood once.

I resolved the conflicts and removed the check for `gamma(a, x)`: We should only define a rule for it if it is defined, so IMO the rule should not exist...

The ReverseDiff test errors are caused by (correct) NaN values. This is not a problem of this PR but rather of ReverseDiff's tests: https://github.com/JuliaDiff/ReverseDiff.jl/blob/d522508aa6fea16e9716607cdd27d63453bb61e6/test/utils.jl#L9-L13 Maybe this could be fixed (and...

@mcabbott Are you fine with updating the SpecialFunctions compat entry to "1.2, 2"?

@mcabbott I updated the PR and fixed some tests, do you have any comments? Otherwise I think this PR can be merged.

ChainRules should suffer from the same problem, possibly the rule was just copied to it from DiffRules: https://github.com/JuliaDiff/ChainRules.jl/blob/40b9058c1a6798a4f72bda1227786d584b44c822/src/rulesets/Base/fastmath_able.jl#L41