Numeric and domain issues with Dirichlet

[itsdfish]

As discussed in Slack, here is a MWE in which sampling from the Dirichlet distribution produces numeric and domain errors.

using Turing, Random 
@model dir(K) = begin
    w ~ Dirichlet(ones(K) / K)
end
#Random.seed!(343) #Domain error
Random.seed!(344) #Numerical Errors
s = sample(dir(4), NUTS(1000, 0.8), 2000, progress=false)

Version Info:

Julia 1.2

(v1.2) pkg> st Turing
    Status `~/.julia/environments/v1.2/Project.toml`
  [0bf59076] AdvancedHMC v0.2.7
  [31c24e10] Distributions v0.21.3
  [276daf66] SpecialFunctions v0.7.2
  [4c63d2b9] StatsFuns v0.8.0
  [fce5fe82] Turing v0.7.0
  [e88e6eb3] Zygote v0.3.4

[yebai]

This is probably fixed with improvements to DistributionsAD and Bijectors. Please reopen if otherwise.