How to use of CDF function in Turing module of Julia?

Question

I want to know the parameters of Gamma Distribution of Awareness. Awareness is 0.336 at 1 week, 0.554 at 4 week , and 0.64 at 13 week. data set is builed here. data is cdf of Gamma dist.

 xs = [ 1 0.336 ; 4 0.554 ; 13 0.64 ]

i coded this in Julia and using Turing

@model function gmodel(ds)
    m,n = size(ds)
    k ~ InverseGamma(3,2)
    a ~ InverseGamma(3,2)
    for i in 1:m
        cdf_g = cdf(Gamma(k,a),ds[i,1])
        ds[i,2] ~ Normal(cdf_g, 3)
    end
end
c = sample(gmodel(xs),NUTS(),1000)

but, i get an error of this.

MethodError: no method matching gammacdf(::ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.VarInfo{NamedTuple{(:k, :a),Tuple{DynamicPPL.Metadata{Dict{DynamicPPL.VarName{:k,Tuple{}},Int64},Array{InverseGamma{Float64},1},Array{DynamicPPL.VarName{:k,Tuple{}},1},Array{Float64,1},Array{Set{DynamicPPL.Selector},1}},DynamicPPL.Metadata{Dict{DynamicPPL.VarName{:a,Tuple{}},Int64},Array{InverseGamma{Float64},1},Array{DynamicPPL.VarName{:a,Tuple{}},1},Array{Float64,1},Array{Set{DynamicPPL.Selector},1}}}},Float64},DynamicPPL.Model{var"#33#34",(:ds,),(),(),Tuple{Array{Float64,2}},Tuple{}},DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},(),AdvancedHMC.DiagEuclideanMetric}},DynamicPPL.DefaultContext},Float64},Float64,2}, ::ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.VarInfo{NamedTuple{(:k, :a),Tuple{DynamicPPL.Metadata{Dict{DynamicPPL.VarName{:k,Tuple{}},Int64},Array{InverseGamma{Float64},1},Array{DynamicPPL.VarName{:k,Tuple{}},1},Array{Float64,1},Array{Set{DynamicPPL.Selector},1}},DynamicPPL.Metadata{Dict{DynamicPPL.VarName{:a,Tuple{}},Int64},Array{InverseGamma{Float64},1},Array{DynamicPPL.VarName{:a,Tuple{}},1},Array{Float64,1},Array{Set{DynamicPPL.Selector},1}}}},Float64},DynamicPPL.Model{var"#33#34",(:ds,),(),(),Tuple{Array{Float64,2}},Tuple{}},DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},(),AdvancedHMC.DiagEuclideanMetric}},DynamicPPL.DefaultContext},Float64},Float64,2}, ::Float64)
Closest candidates are:
  gammacdf(!Matched::Union{Float64, Int64}, !Matched::Union{Float64, Int64}, ::Union{Float64, Int64}) at C:\Users\kimse\.julia\packages\StatsFuns\zJ1EI\src\rmath.jl:77

How implement and use the Function of CDF or PDF functions in Turing ?

score 0 · Answer 1 · answered Jan 11 '21 at 11:17

That's not really a Turing problem -- NUTS, as a HMC sampler, uses automatic differentiation to obtain the gradient of the logpdf. gammacdf is from StatsFuns, and not registered for AD with ForwardDiff. Also, the implementation is probably a ccall in Rmath.

Possible resolutions:

Use another sampler, not based on AD.
Try a different AD backend with Turing.setadbackend.
Express gammacdf in pure Julia, composed of primitively differentiable functions.
Add the necessary pullback or pushforward (i.e., an implementation of the gradient suitable for forward or backward mode AD), possibly with a different backend.

And I recommend asking on the #autodiff channel on the Julia slack, there's a load of really helpful people there.

How to use of CDF function in Turing module of Julia?

1 Answers1