# Turing's negative binomial regression with horseshoe prior failing sometimes

**URL:** https://discourse.julialang.org/t/turings-negative-binomial-regression-with-horseshoe-prior-failing-sometimes/121574
**Category:** Statistics
**Tags:** question, turing
**Created:** [October 22, 2024, 9:01am UTC](https://discourse.julialang.org/t/turings-negative-binomial-regression-with-horseshoe-prior-failing-sometimes/121574 "2024-10-22T09:01:07Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![ayushpatnaikgit](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ayushpatnaikgit/32/25229_2.png) [@ayushpatnaikgit](https://discourse.julialang.org/u/ayushpatnaikgit)
#### Post date: [October 22, 2024, 9:01am UTC](https://discourse.julialang.org/t/turings-negative-binomial-regression-with-horseshoe-prior-failing-sometimes/121574/1 "2024-10-22T09:01:07Z")

</div>

Hi,  
I am trying to do a negative binomial regression using Turing. I am using the horseshoe prior. Here is my code:

```julia
using Turing, StatsModels, RDatasets, Random

sanction = dataset("Zelig", "sanction")

function NegativeBinomial2(μ, ϕ)
    p = 1 / (1 + μ / ϕ)
    r = ϕ

    return NegativeBinomial(r, p)
end

@model NegativeBinomialRegression(X, y) = begin
    p = size(X, 2)
    n = size(X, 1)
    h = 1.0
    #priors
    
    halfcauchy = Truncated(TDist(1), 0, Inf)
    
    τ ~ halfcauchy ## Global Shrinkage
    λ ~ filldist(halfcauchy, p) ## Local Shrinkage
    σ ~ InverseGamma(h, h)
    β0 = repeat([0], p) ## prior mean
    β ~ MvNormal(β0, λ * τ)

    ## link
    #z = α .+ X * β
    z = X * β
    mu = exp.(z)

    #likelihood
    for i = 1:n
        y[i] ~ NegativeBinomial2(mu[i], σ)
    end
end

frm = @formula(Num ~ Target + Coop + NCost)

frm = apply_schema(frm, schema(frm, sanction), RegressionModel)
y, X = modelcols(frm, sanction)

chain = sample(MersenneTwister(), NegativeBinomialRegression(X, y), NUTS(), 1000)

```

This often works, but occasionally, I get the following error:

```julia
ERROR: DomainError with Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}}(0.0,NaN,NaN,NaN,NaN,NaN,NaN,NaN):
NegativeBinomial: the condition zero(p) < p <= one(p) is not satisfied.

```

Running the sampler a few times should reproduce this error:

```julia
for i in 1:20
    sample(MersenneTwister(), NegativeBinomialRegression(X, y), NUTS(), 100)
end

```

Thanks,  
Ayush

---

<div class="post-metadata">

### Author: ![Red-Portal](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/red-portal/32/9102_2.png) [@Red-Portal](https://discourse.julialang.org/u/Red-Portal)
#### Post date: [November 18, 2024, 6:46am UTC](https://discourse.julialang.org/t/turings-negative-binomial-regression-with-horseshoe-prior-failing-sometimes/121574/2 "2024-11-18T06:46:32Z")

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Of course, global shrinkage being zero doesn’t make sense. But this can happen due to numerical accuracy. If this happens, you can try simple things like setting the lower bound on the `Truncated` to be something like `eps(Float64)` and whatnot.