Poisson with Dirichlet prior samples negative values

### Minimal working example

```julia
using Distributions
using Turing
using MCMCChains

N = 2*2
D = 10*ones(N)
W_pump = 20
W_probe = 40
N_pump = 4
N_probe = 8
ϵ = 0.5

@model function unconditional_model(y)
    # Our prior belief that each pixel comes from the pump
    p_pump ~ Dirichlet(N, 1.0)
    p_probe ~ Dirichlet(N, 1.0)

    λ_pump = N_pump * p_pump
    λ_probe = N_probe * p_probe
    # I_pump ~ arraydist(Normal.(λ_pump, sqrt.(λ_pump)))
    # I_probe ~ arraydist(Normal.(λ_probe, sqrt.(λ_probe)))
    # λ_pump = N_pump * p_pump .+ 1e-3
    # λ_probe = N_probe * p_probe .+ 1e-3
    I_pump ~ arraydist(Poisson.(λ_pump))
    I_probe ~ arraydist(Poisson.(λ_probe))

    # draw the data
    for i in 1:N
        y[i] ~ Normal(W_pump * I_pump[i] + W_probe * I_probe[i], ϵ)
    end
end;

sampler = NUTS();
nsamples = 200
nchains = 4
burn = 10

chain = sample(unconditional_model(D), sampler, MCMCThreads(), nsamples, nchains; discard_initial=burn);
```

### Description

Dear Turing developers,

I have tried creating a relatively simple model in which two Dirichlets priors are combined with Poissons a linear combination of them is sampled from a Normal distribution. When attempting to perform inference on this model, an error happens due to negative $\lambda$ values for the Poisson, although this should not be possible, as for each (multi-dimensional) Poisson, $\lambda = N p$, where $N$ is a positive constant and $p$ is sampled from a Dirichlet distribution.

The error I obtain is the following (Julia 1.11):

```
TaskFailedException

    nested task error: TaskFailedException
    
        nested task error: DomainError with -18.055936637738895:
        `gamma(x)` must be non-negative
        Stacktrace:
          [1] _loggamma
            @ [/gpfs/exfel/sw/software/julia-depot/packages/SpecialFunctions/mf0qH/src/gamma.jl:670](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/SpecialFunctions/mf0qH/src/gamma.jl#line=669) [inlined]
          [2] loggamma
            @ [/gpfs/exfel/sw/software/julia-depot/packages/SpecialFunctions/mf0qH/src/gamma.jl:666](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/SpecialFunctions/mf0qH/src/gamma.jl#line=665) [inlined]
          [3] loggamma
            @ [/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/dual.jl:244](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/dual.jl#line=243) [inlined]
          [4] poislogpdf(λ::ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}, x::ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7})
            @ StatsFuns [/gpfs/exfel/sw/software/julia-depot/packages/StatsFuns/gSNRw/src/distrs/pois.jl:21](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/StatsFuns/gSNRw/src/distrs/pois.jl#line=20)
          [5] logpdf
            @ [/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/univariates.jl:645](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/univariates.jl#line=644) [inlined]
          [6] #533
            @ [/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/multivariate/product.jl:50](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/multivariate/product.jl#line=49) [inlined]
          [7] _mapreduce(f::Distributions.var"#533#534"{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Poisson{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}, op::typeof(Base.add_sum), ::IndexLinear, A::UnitRange{Int64})
            @ Base ./reduce.jl:437
          [8] _mapreduce_dim
            @ ./reducedim.jl:337 [inlined]
          [9] mapreduce
            @ ./reducedim.jl:329 [inlined]
         [10] _sum
            @ ./reducedim.jl:987 [inlined]
         [11] sum
            @ ./reducedim.jl:983 [inlined]
         [12] _logpdf
            @ [/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/multivariate/product.jl:50](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/multivariate/product.jl#line=49) [inlined]
         [13] logpdf
            @ [/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/common.jl:269](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/Distributions/YQSrn/src/common.jl#line=268) [inlined]
         [14] invlink_with_logpdf(vi::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}}, ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Base.RefValue{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}, vn::AbstractPPL.VarName{:I_pump, typeof(identity)}, dist::Product{Discrete, Poisson{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Poisson{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}, y::SubArray{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}, 1, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Tuple{UnitRange{Int64}}, true})
            @ DynamicPPL [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/abstract_varinfo.jl:856](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/abstract_varinfo.jl#line=855)
         [15] invlink_with_logpdf
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/abstract_varinfo.jl:850](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/abstract_varinfo.jl#line=849) [inlined]
         [16] assume
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl:227](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl#line=226) [inlined]
         [17] assume
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl:502](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl#line=501) [inlined]
         [18] tilde_assume
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl:72](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl#line=71) [inlined]
         [19] tilde_assume
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl:67](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl#line=66) [inlined]
         [20] tilde_assume
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl:52](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl#line=51) [inlined]
         [21] tilde_assume!!(context::DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}, right::Product{Discrete, Poisson{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Poisson{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}, vn::AbstractPPL.VarName{:I_pump, typeof(identity)}, vi::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}}, ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Base.RefValue{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}})
            @ DynamicPPL [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl:144](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/context_implementations.jl#line=143)
         [22] unconditional_model(__model__::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}}, ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Base.RefValue{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}, __context__::DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}, y::Vector{Float64})
            @ Main ./In[3]:12
         [23] _evaluate!!(model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, varinfo::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}}, ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Base.RefValue{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}, context::DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro})
            @ DynamicPPL [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/model.jl:973](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/model.jl#line=972)
         [24] evaluate_threadsafe!!
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/model.jl:962](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/model.jl#line=961) [inlined]
         [25] evaluate!!(model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, varinfo::DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, Vector{Set{DynamicPPL.Selector}}}}, ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}, context::DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro})
            @ DynamicPPL [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/model.jl:892](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/model.jl#line=891)
         [26] logdensity
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/logdensityfunction.jl:140](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/logdensityfunction.jl#line=139) [inlined]
         [27] Fix1
            @ ./operators.jl:1127 [inlined]
         [28] chunk_mode_gradient!(result::DiffResults.MutableDiffResult{1, Float64, Tuple{Vector{Float64}}}, f::Base.Fix1{typeof(LogDensityProblems.logdensity), LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}}, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}})
            @ ForwardDiff [/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/gradient.jl:125](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/gradient.jl#line=124)
         [29] gradient!
            @ [/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/gradient.jl:41](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/gradient.jl#line=40) [inlined]
         [30] gradient!
            @ [/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/gradient.jl:36](https://max-jhub.desy.de/gpfs/exfel/sw/software/julia-depot/packages/ForwardDiff/UBbGT/src/gradient.jl#line=35) [inlined]
         [31] logdensity_and_gradient
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/LogDensityProblemsAD/rBlLq/ext/LogDensityProblemsADForwardDiffExt.jl:118](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/LogDensityProblemsAD/rBlLq/ext/LogDensityProblemsADForwardDiffExt.jl#line=117) [inlined]
         [32] ∂logπ∂θ
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl:180](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl#line=179) [inlined]
         [33] ∂H∂θ
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/hamiltonian.jl:38](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/hamiltonian.jl#line=37) [inlined]
         [34] step(lf::AdvancedHMC.Leapfrog{Float64}, h::AdvancedHMC.Hamiltonian{AdvancedHMC.DiagEuclideanMetric{Float64, Vector{Float64}}, AdvancedHMC.GaussianKinetic, Base.Fix1{typeof(LogDensityProblems.logdensity), LogDensityProblemsADForwardDiffExt.ForwardDiffLogDensity{LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}, ForwardDiff.Chunk{7}, ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}}, Turing.Inference.var"#∂logπ∂θ#32"{LogDensityProblemsADForwardDiffExt.ForwardDiffLogDensity{LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}, ForwardDiff.Chunk{7}, ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}}}, z::AdvancedHMC.PhasePoint{Vector{Float64}, AdvancedHMC.DualValue{Float64, Vector{Float64}}}, n_steps::Int64; fwd::Bool, full_trajectory::Val{false})
            @ AdvancedHMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/integrator.jl:229](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/integrator.jl#line=228)
         [35] step (repeats 2 times)
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/integrator.jl:199](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/integrator.jl#line=198) [inlined]
         [36] A
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/trajectory.jl:759](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/trajectory.jl#line=758) [inlined]
         [37] find_good_stepsize(rng::Random.Xoshiro, h::AdvancedHMC.Hamiltonian{AdvancedHMC.DiagEuclideanMetric{Float64, Vector{Float64}}, AdvancedHMC.GaussianKinetic, Base.Fix1{typeof(LogDensityProblems.logdensity), LogDensityProblemsADForwardDiffExt.ForwardDiffLogDensity{LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}, ForwardDiff.Chunk{7}, ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}}, Turing.Inference.var"#∂logπ∂θ#32"{LogDensityProblemsADForwardDiffExt.ForwardDiffLogDensity{LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}, ForwardDiff.Chunk{7}, ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}}}, θ::Vector{Float64}; max_n_iters::Int64)
            @ AdvancedHMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/trajectory.jl:781](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/trajectory.jl#line=780)
         [38] find_good_stepsize(rng::Random.Xoshiro, h::AdvancedHMC.Hamiltonian{AdvancedHMC.DiagEuclideanMetric{Float64, Vector{Float64}}, AdvancedHMC.GaussianKinetic, Base.Fix1{typeof(LogDensityProblems.logdensity), LogDensityProblemsADForwardDiffExt.ForwardDiffLogDensity{LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}, ForwardDiff.Chunk{7}, ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}}, Turing.Inference.var"#∂logπ∂θ#32"{LogDensityProblemsADForwardDiffExt.ForwardDiffLogDensity{LogDensityFunction{DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random.Xoshiro}}, ForwardDiff.Chunk{7}, ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, ForwardDiff.GradientConfig{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 7}}}}}}, θ::Vector{Float64})
            @ AdvancedHMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/trajectory.jl:765](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AdvancedHMC/9NhHg/src/trajectory.jl#line=764)
         [39] initialstep(rng::Random.Xoshiro, model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, spl::DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, vi_original::DynamicPPL.TypedVarInfo{@NamedTuple{p_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_pump, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_pump, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, p_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:p_probe, typeof(identity)}, Int64}, Vector{Dirichlet{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}, Float64}}, Vector{AbstractPPL.VarName{:p_probe, typeof(identity)}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, I_pump::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_pump, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_pump, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}, I_probe::DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:I_probe, typeof(identity)}, Int64}, Vector{Product{Discrete, Poisson{Float64}, Vector{Poisson{Float64}}}}, Vector{AbstractPPL.VarName{:I_probe, typeof(identity)}}, Vector{Int64}, Vector{Set{DynamicPPL.Selector}}}}, Float64}; initial_params::Nothing, nadapts::Int64, kwargs::@Kwargs{})
            @ Turing.Inference [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl:211](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl#line=210)
         [40] step(rng::Random.Xoshiro, model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, spl::DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}; initial_params::Nothing, kwargs::@Kwargs{nadapts::Int64})
            @ DynamicPPL [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/sampler.jl:116](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/sampler.jl#line=115)
         [41] step
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/sampler.jl:99](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/DynamicPPL/MjWTB/src/sampler.jl#line=98) [inlined]
         [42] macro expansion
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl:171](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl#line=170) [inlined]
         [43] macro expansion
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl:137](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl#line=136) [inlined]
         [44] mcmcsample(rng::Random.Xoshiro, model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, N::Int64; progress::AbstractMCMC.ChannelProgress{Channel{Bool}}, progressname::String, callback::Nothing, num_warmup::Int64, discard_initial::Int64, thinning::Int64, chain_type::Type, initial_state::Nothing, kwargs::@Kwargs{nadapts::Int64, initial_params::Nothing})
            @ AbstractMCMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl:151](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl#line=150)
         [45] #sample#30
            @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl:123](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/hmc.jl#line=122) [inlined]
         [46] (::AbstractMCMC.var"#38#50"{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, Random.Xoshiro, UnitRange{Int64}, Nothing, Nothing, @Kwargs{chain_type::UnionAll, discard_initial::Int64}, Int64, Vector{Any}, Vector{UInt64}})()
            @ AbstractMCMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl:550](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl#line=549)
    
    ...and 3 more exceptions.
    
    Stacktrace:
     [1] sync_end(c::Channel{Any})
       @ Base ./task.jl:466
     [2] macro expansion
       @ ./task.jl:499 [inlined]
     [3] (::AbstractMCMC.var"#37#49"{Nothing, Nothing, @Kwargs{chain_type::UnionAll, discard_initial::Int64}, Int64, Vector{Any}, Vector{UInt64}, Int64, Int64, Vector{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random.Xoshiro}, UnitRange{Int64}})()
       @ AbstractMCMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl:507](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl#line=506)

Stacktrace:
  [1] sync_end(c::Channel{Any})
    @ Base ./task.jl:466
  [2] macro expansion
    @ ./task.jl:499 [inlined]
  [3] macro expansion
    @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl:482](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl#line=481) [inlined]
  [4] (::AbstractMCMC.var"#34#46"{String, Nothing, Nothing, @Kwargs{chain_type::UnionAll, discard_initial::Int64}, Int64, Int64, Vector{Any}, Vector{UInt64}, Int64, Int64, Vector{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random.Xoshiro}, UnitRange{Int64}})()
    @ AbstractMCMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl:134](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl#line=133)
  [5] with_logstate(f::AbstractMCMC.var"#34#46"{String, Nothing, Nothing, @Kwargs{chain_type::UnionAll, discard_initial::Int64}, Int64, Int64, Vector{Any}, Vector{UInt64}, Int64, Int64, Vector{DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}}, Vector{DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}}, Vector{Random.Xoshiro}, UnitRange{Int64}}, logstate::Base.CoreLogging.LogState)
    @ Base.CoreLogging ./logging/logging.jl:522
  [6] with_logger(f::Function, logger::LoggingExtras.TeeLogger{Tuple{LoggingExtras.EarlyFilteredLogger{ConsoleProgressMonitor.ProgressLogger, AbstractMCMC.var"#1#3"{Module}}, LoggingExtras.EarlyFilteredLogger{Base.CoreLogging.ConsoleLogger, AbstractMCMC.var"#2#4"{Module}}}})
    @ Base.CoreLogging ./logging/logging.jl:632
  [7] with_progresslogger(f::Function, _module::Module, logger::Base.CoreLogging.ConsoleLogger)
    @ AbstractMCMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl:157](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl#line=156)
  [8] macro expansion
    @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl:133](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/logging.jl#line=132) [inlined]
  [9] mcmcsample(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, ::MCMCThreads, N::Int64, nchains::Int64; progress::Bool, progressname::String, initial_params::Nothing, initial_state::Nothing, kwargs::@Kwargs{chain_type::UnionAll, discard_initial::Int64})
    @ AbstractMCMC [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl:452](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/AbstractMCMC/7f1oY/src/sample.jl#line=451)
 [10] sample(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{typeof(unconditional_model), (:y,), (), (), Tuple{Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, sampler::DynamicPPL.Sampler{NUTS{AutoForwardDiff{nothing, Nothing}, (), AdvancedHMC.DiagEuclideanMetric}}, ensemble::MCMCThreads, N::Int64, n_chains::Int64; chain_type::Type, progress::Bool, kwargs::@Kwargs{discard_initial::Int64})
    @ Turing.Inference [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl:317](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl#line=316)
 [11] sample
    @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl:306](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl#line=305) [inlined]
 [12] #sample#6
    @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl:302](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl#line=301) [inlined]
 [13] sample
    @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl:291](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl#line=290) [inlined]
 [14] #sample#5
    @ [/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl:287](https://max-jhub.desy.de/gpfs/exfel/data/scratch/danilo/julia-depot/packages/Turing/QN7BL/src/mcmc/Inference.jl#line=286) [inlined]
 [15] top-level scope
    @ In[5]:1
```

### Julia version info

<details><summary>versioninfo()</summary>

```
Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7543 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
  JULIA_CPU_TARGET = generic;broadwell,clone_all;skylake-avx512,clone_all;cascadelake,clone_all;sapphirerapids,clone_all;znver3,clone_all;znver2,clone_all
  JULIA_CONDAPKG_BACKEND = Null
  JULIA_PYTHONCALL_EXE = /gpfs/exfel/sw/software/mambaforge/22.11/envs/202501/bin/python
  JULIA_EXFEL_SYSIMAGE = /gpfs/exfel/sw/software/euxfel-environment-management/environments/202501/julia-exfel-sysimage.so
  JULIA_EXFEL_BINDIR = /gpfs/exfel/sw/software/julia-depot/bin
  JULIA_DEPOT_PATH = /gpfs/exfel/data/scratch/danilo/julia-depot:/gpfs/exfel/sw/software/julia-depot:
  JULIA_REVISE_POLL = 1
  JULIA_EXFEL_ENV = /gpfs/exfel/sw/software/euxfel-environment-management/environments/202501
```
</details>


### Manifest

<details><summary>]st --manifest</summary>

```
(@v1.11) pkg> st --manifest
Status `/gpfs/exfel/data/scratch/danilo/julia-depot/environments/v1.11/Manifest.toml`
⌅ [47edcb42] ADTypes v0.2.7
  [621f4979] AbstractFFTs v1.5.0
  [80f14c24] AbstractMCMC v5.7.2
⌅ [7a57a42e] AbstractPPL v0.8.4
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
⌅ [79e6a3ab] Adapt v3.7.2
⌅ [0bf59076] AdvancedHMC v0.6.4
  [5b7e9947] AdvancedMH v0.8.8
⌅ [576499cb] AdvancedPS v0.6.2
⌅ [b5ca4192] AdvancedVI v0.2.12
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.5.0
  [c7e460c6] ArgParse v1.2.0
  [7d9fca2a] Arpack v0.5.4
⌃ [4fba245c] ArrayInterface v7.7.1
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.7
  [198e06fe] BangBang v0.4.4
  [9718e550] Baselet v0.1.1
  [0e736298] Bessels v0.2.8
⌅ [76274a88] Bijectors v0.13.18
  [d1d4a3ce] BitFlags v0.1.9
  [082447d4] ChainRules v1.72.5
  [d360d2e6] ChainRulesCore v1.26.0
  [9e997f8a] ChangesOfVariables v0.1.10
  [aaaa29a8] Clustering v0.15.8
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.30.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
  [861a8166] Combinatorics v1.0.3
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.0
  [a33af91c] CompositionsBase v0.1.2
  [f0e56b4a] ConcurrentUtilities v2.5.0
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.6.0
  [d38c429a] Contour v0.6.3
  [150eb455] CoordinateTransformations v0.6.4
  [a8cc5b0e] Crayons v4.1.1
  [717857b8] DSP v0.8.4
  [9a962f9c] DataAPI v1.16.0
⌅ [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [8bb1440f] DelimitedFiles v1.9.1
  [b429d917] DensityInterface v0.4.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.120
  [ced4e74d] DistributionsAD v0.6.58
  [ffbed154] DocStringExtensions v0.9.5
⌅ [366bfd00] DynamicPPL v0.28.3
  [cad2338a] EllipticalSliceSampling v2.0.0
  [4e289a0a] EnumX v1.0.5
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.4
  [7a1cc6ca] FFTW v1.9.0
  [5789e2e9] FileIO v1.17.0
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.28.1
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
⌅ [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
⌅ [d9f16b24] Functors v0.4.12
⌅ [46192b85] GPUArraysCore v0.1.5
  [28b8d3ca] GR v0.73.17
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.17
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.28
  [c817782e] ImageBase v0.1.7
  [a09fc81d] ImageCore v0.10.5
  [02fcd773] ImageTransformations v0.10.2
  [22cec73e] InitialValues v0.3.1
  [505f98c9] InplaceOps v0.3.0
⌅ [a98d9a8b] Interpolations v0.15.1
  [8197267c] IntervalSets v0.7.11
  [3587e190] InverseFunctions v0.1.17
  [41ab1584] InvertedIndices v1.3.1
  [92d709cd] IrrationalConstants v0.2.4
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v0.21.4
  [63c18a36] KernelAbstractions v0.9.38
  [5ab0869b] KernelDensity v0.6.10
  [8ac3fa9e] LRUCache v1.6.2
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.9
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.1
⌅ [6f1fad26] Libtask v0.8.8
  [d3d80556] LineSearches v7.4.0
  [b20c7882] LinearInterpolations v0.1.6
  [6fdf6af0] LogDensityProblems v2.1.2
⌃ [996a588d] LogDensityProblemsAD v1.9.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.1.0
⌅ [c7f686f2] MCMCChains v6.0.7
  [be115224] MCMCDiagnosticTools v0.3.15
  [e80e1ace] MLJModelInterface v1.12.0
  [1914dd2f] MacroTools v0.5.16
  [dbb5928d] MappedArrays v0.4.2
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [128add7d] MicroCollections v0.2.0
  [e1d29d7a] Missings v1.2.0
  [e94cdb99] MosaicViews v0.3.4
  [6f286f6a] MultivariateStats v0.10.3
⌃ [d41bc354] NLSolversBase v7.8.3
  [872c559c] NNlib v0.9.31
  [15e1cf62] NPZ v0.4.3
  [77ba4419] NaNMath v1.1.3
  [86f7a689] NamedArrays v0.10.4
  [c020b1a1] NaturalSort v1.0.0
  [b8a86587] NearestNeighbors v0.4.22
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.5.0
⌃ [429524aa] Optim v1.11.0
⌃ [3bd65402] Optimisers v0.4.1
⌅ [7f7a1694] Optimization v3.24.3
⌅ [bca83a33] OptimizationBase v0.0.5
⌅ [36348300] OptimizationOptimJL v0.3.2
  [bac558e1] OrderedCollections v1.8.1
  [90014a1f] PDMats v0.11.35
  [5432bcbf] PaddedViews v0.5.12
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.19
  [f27b6e38] Polynomials v4.1.0
  [85a6dd25] PositiveFactorizations v0.2.4
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v2.4.0
  [33c8b6b6] ProgressLogging v0.1.5
  [92933f4c] ProgressMeter v1.10.4
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [94ee1d12] Quaternions v0.7.6
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌃ [731186ca] RecursiveArrayTools v3.13.0
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [79098fc4] Rmath v0.8.0
  [f2b01f46] Roots v2.2.9
  [6038ab10] Rotations v1.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.15
⌅ [26aad666] SSMProblems v0.5.2
⌃ [0bca4576] SciMLBase v2.31.0
⌅ [c0aeaf25] SciMLOperators v0.3.12
⌃ [53ae85a6] SciMLStructures v1.2.0
  [30f210dd] ScientificTypesBase v3.0.0
  [7e506255] ScopedValues v1.4.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.8
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.2
  [dc90abb0] SparseInverseSubset v0.1.2
  [276daf66] SpecialFunctions v2.5.1
  [171d559e] SplittablesBase v0.1.15
  [860ef19b] StableRNGs v1.0.3
  [cae243ae] StackViews v0.1.2
  [90137ffa] StaticArrays v1.9.14
  [1e83bf80] StaticArraysCore v1.4.3
  [64bff920] StatisticalTraits v3.5.0
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.6
  [4c63d2b9] StatsFuns v1.5.0
  [f3b207a7] StatsPlots v0.15.7
  [892a3eda] StringManipulation v0.4.1
⌃ [09ab397b] StructArrays v0.6.18
⌃ [2efcf032] SymbolicIndexingInterface v0.3.11
  [ab02a1b2] TableOperations v1.2.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
  [5d786b92] TerminalLoggers v0.1.7
  [b718987f] TextWrap v1.0.2
  [9f7883ad] Tracker v0.2.38
  [3bb67fe8] TranscodingStreams v0.11.3
  [28d57a85] Transducers v0.4.84
⌃ [fce5fe82] Turing v0.34.1
  [5c2747f8] URIs v1.6.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.24.0
  [45397f5d] UnitfulLatexify v1.7.0
  [013be700] UnsafeAtomics v0.3.0
  [41fe7b60] Unzip v0.2.0
  [cc8bc4a8] Widgets v0.6.7
  [efce3f68] WoodburyMatrices v1.0.0
  [a5390f91] ZipFile v0.10.1
  [700de1a5] ZygoteRules v0.2.7
⌅ [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.5+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.7.1+0
⌃ [b22a6f82] FFMPEG_jll v6.1.3+0
  [f5851436] FFTW_jll v3.3.11+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.4.0+2
  [d2c73de3] GR_jll v0.73.17+0
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [7746bdde] Glib_jll v2.84.3+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.1.2+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.0.1+0
  [1d63c593] LLVMOpenMP_jll v18.1.8+0
  [dd4b983a] LZO_jll v2.10.3+0
  [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.1+0
  [89763e89] Libtiff_jll v4.7.1+0
  [38a345b3] Libuuid_jll v2.41.1+0
  [856f044c] MKL_jll v2025.2.0+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [458c3c95] OpenSSL_jll v3.5.2+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.5.2+0
  [36c8627f] Pango_jll v1.56.3+0
⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.8.2+1
  [629bc702] Qt6Declarative_jll v6.8.2+1
  [ce943373] Qt6ShaderTools_jll v6.8.2+1
  [e99dba38] Qt6Wayland_jll v6.8.2+1
  [f50d1b31] Rmath_jll v0.5.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.1+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.12+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.7+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.1+0
  [a51aa0fd] Xorg_libXi_jll v1.8.3+0
  [d1454406] Xorg_libXinerama_jll v1.1.6+0
  [ec84b674] Xorg_libXrandr_jll v1.5.5+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.3+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.5+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.44.0+0
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
  [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.12.1+0
  [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.50+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
  [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.9.2+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

(@v1.11) pkg> 
```
</details>


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Poisson with Dirichlet prior samples negative values #2663

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Poisson with Dirichlet prior samples negative values #2663

Description

Minimal working example

Description

Julia version info

Manifest

Metadata

Metadata

Assignees

Labels

Type

Projects

Milestone

Relationships

Development

Issue actions