# Why isn't mixture model sampling in Turing?

**URL:** <https://discourse.julialang.org/t/why-isnt-mixture-model-sampling-in-turing/115752>\
**Category:** General Usage\
**Tags:** question\
**Created:** [June 17, 2024, 11:59am UTC](https://discourse.julialang.org/t/why-isnt-mixture-model-sampling-in-turing/115752 "2024-06-17T11:59:44Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Cascobayesian](https://avatars.discourse-cdn.com/v4/letter/c/90ced4/32.png) [@Cascobayesian](https://discourse.julialang.org/u/Cascobayesian)\
**Post date:** [June 17, 2024, 11:59am UTC](https://discourse.julialang.org/t/why-isnt-mixture-model-sampling-in-turing/115752/1 "2024-06-17T11:59:44Z")

</div>

Hello!

I’m new to Julia but very excited by the possibilities. I’m particularly interested in using Turing to fit mixture models. However, in building up some non-trivial mixture examples, I’ve encountered an issue I just can’t figure. I wrote up the same model in R and Julia itself and it works fine in both cases so this is something about my understanding about how Turing works.

I have stripped down version of a binomial mixture model with multiple observations (i.e. each sample contains Q distinct observations, each its own binomial). To further reduce the problem, I feed the model the correct parameters except for the indicator variables. However, I cannot get Turing to sample the indicator parameters correctly. What is going wrong?! Any help would be greatly appreciated.

Here is the code for the model itself.

```julia

@model function binomial_replicate_mixture_model_p(t_counts,W,K,p,lambda)
 
    N,Q = size(t_counts)

    # Priors for the mixture weights
    #lambda ~ Dirichlet(K, 1.0)
    # Priors for the multinomial parameters

    z ~ filldist(Categorical(lambda),N)
    for n in 1:N
        for q in 1:Q          
           t_counts[n,q,:] ~ Multinomial(W[n,q],vec([1-p[z[n],q],p[z[n],q]]))
        end
    end
end

```

> **Simulation and control script**
>
> Here is the code for the data simulation:
> 
> ```julia
> using Distributions,LinearAlgebra
> using CSV,DataFrames
> using Random,Turing,MCMCChains
> 
> function sim_bmm(N,Q,K)
>     
> v = rand(1:K,N)
> 
> y_counts = zeros(Int64,N,Q)
> n_counts = zeros(Int64,N,Q)
> 
> alpha = Matrix{Float64}(undef, K,Q)
> beta = Matrix{Float64}(undef, K,Q)
> p = Matrix{Float64}(undef, K,Q)
> 
> for k in 1:K
> for q in 1:Q
> alpha[k,q] = rand([3.0,10.0,30.0])
> beta[k,q] = rand([3.0,10.0,30.0])
> p[k,q] = alpha[k,q]./(alpha[k,q]+beta[k,q])
> end
> end
> 
> #p_mat = alpha ./ (alpha + beta)
> 
> for i in 1:N
> for q in 1:Q
> tmp = rand(Multinomial(10000,vec([p[v[i],q],1-p[v[i],q]])),1)
> y_counts[i,q] = tmp[1]
> n_counts[i,q] = tmp[2]
> end
> end
> 
> return y_counts,n_counts,p,v
> end
> 
> ```
> 
> And here’s the control script:
> 
> ```julia
> 
> ## simulation parameters
> N = 100 ## num of samples 
> Q = 5 ## num of questions
> K = 7 ## num of components
> y_c,n_c,p,v = sim_bmm(N,Q,K)
> t_c = cat(y_c, n_c, dims=3)
> W = y_c+n_c
> lambda = fill(1/K,K)
> ## sampler parameters
> nsamples=5000
> nchains=1
> sampler_p = Gibbs(MH(:z))
> 
> ## model definition
> bbmm_p = binomial_replicate_mixture_model_p(t_c,W,K,p,lambda)
> chain_p = sample(bbmm_p,sampler_p,MCMCThreads(),nsamples,nchains);
> 
> ```

---

<div class="post-metadata">

**Author:** ![dqeeq](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@dqeeq](https://discourse.julialang.org/u/dqeeq)\
**Post date:** [June 17, 2024, 10:39pm UTC](https://discourse.julialang.org/t/why-isnt-mixture-model-sampling-in-turing/115752/2 "2024-06-17T22:39:33Z")

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> [@Cascobayesian](#):
>
> `bbmm_p = beta_binomial_replicate_mixture_model_p(t_c,W,K,p,pi)`

I think you meant

```julia
bbmm_p = binomial_replicate_mixture_model_p(t_c,W,K,p,pi)

```

I am getting a TaskFailedException when executing the last line, I mean

> [@Cascobayesian](#):
>
> `chain_p = sample(bbmm_p,sampler_p,MCMCThreads(),nsamples,nchains);`

, is that your question?

---

<div class="post-metadata">

**Author:** ![Cascobayesian](https://avatars.discourse-cdn.com/v4/letter/c/90ced4/32.png) [@Cascobayesian](https://discourse.julialang.org/u/Cascobayesian)\
**Post date:** [June 18, 2024, 1:43am UTC](https://discourse.julialang.org/t/why-isnt-mixture-model-sampling-in-turing/115752/4 "2024-06-18T01:43:43Z")

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Thank you for taking a look! Foolishly, that was not my issue: I just didn’t edit down my code correctly from the problem I was working on to this example. I’ve updated the code so it reflects the problem I’m hoping folks can look at (not the ones I unintentionally presented).