arraydist() errors when custom distribution uses non-Real data

[PTWaade]

Minimal working example

using Turing, SequentialSamplingModels

#Create example data
data = [
    (choice = 1, rt = 0.8),
    (choice = 1, rt = 0.8)
    ]

#This will work
@model function m1(data)
    
    #Sample parameter
    τ ~ truncated(Normal(0.3, 0.1), lower = 0)
    
    #Fit to data
    for i in 1:length(data)
        data[i] ~ DDM(τ = τ)
    end
end

#This will error
@model function m2(data)
    
    #Sample parameter
    τ ~ truncated(Normal(0.3, 0.1), lower = 0)
    
    #Fit to data
    data ~ filldist(DDM(τ = τ), length(data))

end

#This will error
@model function m3(data)
    
    #Sample parameter
    τ ~ truncated(Normal(0.3, 0.1), lower = 0)

    #Fit to data
    data ~ arraydist([DDM(τ = τ) for _ in 1:length(data)])

end

#This will error
@model function m4(data)
    
    #Sample parameter
    τ ~ truncated(Normal(0.3, 0.1), lower = 0)

    #Fit to data
    data ~ product_distribution([DDM(τ = τ) for _ in 1:length(data)]...)

end

sample(m1(data), NUTS(), 1000)

sample(m2(data), NUTS(), 1000)

sample(m3(data), NUTS(), 1000)

sample(m4(data), NUTS(), 1000)

Description

Hi Turing - thanks for your incredible work!

I get an error when using arraydist and related methods with a distribution which is defined over non-Real/Array{Real} data. The error is because the loglikelihood function isn't defined for non-Real data.

I here use a custom distribution from the SequentialSamplingModels.jl package.
It works if I iterate over the data, but errors specifically if I use arraydist.

Julia version info

versioninfo()

Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 8 × Apple M1
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
Threads: 2 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1
  JULIA_NUM_THREADS = 2

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[penelopeysm]

Hmmmmmmmm. We could implement extra methods on our end to make this work, but I fear that might involve pirating Distributions and/or SequentialSamplingModels types.

Fundamentally it seems that the issue is that DDM isa MultivariateDistribution and although loglikelihood is faithfully implemented for DDM (https://github.com/itsdfish/SequentialSamplingModels.jl/blob/8a2fede77526f2b44143b87d7cf111dcc9d8542c/src/type_system.jl#L205), loglikelihood for a product of multivariates is defined in Distributions.jl and those methods assume that multivariate distributions only take vectors.

@itsdfish Do you think this is something you could fix by implementing a method for loglikelihood / logpdf on this type?
(or i suppose something like ProductDistribution{M, N, Vector{<:SSM2D}})

julia> typeof(product_distribution([DDM(τ = 0.3) for _ in 1:3]))
Distributions.ProductDistribution{2, 1, Vector{DDM{Float64}}, SequentialSamplingModels.Mixed, Any}

[penelopeysm]

Only tangentially related but on the Turing side I think we really need to revisit filldist and arraydist and see how much of that code is really needed. I'm not 100% sure on this, but my impression is that those methods pre-date Distributions.jl's product_distribution and we may not actually need them anymore. arraydist is basically product_distribution but with some custom code, but I don't see why that shouldn't all be in Distributions (and there's a good chance it already is).

Right now everything 'just works' and that's why we've been unwilling to touch it, but I wouldn't be surprised if the entire DistributionsAD.jl package could be condensed to two lines

filldist(d::Distribution, n1::Int, ns::Int...) = product_distribution(fill(d, n1, ns...))
arraydist = product_distribution

Edit: I benchmarked it and it can almost be condensed to two lines #2613

[itsdfish]

@itsdfish Do you think this is something you could fix by implementing a method for loglikelihood / logpdf on this type?
(or i suppose something like ProductDistribution{M, N, Vector{<:SSM2D}})

Yeah. I think I could do that. If I understand correctly, it works like loglikelihood:

using Distributions 

data = [0,1]

prod_dist = product_distribution([Normal(0,1), Normal(0,1)])

logpdf(prod_dist, data) ≈ sum(logpdf(Normal(0,1), data))

Now that I understand the design of Distributions.jl better, I realize that logpdf is not implemented correctly. It returns a single value (similar to loglikelihood), but should return a vector of pointwise likelihoods. This is something I should fix in the future. It looks like this was only and issue for DDM, which is now fixed.

This points to a deeper challenge I encountered when developing the type system for SequentialSamplingModels.jl. There is no mixed type in Distributions.jl for a discrete-continuous joint distribution. There are several ways to handle this issue, each with different tradeoffs. I decided to use a NamedTuple, where one tuple contained a vector of discrete variables, and the other entry contained a vector of continuous variables. I implemented it as follows

julia> rand(DDM())
(choice = 2, rt = 0.3727130544870708)

julia> rand(DDM(), 1)
(choice = [1], rt = [0.3648738798812269])

I would be willing to entertain other ideas.

@PTWaade for the time being, you can do the following:

julia> data = rand(DDM(τ = .3), 5)
(choice = [1, 2, 2, 1, 2], rt = [0.5040677024515023, 0.5242506376120015, 0.3591790672569014, 1.20554620920633, 0.33637971998465854])

which will allow you to do the following:

#This will work
@model function m5(data)
    
    #Sample parameter
    τ ~ truncated(Normal(0.3, 0.1), lower = 0)
    
    #Fit to data
    data ~ DDM(τ = τ)
end

sample(m5(data), NUTS(), 1000)

[penelopeysm]

I'm not intimately familiar with the Distributions.jl codebase, but what you did makes sense to me (at least at my current level of understanding). IMO it doesn't really matter what type rand returns as long as you can call logpdf on it, and NamedTuple is a fine type. The unfortunate bit of it I suppose is that you'd have to overload the entire interface of Distributions to work with your custom distribution (so that logpdf/etc is dispatched to your more specific implementation rather than the generic one in Distributions), and there's no way to know if you've exhaustively implemented every interface function (in this case we are missing Product{MyDist}). But that's a broader problem with Julia "interfaces" in general, it's impossible to know what an abstract type does apart from reading the docs, which may not exist (DynamicPPL has a lot of undocumented interfaces).

[PTWaade]

Dear both,

Thank you for the responses and discussion!

Perhaps we should get in touch with Distributions.jl and ask if it is possible for them to implement a mixed continuous-discrete multivariate distribution type then? It seems that this would be the ideal solution in the long run, and I don't think SequentialSamplingModels would necessarily be the only use case for it, even if it is not too common.
I'd happily help reaching out to them if this is useful.

@itsdfish Thank you for the suggestion! I can't follow it, unfortunately, because I am implementing models where the DDM parameters can change across trials (a project I would be excited to tell you about when convenient!).
In my code I have for now gone with the for loop option, even if it is slower. I wanted to implement that anyway for the pointwise loglikelihoods -> PSIS-LOO.

@penelopeysm I also think that deprecating DistributionsAD and moving everything upstream sounds ideal. Then filldist() would just be a convenience function on top of product_distribution (whihc, tbh, could actually also be in Distributions.jl). Full support from here on that.

Warm thoughts, and let me know if I can be helpful!

[itsdfish]

@itsdfish Thank you for the suggestion! I can't follow it, unfortunately, because I am implementing models where the DDM parameters can change across trials (a project I would be excited to tell you about when convenient!).
In my code I have for now gone with the for loop option, even if it is slower. I wanted to implement that anyway for the pointwise loglikelihoods -> PSIS-LOO.

That sounds like an interesting model. I would love to learn more about it sometime when you are ready. I would welcome a simple example as a PR for documentation. I'm glad the for loop is working for you. I'm not sure if product_distribution will be faster, but I intend to implement a new method for that this weekend.

Regarding the mixed type, I believe I discussed that with one of the maintainers of Distributions.jl and he said it would be preferable to maintain in SequentialSamplingModels.jl. However, I think we could make the case for changing that if we see demand for a mixed type from other packages.

[PTWaade]

@itsdfish I will contact you directly to discuss what I am doing - I am also using your ACTRModels package, and have been wanting to discuss things with you for a while, actually. I am working on software for cognitive modeling in general, and want to make sure I am compatible with your incredibly useful packages.
Perhaps I can write you on email, or open an issue on your Github repo?

Regarding where a mixed type should be maintained, then I suppose if @penelopeysm is right that maintaining dispatches for all the relevant interfaces is difficult, I think that would be another argument for it being included in Distributions.jl. It became a difficulty here, for example.

I'll think about other examples where mixed type distributions would be relevant, but I think cognitive modeling is a good use-case, especially as we are moving towards in general modeling behaviour together with other signatures (confidence, reaction time, physiology). Current models (apart from sequential sampling models) usually at best just have independent distributions (for actiosn and confidences/RTs for example), in my experience, but I think it would be useful to be able to go beyond that.

Thank you for implementing the product_distribution dispatch - that's very useful!

[PTWaade]

(Whoops; closed this issue - I don't know if you would like it to remain open @penelopeysm)

[penelopeysm]

Then filldist() would just be a convenience function on top of product_distribution (whihc, tbh, could actually also be in Distributions.jl)

product_distribution is indeed from Distributions.jl.

Whoops; closed this issue

No problem, I was going to close it anyway :)

[PTWaade]

Ah I meant that filldist() could be in Distributions.jl, too. It might also be useful outside of the Turing context, I'd think.

Thanks for the talk!

[penelopeysm]

Ahhhhh, I see, the semantic ambiguity of English 😄

[itsdfish]

@itsdfish I will contact you directly to discuss what I am doing - I am also using your ACTRModels package, and have been wanting to discuss things with you for a while, actually. I am working on software for cognitive modeling in general, and want to make sure I am compatible with your incredibly useful packages.
Perhaps I can write you on email, or open an issue on your Github repo?

Awesome. I am glad the packages have been useful to others aside from myself 😃

Please open an Issue or Discussion in one of the repos.