# Vectors of vector parameters in Turing.jl?

**URL:** <https://discourse.julialang.org/t/vectors-of-vector-parameters-in-turing-jl/83645>\
**Category:** General Usage\
**Tags:** turing\
**Created:** [July 1, 2022, 9:58pm UTC](https://discourse.julialang.org/t/vectors-of-vector-parameters-in-turing-jl/83645 "2022-07-01T21:58:55Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![dlakelan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlakelan/32/8491_2.png) [@dlakelan](https://discourse.julialang.org/u/dlakelan)\
**Post date:** [July 1, 2022, 9:58pm UTC](https://discourse.julialang.org/t/vectors-of-vector-parameters-in-turing-jl/83645/1 "2022-07-01T21:58:55Z")

</div>

I want to run a Bayesian model in which there’s an overall US average behavior, which is the mean for a set of regional behaviors, and that is the mean for all the states in the region… the behavior is defined in terms of a basis expansion which has a certain number of coefficients… let’s say it’s 10 coefficients.

Defining the overall US average is easy:

```julia
nationcoefs ~ MvNormal(10,2.0)

```

Now, suppose I have defined 8 regions, and want to do something like:

```julia
for i in 1:8
   regioncoefs[i] ~ MvNormal(nationcoefs,scale)
end

```

And then for each state want something like:

```julia
for i in 1:51
   statecoefs[region[i]] ~ MvNormal(regioncoefs[region[i]],scale2)
end

```

and then I’ll set up a likelihood based on the expansions and the observed data.

The issue is how do I define/declare/inform Turing that “regioncoefs” is a certain sized vector of vectors, and similarly for “statecoefs”?

Can I just declare something like:

```julia
regioncoefs = [zeros(Float64,k) for i in 1:nregion]

```

before I do the ~ statements?

---

<div class="post-metadata">

**Author:** ![dlakelan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlakelan/32/8491_2.png) [@dlakelan](https://discourse.julialang.org/u/dlakelan)\
**Post date:** [July 3, 2022, 7:25pm UTC](https://discourse.julialang.org/t/vectors-of-vector-parameters-in-turing-jl/83645/2 "2022-07-03T19:25:49Z")

</div>

Ok, I’ve tried to do something like this, but am getting an error:

```julia
    regioncoefs = fill(nationcoefs,nregions)
    for i in 1:length(regioncoefs)
        regioncoefs[i] ~ MvNormal(nationcoefs,2.0)
    end

```

The error is:

```julia
ERROR: ArgumentError: Converting an instance of ReverseDiff.TrackedReal{Float64, Float64, Nothing} to Float64 is not defined. Please use `ReverseDiff.value` instead.

```

And I’m not sure it’s related to this code, but it seems to be that others have had similar issues with mutation based code.

I can’t figure out any other way to express the idea that there’s a vector of vectors and each vector in the collection should be distributed as some Distribution type. I’m not sure if something like

```julia
thing = [foo ~ MvNormal(bar,scale) for i in 1:n]

```

is legal syntax / meaningful. but I’ll give that a try too

---

<div class="post-metadata">

**Author:** ![dlakelan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlakelan/32/8491_2.png) [@dlakelan](https://discourse.julialang.org/u/dlakelan)\
**Post date:** [July 4, 2022, 4:26am UTC](https://discourse.julialang.org/t/vectors-of-vector-parameters-in-turing-jl/83645/3 "2022-07-04T04:26:28Z")

</div>

The error I was getting was because I was calling

```julia
sample(model,NUTS(0.8,500))

```

instead of

```julia
sample(model,NUTS(500,0.8))

```

So, I can basically say that yes it work to do the following:

```julia
    nationcoefs ~ MvNormal(zeros(Float64,nc),2.0)
    regioncoefs = fill(nationcoefs,nregions)
    for i in 1:length(regioncoefs)
        regioncoefs[i] ~ MvNormal(nationcoefs,2.0)
    end

```

It’s important to avoid doing something like `fill(0.0,nregions)` because it screws up the type system when Turing starts to use ReverseDiff types or ForwardDiff types etc.