# Making Turing Fast with large numbers of parameters?

**URL:** <https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072>\
**Category:** General Usage\
**Tags:** turing\
**Created:** [October 1, 2021, 7:53pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072 "2021-10-01T19:53:43Z")\
**Posts on this page:** 20\
**Page:** 5

<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:** [October 27, 2021, 3:28pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/81 "2021-10-27T15:28:10Z")

</div>

I tried this:

```julia

function truncatenormal(a,b)::UnivariateDistribution
    truncated(Normal(a,b),0.0,Inf)
end

@model function estweights3lazy(nstaff,staffid,npatients,patientid,usewch,totweight)
    wcwt ~ Gamma(20.0,15.0/19)
    measerr ~ Gamma(10.0,20.0/9)
    staffweights ~ filldist(truncated(Normal(150,30),90.0,Inf),nstaff)
    patientweights ~ filldist(truncated(Normal(150,30),90.0,Inf),npatients)
    theta = LazyArray(@~ view(staffweights,staffid) .+ view(patientweights,patientid) .+ usewch .* wcwt)
    totweight ~ arraydist(LazyArray(@~ truncatenormal.(theta,measerr)))
end

```

But it gives a backtrace:

```julia
ERROR: MethodError: no method matching arraydist(::BroadcastVector{Any, typeof(truncatenormal), Tuple{BroadcastVector{Float64, typeof(+), Tuple{BroadcastVector{Float64, typeof(+), Tuple{SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}, SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}}}, BroadcastVector{Float64, typeof(*), Tuple{Vector{Int64}, Float64}}}}, Float64}})
Closest candidates are:
  arraydist(::AbstractVector{<:UnivariateDistribution}) at /home/dlakelan/.julia/packages/DistributionsAD/b93cZ/src/arraydist.jl:5
  arraydist(::AbstractMatrix{<:UnivariateDistribution}) at /home/dlakelan/.julia/packages/DistributionsAD/b93cZ/src/arraydist.jl:17
  arraydist(::AbstractVector{<:MultivariateDistribution}) at /home/dlakelan/.julia/packages/DistributionsAD/b93cZ/src/arraydist.jl:47
Stacktrace:
  [1] estweights3lazy( __model__ ::DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__ ::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, Vector{Base.RefValue{Float64}}}, __context__ ::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG}, nstaff::Int64, staffid::Vector{Int64}, npatients::Int64, patientid::Vector{Int64}, usewch::Vector{Int64}, totweight::Vector{Float64})
    @ Main ./REPL[81]:7
  [2] macro expansion
    @ ~/.julia/packages/DynamicPPL/RcfQU/src/model.jl:465 [inlined]
  [3] _evaluate(model::DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, varinfo::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, Vector{Base.RefValue{Float64}}}, context::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/RcfQU/src/model.jl:448
  [4] evaluate_threadsafe(model::DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, varinfo::DynamicPPL.UntypedVarInfo{DynamicPPL.Metadata{Dict{AbstractPPL.VarName, Int64}, Vector{Distribution}, Vector{AbstractPPL.VarName}, Vector{Real}, Vector{Set{DynamicPPL.Selector}}}, Float64}, context::DynamicPPL.SamplingContext{DynamicPPL.SampleFromUniform, DynamicPPL.DefaultContext, Random._GLOBAL_RNG})
...

```

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 3:31pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/82 "2021-10-27T15:31:26Z")

</div>

Please post a full MWE for me to copy and paste.

---

<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:** [October 27, 2021, 3:37pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/83 "2021-10-27T15:37:06Z")

</div>

Sure, it’s the same as the above MWE, but here it is in just copy-paste form:

```julia
using Pkg
Pkg.activate(".")
using Turing, DataFrames,DataFramesMeta,LazyArrays,Distributions,DistributionsAD
using LazyArrays

## every few hours a random staff member comes and gets a random
## patient to bring them outside to a garden through a door that has a
## scale. Sometimes using a wheelchair, sometimes not. knowing the
## total weight of the two people and the wheelchair plus some errors
## (from the scale measurements), infer the individual weights of all
## individuals and the weight of the wheelchair.

nstaff = 100
npat = 100
staffids = collect(1:nstaff)
patientids = collect(1:npat)
staffweights = rand(Normal(150,30),length(staffids))
patientweights = rand(Normal(150,30),length(staffids))
wheelchairwt = 15
nobs = 300

data = DataFrame(staff=rand(staffids,nobs),patient=rand(patientids,nobs))
data.usewch = rand(0:1,nobs)
data.totweights = [staffweights[data.staff[i]] + patientweights[data.patient[i]] for i in 1:nrow(data)] .+ data.usewch .* wheelchairwt .+ rand(Normal(0.0,20.0),nrow(data))

function truncatenormal(a,b)::UnivariateDistribution
    truncated(Normal(a,b),0.0,Inf)
end

@model function estweights3lazy(nstaff,staffid,npatients,patientid,usewch,totweight)
    wcwt ~ Gamma(20.0,15.0/19)
    measerr ~ Gamma(10.0,20.0/9)
    staffweights ~ filldist(truncated(Normal(150,30),90.0,Inf),nstaff)
    patientweights ~ filldist(truncated(Normal(150,30),90.0,Inf),npatients)
    theta = LazyArray(@~ view(staffweights,staffid) .+ view(patientweights,patientid) .+ usewch .* wcwt)
    totweight ~ arraydist(LazyArray(@~ truncatenormal.(theta,measerr)))
end

ch3l = sample(estweights3lazy(nstaff,data.staff,npat,data.patient,data.usewch,data.totweights),NUTS(500,.75),1000)

```

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 3:55pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/84 "2021-10-27T15:55:12Z")

</div>

I am not getting that error but I am getting numerical errors. I am using Turing 0.18.

---

<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:** [October 27, 2021, 3:55pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/85 "2021-10-27T15:55:51Z")

</div>

as am I, let me just restart my Julia session and see if it persists.

Do you get it sampling at all?

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 3:58pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/86 "2021-10-27T15:58:04Z")

</div>

also when I print the type of the `BroadcastVector`, I get

```julia
BroadcastVector{Truncated{Normal{ReverseDiff.TrackedReal{Float64, Float64, Nothing}}, Continuous, ReverseDiff.TrackedReal{Float64, Float64, Nothing}}, typeof(truncatenormal), Tuple{BroadcastVector{ReverseDiff.TrackedReal{Float64, Float64, Nothing}, typeof(+), Tuple{BroadcastVector{ReverseDiff.TrackedReal{Float64, Float64, Nothing}, typeof(+), Tuple{SubArray{ReverseDiff.TrackedReal{Float64, Float64, ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}}, 1, ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}, Tuple{Vector{Int64}}, false}, SubArray{ReverseDiff.TrackedReal{Float64, Float64, ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}}, 1, ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}, Tuple{Vector{Int64}}, false}}}, BroadcastVector{ReverseDiff.TrackedReal{Float64, Float64, Nothing}, typeof(*), Tuple{Vector{Int64}, ReverseDiff.TrackedReal{Float64, Float64, Nothing}}}}}, ReverseDiff.TrackedReal{Float64, Float64, Nothing}}}

```

which seems right to me.

> Do you get it sampling at all?

No. I suspect the prior or model might be bad. Try a smaller dataset or initialising from a good point.

---

<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:** [October 27, 2021, 4:01pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/87 "2021-10-27T16:01:28Z")

</div>

> [@mohamed82008](#):
>
> No. I suspect the prior or model might be bad. Try a smaller dataset or initialising from a good point.

So since the model and data are entirely synthetic, the model is actually essentially perfect. All the real weights are normally distributed from the given priors and the true wheelchair weight is right at the peak density of the prior for the wcwt parameter. However obviously initialization might be the issue. I’ll see if I can figure out an init vector to avoid that… after I get my kids breakfast etc.

Thanks so much for your help!

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 4:03pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/88 "2021-10-27T16:03:32Z")

</div>

> [@dlakelan](#):
>
> So since the model and data are entirely synthetic, the model is actually essentially perfect.

If it’s synthetic from a single set of parameter values and there is sufficient data and your model is identifiable, the posterior will asymptotically tend to a dirac-delta distribution. This will cause numerical issues when you have a large enough data set since you are trying to sample from a very concentrated distribution where the log joint almost everywhere is -Inf. A solution to this is to generate data from multiple sets of parameter values or use a smaller data set.

---

<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:** [October 27, 2021, 5:14pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/89 "2021-10-27T17:14:39Z")

</div>

Yes, or a very good initial point and a very small step size, good point.

However in this case there are 100 patients and 100 staff, and 300 observations so on average each person is only represented around 3 times, so I don’t think that is the issue, but I’m happy to try with 50 or 100 observations and see if it changes anything.

I let this model run for 1 hour and it was still at 0% and the backtrace when I interrupted looked like:

```julia
ERROR: InterruptException:
Stacktrace:
  [1] Array
    @ ./boot.jl:457 [inlined]
  [2] Array
    @ ./boot.jl:466 [inlined]
  [3] Array
    @ ./boot.jl:474 [inlined]
  [4] similar
    @ ./abstractarray.jl:829 [inlined]
  [5] similar
    @ ./abstractarray.jl:828 [inlined]
  [6] similar
    @ ./broadcast.jl:212 [inlined]
  [7] similar
    @ ./broadcast.jl:211 [inlined]
  [8] copy
    @ ./broadcast.jl:929 [inlined]
  [9] materialize
    @ ./broadcast.jl:904 [inlined]
 [10] logabsdetjac(b::Bijectors.TruncatedBijector{1, Float64, Float64}, x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}})
    @ Bijectors ~/.julia/packages/Bijectors/EELoe/src/bijectors/truncated.jl:125
 [11] logpdf_with_trans
    @ ~/.julia/packages/Bijectors/EELoe/src/Bijectors.jl:134 [inlined]
 [12] assume(rng::Random._GLOBAL_RNG, spl::DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, dist::Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}, vn::AbstractPPL.VarName{:patientweights, Tuple{}}, vi::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Base.RefValue{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}}})
    @ Turing.Inference ~/.julia/packages/Turing/uMQmD/src/inference/hmc.jl:484
 [13] tilde_assume
    @ ~/.julia/packages/DynamicPPL/RcfQU/src/context_implementations.jl:63 [inlined]
 [14] tilde_assume
    @ ~/.julia/packages/DynamicPPL/RcfQU/src/context_implementations.jl:58 [inlined]
 [15] tilde_assume
    @ ~/.julia/packages/DynamicPPL/RcfQU/src/context_implementations.jl:43 [inlined]
 [16] tilde_assume!
    @ ~/.julia/packages/DynamicPPL/RcfQU/src/context_implementations.jl:140 [inlined]
 [17] estweights3lazy( __model__ ::DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, __varinfo__ ::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Set{DynamicPPL.Selector}}}}}, ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}, Vector{Base.RefValue{ForwardDiff.Dual{ForwardDiff.Tag{Turing.Core.var"#f#1"{DynamicPPL.TypedVarInfo{NamedTuple{(:wcwt, :measerr, :staffweights, :patientweights), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:wcwt, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:wcwt, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:measerr, Tuple{}}, Int64}, Vector{Gamma{Float64}}, Vector{AbstractPPL.VarName{:measerr, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:staffweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:staffweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:patientweights, Tuple{}}, Int64}, Vector{Product{Continuous, Truncated{Normal{Float64}, Continuous, Float64}, FillArrays.Fill{Truncated{Normal{Float64}, Continuous, Float64}, 1, Tuple{Base.OneTo{Int64}}}}}, Vector{AbstractPPL.VarName{:patientweights, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{typeof(estweights3lazy), (:nstaff, :staffid, :npatients, :patientid, :usewch, :totweight), (), (), Tuple{Int64, Vector{Int64}, Int64, Vector{Int64}, Vector{Int64}, Vector{Float64}}, Tuple{}, DynamicPPL.DefaultContext}, DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext}, Float64}, Float64, 10}}}}, __context__ ::DynamicPPL.SamplingContext{DynamicPPL.Sampler{NUTS{Turing.Core.ForwardDiffAD{40}, (), AdvancedHMC.DiagEuclideanMetric}}, DynamicPPL.DefaultContext, Random._GLOBAL_RNG}, nstaff::Int64, staffid::Vector{Int64}, npatients::Int64, patientid::Vector{Int64}, usewch::Vector{Int64}, totweight::Vector{Float64})

...

```

I tried 50 observations, and put the initial position at exactly the true values and the initial epsilon in NUTS at 1e-9,

as follows:

```julia
julia> ch3l = sample(estweights3lazy(nstaff,data.staff,npat,data.patient,data.usewch,data.totweights),NUTS(500,.75;init_ϵ=1e-9),1000;init_theta=vcat([15.0,20.0],staffweights,patientweights))

```

it still spits out a bunch of warnings like:

```julia
┌ Warning: The current proposal will be rejected due to numerical error(s).
│ isfinite.((θ, r, ℓπ, ℓκ)) = (true, true, false, true)
└ @ AdvancedHMC ~/.julia/packages/AdvancedHMC/HQHnm/src/hamiltonian.jl:47
┌ Warning: The current proposal will be rejected due to numerical error(s).
│ isfinite.((θ, r, ℓπ, ℓκ)) = (true, true, false, true)
└ @ AdvancedHMC ~/.julia/packages/AdvancedHMC/HQHnm/src/hamiltonian.jl:47
┌ Warning: The current proposal will be rejected due to numerical error(s).
│ isfinite.((θ, r, ℓπ, ℓκ)) = (true, true, false, true)
└ @ AdvancedHMC ~/.julia/packages/AdvancedHMC/HQHnm/src/hamiltonian.jl:47

```

and goes nowhere.

---

<div class="post-metadata">

**Author:** ![Akatz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/akatz/32/15164_2.png) [@Akatz](https://discourse.julialang.org/u/Akatz)\
**Post date:** [October 27, 2021, 6:12pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/90 "2021-10-27T18:12:11Z")

</div>

@cscherrer Would this be a good usecase for Soss.jl?

---

<div class="post-metadata">

**Author:** ![cscherrer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cscherrer/32/7631_2.png) [@cscherrer](https://discourse.julialang.org/u/cscherrer)\
**Post date:** [October 27, 2021, 6:27pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/91 "2021-10-27T18:27:34Z")

</div>

Thanks @Akatz for the ping. There’s a lot here, is this the right place to start?

```julia
@model function fit300norms(norms,index)
    sd ~ Gamma(2.0,1.0)
    means ~ filldist(Uniform(0,50),300)
    for i in 1:300
        norms[index[i]] ~ Normal(means[index[i]],sd)
    end
end

```

---

<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:** [October 27, 2021, 6:36pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/92 "2021-10-27T18:36:30Z")

</div>

I think we can rule out a model vs a computational issue by seeing if Stan will run this model. I suspect it will, and it will sample it nearly instantaneously. I personally suspect what’s going on is that ReverseDiff is failing to work properly. I’ll write up a Stan model and try it with Stan.jl, which will be a useful exercise for me anyway.

@csherrer, I think the MWE to start with is in this comment: [Making Turing Fast with large numbers of parameters? - #51 by dlakelan](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/51)

---

<div class="post-metadata">

**Author:** ![ElOceanografo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/eloceanografo/32/624_2.png) [@ElOceanografo](https://discourse.julialang.org/u/ElOceanografo)\
**Post date:** [October 27, 2021, 7:00pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/93 "2021-10-27T19:00:56Z")

</div>

> [@dlakelan](#):
>
> really should be written by someone who actually knows what is going on though 🙂

This was kinda my feeling. I’m happy to make a PR, but I don’t currently understand Turing’s internals,  
LazyArrays, or how they interact well enough to tell someone else in simple terms “if you have this kind of situation, use `lazyarray` inside `arraydist` (but not this other situation), and here’s why…”

My question was getting at this…but also whether it would be possible/desirable to have `arraydist` automatically convert its argument to a `LazyArray`.

I made a naive attempt at this, modifying the model from @Storopoli’s logistic regression [example](https://storopoli.io/Bayesian-Julia/pages/7_logistic_reg/), and did get a sampling speedup relative to a simple `arraydist` (though not as much as with the bare `LazyArray`):

```julia
auto_lazy_arraydist(x) = arraydist(BroadcastArray(xi -> xi, x))

@model logreg(X, y; predictors=size(X, 2)) = begin
    #priors
    α ~ Normal(0, 2.5)
    β ~ filldist(TDist(3), predictors)

    #likelihood
    # Like this, samples in 50 s
    # y .~ BernoulliLogit.(α .+ X * β)

    # Like this, samples in 45 s
    # y ~ arraydist(BernoulliLogit.(α .+ X * β))

    # Like this, samples in 34 s
    y ~ auto_lazy_arraydist(BernoulliLogit.(α .+ X * β))

    # Like this, samples in 15 s
    # y ~ arraydist(LazyArray(@~ BernoulliLogit.(α .+ X * β)))
end;

X = Matrix(select(wells, Not(:switch)))
y = wells[:, :switch]
model = logreg(X, y);
chain = sample(model, NUTS(), MCMCThreads(), 2_000, 4)

```

Or maybe `.~` could automatically parse to do a lazy broadcast or something? Ideally, I feel like users souldn’t need to learn about this external package in the first place, especially since some of its syntax (i.e., `@~`) is confusingly close to Turing’s `~`, but with a completely different meaning.

Sorry if this comes across as greedy or demanding…but that is a risk when you are working with [Julia programmers](https://julialang.org/blog/2012/02/why-we-created-julia/) 😉

---

<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:** [October 27, 2021, 7:17pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/94 "2021-10-27T19:17:48Z")

</div>

Perhaps some kind of macro defined in Turing:

```julia
@lazyarraydist(...broadcasted computation...)

```

which automatically makes a lazy array from a broadcasted array calculation

---

<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:** [October 27, 2021, 8:08pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/95 "2021-10-27T20:08:53Z")

</div>

> [@dlakelan](#):
>
> I’ll write up a Stan model and try it with Stan.jl, which will be a useful exercise for me anyway.

Ugh, now I realize that I don’t have Stan installed, and this means I have to install Stan, which is a whole kettle of fish by itself … so I probably am not going to do this right away.

Since I got the arraydist with lazy arrays thing working ish, I am going to see if it works well with gamma distributions, and then compare to the non-working of the truncated normal. This is easier and faster to work on so it might produce some results more quickly.

Ok, so in fact the gamma version with lazy arrays and 300 observations samples quickly, a minute or so with a few numerical warnings.

```julia

@model function estweightslazygamma(nstaff,staffid,npatients,patientid,usewch,totweight)
    wcwt ~ Gamma(20.0,15.0/19)
    measerr ~ Gamma(10.0,20.0/9)
    staffweights ~ filldist(truncated(Normal(150,30),90.0,Inf),nstaff)
    patientweights ~ filldist(truncated(Normal(150,30),90.0,Inf),npatients)
    theta = LazyArray(@~ view(staffweights,staffid) .+ view(patientweights,patientid) .+ usewch .* wcwt)
    totweight ~ arraydist(LazyArray(@~ Gamma.(15, theta ./ 14)))
end

ch5 = sample(estweightslazygamma(nstaff,data.staff,npat,data.patient,data.usewch,data.totweights),NUTS(500,.75),1000)

```

So now I’m guessing that truncated distributions specifically somehow use if statements that prevent ReverseDiff from compiling the tape?

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<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 9:51pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/96 "2021-10-27T21:51:26Z")

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> [@dlakelan](#):
>
> So now I’m guessing that truncated distributions specifically somehow use if statements that prevent ReverseDiff from compiling the tape?

I didn’t use tape compilation when I used ReverseDiff above. You can generally rule out AD issues if you try 2 different reverse-mode packages and get similar behaviours.

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**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:** [October 27, 2021, 9:58pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/97 "2021-10-27T21:58:15Z")

</div>

Did you get a version using Truncated Normal to work? For me it always fails to do anything after tens of minutes to hours.

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<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 10:29pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/98 "2021-10-27T22:29:53Z")

</div>

> [@dlakelan](#):
>
> Did you get a version using Truncated Normal to work?

No but I didn’t try changing anything. When you get sampling issues, printing numbers inside the model can be helpful debugging info. Also try starting from just the prior, then add a few observations at a time and see where sampling stops working.

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<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:** [October 27, 2021, 11:07pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/99 "2021-10-27T23:07:24Z")

</div>

Well, debug printf let me realize I wasn’t turning on reverse diff, so inconsistent results depending on whether I was using a brand new Julia vs one where reverse diff had been enabled before…

debug printf also shows me that either it’s not really using my initialization or something weird is going on… I initialize it as:

```julia
ch3l = sample(estweights3lazy(nstaff,data.staff,npat,data.patient,data.usewch,data.totweights),NUTS(500,.75,init_ϵ=.002),1000;
              init_theta = vcat([15.0,20.0],staffweights,patientweights))

```

and then use this println:

```julia
    println("""Evaluating model... 
wcwt: $wcwt
measerr: $measerr
exstaffweights: $(staffweights[1:10])
expatweights: $(patientweights[1:10])
""")

```

inside the model

So initially wcwt and measerr should be 15.0 and 20.0, and all the estimated weights should be exactly correct… but the first print command says:

```julia
Evaluating model... 
wcwt: 0.6727279716358009
measerr: 0.19350227287063274
exstaffweights: [164.7901299487081, 217.52372933554884, 137.6205473016958, 175.4254441162211, 188.02642630005334, 175.8530682604024, 215.85351
585263436, 113.79632650916365, 109.91764961851418, 99.87309516255067]
expatweights: [168.51306657319324, 130.17891134846482, 148.83838569329237, 192.57929839739077, 137.26394389850617, 149.17636016275125, 174.854
40785493637, 109.5090910975809, 151.17248643226876, 205.4490091028178]

```

so measerr goes to nearly zero and of course this means serious numerical issues. Why is the initial vector not being used?

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**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [October 27, 2021, 11:12pm UTC](https://discourse.julialang.org/t/making-turing-fast-with-large-numbers-of-parameters/69072/100 "2021-10-27T23:12:59Z")

</div>

> [@dlakelan](#):
>
> Why is the initial vector not being used?

could be a bug, please open an issue

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