David Widmann

I guess you should also [use `$` to interpolate `x`](https://github.com/JuliaCI/BenchmarkTools.jl#quick-start). It might affect the results since you're benchmarking with a global variable.

> Tracker is quite bad with loops, not sure about indexing. Tracker is actually the fastest in the loop benchmark, isn't it?

Just a heads up, my plan is to remove `arraydist` and integrate and generalize it into the product distribution in Distributions.

`class` and `pos` are no TArrays in the last example, which is problematic I assume? The model formulation also looks a bit strange (there are no variables sampled/no hidden states...

Since this is about HMC diagnostics, maybe AdvancedHMC is more suitable? On the other hand, ESS and rhat are not specific for HMC. I suggested to highlight potentially worrisome estimates...

> I find the statistical summary useful because sometimes I can see if I get values which are completely unreasonable so something must be going wrong smile Sure, `describe` etc...

Probably it is better to check the implementation in https://github.com/TuringLang/DynamicPPL.jl/pull/150/ instead of the current one in Turing. The implementation in https://github.com/TuringLang/DynamicPPL.jl/pull/150/files#diff-2c85169e13f65836353350667ef4fa08dc52d726a6c20f6c1b4869bd099e4498 first sets the initial parameters, either specified by the...

That looks like the parameters are saved in a `Vector{Float64}` which can't be updated with dual numbers. I think maybe this could be solved by not using `t.vi` in https://github.com/TuringLang/Turing.jl/blob/f0fc1ea1e15e384f039fe9ab86fc7793a024a1f4/src/modes/ModeEstimation.jl#L224...

DynamicPPL-specific tests also take more time, and went up from 10-15 mins to 22-28mins recently: https://github.com/TuringLang/DynamicPPL.jl/actions/workflows/CI.yml?query=branch%3Amaster

Also related to https://github.com/TuringLang/Turing.jl/issues/976