Unify HMC + externalsampler + DynamicHMC parameter initialisation; re-export DynamicPPL.set_logprob_type!

[penelopeysm]

Closes #2739.

As a nice by-product of using rand(ldf) rather than vi[:], we also avoid accidentally promoting Float32 to Float64. This means that (together with TuringLang/DynamicPPL.jl#1328 and tpapp/DynamicHMC.jl#199) one can do

julia> using DynamicPPL; DynamicPPL.set_logprob_type!(Float32)
┌ Info: DynamicPPL's log probability type has been set to Float32.
└ Please note you will need to restart your Julia session for this change to take effect.

and then after restarting

julia> using Turing, FlexiChains, DynamicHMC

julia> @model function f()
           x ~ Normal(0.0f0, 1.0f0)
       end
f (generic function with 2 methods)

julia> chn = sample(f(), externalsampler(DynamicHMC.NUTS()), 100; chain_type=VNChain)
Sampling 100%|████████████████████████████████████████████| Time: 0:00:02
FlexiChain (100 iterations, 1 chain)
↓ iter=1:100 | → chain=1:1

Parameter type   VarName
Parameters       x
Extra keys       :logprior, :loglikelihood, :logjoint


julia> eltype(chn[@varname(x)])
Float32

julia> eltype(chn[:logjoint])
Float32

(Previously, the values of x would be Float32, but logjoint would be Float64. And if you used MCMCChains, everything would be Float64.)

[github-actions]

Turing.jl documentation for PR #2794 is available at:
https://TuringLang.github.io/Turing.jl/previews/PR2794/

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.44%. Comparing base (838ae6a) to head (8eafaba).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2794   +/-   ##
=======================================
  Coverage   86.44%   86.44%           
=======================================
  Files          22       22           
  Lines        1446     1446           
=======================================
  Hits         1250     1250           
  Misses        196      196           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.