feat: hold a leaf parameter fixed in the priors front-door (#752)

[seabbs-bot]

Closes #752.

Problem

The priors front-door samples every inventory parameter through
tilde_assume!!, and a Dirac point mass is rejected by DynamicPPL's
discrete-distribution guard under NUTS. There was no way to hold one leaf
parameter fixed while fitting the others (e.g. fit a Gamma's shape while
pinning its scale).

API

A leaf parameter is held fixed by placing a plain value (not a
distribution) in its prior slot. The sampling models classify each slot:
a Distribution is sampled via tilde_assume!! as before; a
non-distribution value is substituted directly as a constant. A fixed
parameter therefore never enters the sampler (no tilde, no point mass), so
it is absent from the VarInfo and the chain, while the fitted parameters
flow exactly as today.

Two equivalent ways to set the pin, both extending the existing override
mechanism rather than forking it:

# build_priors gains a `fix` keyword, a nested NamedTuple keyed like the
# tree whose leaf values are the plain constants.
priors = build_priors(template; fix = (onset_admit = (scale = 1.5,),))

# Or edit a built prior by path, the same override the API already uses.
priors = update(build_priors(template), :onset_admit => (scale = 1.5,))

fix takes precedence over a priors override for the same parameter and
is validated against the inventory (a typo errors rather than pinning
nothing silently).

Reading the fit back, the pinned constant is absent from the chain, so
chain_to_params / update(template, chain) / param_draws gain a fix
keyword that fills the constants back into the reconstructed distribution:

ready = update(template, chain; fix = priors)  # pinned scale reappears

Composes with the override API

Yes. The pin lives in the same nested prior NamedTuple that build_priors,
the priors= override, and update(priors, path => fields) already
produce and edit. fix is a convenience that writes plain values into that
structure; the update-by-path route reaches the identical result with no
new surface.

DynamicPPL note

No DynamicPPL limitation blocks the clean approach: because a fixed
parameter is substituted as a constant before any ~, the rejected-Dirac
path is never taken. The guard that motivated #752 is sidestepped entirely.

Tests

Red/green TDD. New tests:

• build_priors fix pins a parameter as a constant (#752) (unit): fix
  inserts a plain value, takes precedence over a priors override, matches
  the update-by-path pin, and errors on an unknown parameter.
• fixed leaf parameter: held constant, absent from VarInfo (turing): the
  fixed scale is in the reconstructed leaf and absent from the VarInfo,
  the free shape is sampled.
• fixed leaf parameter: update from chain keeps the pin (turing): a real
  NUTS fit recovers the free shape (~3.0) with the scale pinned at 1.5; the
  pinned value is absent from the chain yet reappears via
  update(template, chain; fix = priors).

Passing locally: the three new testitems and the build_priors unit test.
The full ComposedParametersModel.jl suite is re-running locally to
confirm no regression; CI runs the whole suite (Turing + AD backends) on
this PR.

This was opened by a bot. Please ping @seabbs for any questions.

[github-actions]

Try this Pull Request!

Option 1: Julia Package Manager

Open Julia and type:

import Pkg
Pkg.activate(temp=true)
Pkg.add(url="https://github.com/EpiAware/CensoredDistributions.jl", rev="feat/fixed-param-752")
using CensoredDistributions

Option 2: Local Checkout

If you have the repo locally:

git checkout feat/fixed-param-752
julia --project=. -e "using Pkg; Pkg.instantiate()"

[codecov]

Codecov Report

❌ Patch coverage is 58.97436% with 16 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
ext/CensoredDistributionsFlexiChainsExt.jl	0.00%	10 Missing ⚠️
ext/CensoredDistributionsDynamicPPLExt.jl	0.00%	6 Missing ⚠️

Flag	Coverage Δ
ad-enzyme-forward	23.51% <0.00%> (-0.21%)	⬇️
ad-enzyme-reverse	23.51% <0.00%> (-0.21%)	⬇️
ad-forwarddiff	29.89% <0.00%> (-0.17%)	⬇️
ad-mooncake-forward	22.40% <0.00%> (-0.22%)	⬇️
ad-mooncake-reverse	26.96% <0.00%> (-0.26%)	⬇️
ad-reversediff	23.87% <0.00%> (-0.19%)	⬇️
unit	90.03% <100.00%> (+0.10%)	⬆️

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Files with missing lines	Coverage Δ
src/composers/introspection.jl	83.11% <100.00%> (+0.82%)	⬆️
ext/CensoredDistributionsDynamicPPLExt.jl	0.00% <0.00%> (ø)
ext/CensoredDistributionsFlexiChainsExt.jl	0.00% <0.00%> (ø)

... and 4 files with indirect coverage changes

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