Allow posterior prediction to extend state-centered temporal processes beyond the fitted time horizon.

[cdc-mitzimorris]

This PR lets users can select either parameterization and get the same forecast-horizon behavior:

• Posterior prediction at the fitted horizon replays the fitted trajectory.
• Posterior prediction at a longer horizon replays the fitted trajectory and samples the missing suffix.

Changes made:

• Converted state branches of RandomWalk, AR1, and DifferencedAR1 to NumPyro scan.
• _state sites now use (time, process) layout as innovation processes.
• Added posterior-extension and terminal-carry tests.
• Added forecasting parity tests for state and innovation parameterizations.

Files changed:

• pyrenew/latent/temporal_processes.py
• test/test_temporal_processes.py
• latent/init.py (pyrenew/latent/init.py)

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Pull request overview

Enables state-centered temporal processes to extend posterior forecasts beyond fitted horizons.

Changes:

• Reimplemented state transitions with NumPyro scan.
• Added replay, extension, terminal-carry, and parity tests.
• Preserved state-distribution exports and added repository guidance.

File summaries

File	Description
pyrenew/latent/temporal_processes.py	Implements time-leading scanned state transitions.
test/test_temporal_processes.py	Tests state replay and forecast extension.
pyrenew/latent/__init__.py	Preserves state-distribution exports.
AGENTS.md	Adds unrelated repository-wide contributor guidance.

Review details

• Files reviewed: 4/4 changed files
• Comments generated: 1
• Review effort level: Balanced

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[github-actions]

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.82%. Comparing base (9493a0a) to head (c477d4f).
⚠️ Report is 7 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #888      +/-   ##
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+ Coverage   98.79%   98.82%   +0.02%     
==========================================
  Files          59       58       -1     
  Lines        2240     2124     -116     
==========================================
- Hits         2213     2099     -114     
+ Misses         27       25       -2     

Flag	Coverage Δ
unittests	98.82% <100.00%> (+0.02%)	⬆️

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[dylanhmorris]

A couple key things.

[cdc-mitzimorris]

A couple key things.

@dylanhmorris - all requested changes made.

[dylanhmorris]

Thanks @cdc-mitzimorris. Please reconcile merge conflicts with main so there's no AGENTS.md in this diff.

Longer term we may wish to think about a full refactor of how we handle processes (as PyRenew base RVs vs NumPyro distributions vs TemporalProcess wrappers of PyRenew base RVs. But I think we should land this to unblock you.