Add JET static analysis tests and type annotations

[ChrisRackauckas-Claude]

Summary

• Add JET.jl as a test dependency
• Add JET test in test/jet.jl to verify package has no static analysis issues
• Add ::Integer type annotation to generate_priors and generate_theta functions in stan_inference.jl
• Add "JET" test group to test/runtests.jl

Details

JET analysis confirms DiffEqBayes has 0 issues when filtering to target module only (using target_modules=(DiffEqBayes,)). All 388 issues in the initial unfiltered report were from dependencies like StanSample, SymbolicUtils, AbstractPPL, etc.

The type annotations added are conservative - only adding ::Integer where the function clearly expects an integer count. These help with static analysis without over-constraining the code.

Test plan

• JET test passes (ENV["GROUP"]="JET" Pkg.test())
• Core tests pass (13/14, the 1 error is a pre-existing upstream issue with SteadyStateProblem not being a subtype of AbstractDEProblem)

Note: The pre-existing test failure in test/turing.jl for SteadyStateProblem is unrelated to these changes and exists on master.

cc @ChrisRackauckas

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Additional Changes

Rebased on master and added a fix for the SteadyStateProblem type restriction issue.

Changes in this update:

1. Rebased onto latest master - Now includes the Runic.jl formatting changes from PR Switch from JuliaFormatter to Runic.jl for code formatting #365.

2. Fixed type restriction for SteadyStateProblem - Changed prob::DiffEqBase.DEProblem to prob::Union{DiffEqBase.DEProblem, DiffEqBase.AbstractNonlinearProblem} in:

   • turing_inference (src/turing_inference.jl)
   • dynamichmc_inference (src/dynamichmc_inference.jl)
   • stan_inference (src/stan_inference.jl)

This fixes the pre-existing test failure where SteadyStateProblem was not a subtype of DEProblem. SteadyStateProblem is a subtype of AbstractNonlinearProblem, which is a sibling of AbstractDEProblem in the type hierarchy (both are subtypes of AbstractSciMLProblem).

All Turing tests now pass including the SteadyStateProblem test case.

🤖 Generated with Claude Code