Numerical Validation Suite

The numerical validation suite in cases/numerical_validation/ independently audits the core mathematical engines of Risk Bridge.

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What the Suite Audits

1. Analytic Gradient Checks: Evaluates closed-form negative log-likelihood gradients against two-point finite-difference approximations across randomized parameter vectors \(\theta\).
2. Constraint Jacobian Checks: Verifies that the \(K \times p\) analytic constraint Jacobian matrix \(J(\theta)\) matches finite-difference approximations within \(\le 10^{-6}\).
3. Solver Ladder Trajectories: Audits convergence pathways across BFGS, trust-constr, and SLSQP, logging objective values and iteration counts.
4. Parameter Recovery: Tests that synthetic data generated from known parameters \(\theta^*\) recovers the true parameters as sample size \(n \to \infty\).

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Execution

Run the complete suite:

python -m cases.numerical_validation.run_suite

Expected Output

The runner generates validation tables under data/numerical_validation/ and reports passing status on all numerical tolerance gates.