numerical-validation

Numerical validation captures baseline outputs before changes, then compares post-change results to detect numerical differences. This process ensures mathematical correctness in algorithms, HMM components, and JAX-based computations by checking if outputs remain within fixed tolerances—typically 1e-14 for refactoring or 1e-10 for algorithm modifications.

Critical invariants include probabilities summing to one, transition matrices being stochastic, log-probabilities remaining finite, and covariance matrices being positive semi-definite. Validating these properties alongside numerical outputs prevents subtle logical errors in HMM filters, likelihood models, and state transitions that could compromise research conclusions.

Yes. Property-based testing verifies invariants across random inputs and edge cases automatically. Combined with golden regression testing against validated reference outputs on real scientific data, this technique catches subtle numerical changes that basic testing might miss in JAX and NumPy computations.

Baseline comparison captures output values before optimization, makes the code change, then compares new outputs against the baseline. The validation process reports numerical differences and generates analysis showing whether performance improvements introduced numerical drift or maintained accuracy within your specified tolerance.

Numerical validation requires pytest for test execution, NumPy for numerical operations, and JAX for advanced array computing on your scientific code. These dependencies enable baseline capture, invariant verification, property testing, and automated comparison of numerical outputs across code changes.

Unit tests verify logic but may miss subtle numerical errors that accumulate through algorithms, affecting research conclusions. Numerical validation adds rigorous baseline comparison, invariant checking, and regression testing specifically designed to detect accuracy loss in mathematical code—critical for scientific integrity.