Validation

TL;DR

MENoBiS validates exactness mathematically (stationarity/detailed balance), constraint recovery at the realization level, scalability on the benchmark matrix, and calibration statistically. Exact stationary laws do not imply rapid mixing; validation evidence is per-route and per-instance.

Mathematical validation

• Exact enumeration on tiny instances where the full target distribution can be enumerated, comparing implemented kernels against the closed form;
• Detailed balance for Metropolis kernels;
• Stationarity — the target measure is invariant for the kernel;
• Exact conditioning identities — GC conditioned on hard constraints yields the MC target where the identity holds (see Ensemble equivalence).

Constraint validation

• realization-level recovery: sampled networks reproduce the constrained quantities exactly (microcanonical) or in expectation within tolerance (grand-canonical);
• fitted expectation recovery: strengths/degrees/cost/E/T reproduce their input sequences within documented relative tolerance.

Scalability validation

• benchmark sizes and regimes from the benchmark matrix (N=100/500/1000, sparse/dense, with and without self loops);
• memory and wall-time provenance per Practical scaling.

Statistical validation

• null calibration: p-values of null samples are uniform in the compatible region;
• filter false-positive rate control;
• sampled observable comparison: ensemble statistics behave like the observed ones when both come from the same null.

What validation does not prove

Explicitly:

• an exact stationary law does not imply rapid mixing — finite-run autocorrelation must still be assessed (MCMC diagnostics);
• one N=1000 benchmark does not prove every heterogeneous instance is easy;
• necessary feasibility tests are not always sufficient for sparse-domain feasibility;
• empirical ensemble similarity is not a theorem (Ensemble equivalence).

Exactness taxonomy

flowchart TD
    A[Sampler output] --> B{Generation mechanism}
    B -->|Direct conditional draw| D[Exact direct]
    B -->|Validated MCMC kernel| M[Exact stationary MCMC]
    B -->|Hard + expected constraints| H[Hybrid semantics]

    M --> BI[Finite burn-in still matters]
    M --> MI[Mixing still matters]
    H --> EX[Exact constraints named explicitly]
    H --> EP[Expected constraints named explicitly]

The supported-model matrix (Supported models) states the exactness category per route; the smoke-test suite runs a deterministic end-to-end workflow per critical route.