Universal mathematics and statistics
Methods for cross-domain on the Julia and TypeScript compute planes.
38 capabilities
26 of 38 have a bound kernel or engine. States are shown as the registry records them; a request fails closed wherever an adapter, specialist model or governed data is still missing.
| पद्धत | Capability ID | स्थिती | Runs on |
|---|---|---|---|
| Robust Distribution | risk.capability.universal-mathematics-statistics.robust.distribution.v1 |
Reference implementation | Julia · frontier_risk_math.robust_distribution |
| Empirical Distribution | risk.capability.universal-mathematics-statistics.empirical.distribution.v1 |
Reference implementation | Python · stats.empirical_distribution |
| Bayesian Updating | risk.capability.universal-mathematics-statistics.bayesian.updating.v1 |
Reference implementation | Julia · frontier_risk_math.beta_binomial |
| Hierarchical Bayesian | risk.capability.universal-mathematics-statistics.hierarchical.bayesian.v1 |
Adapter required | – |
| Extreme Value | risk.capability.universal-mathematics-statistics.extreme.value.v1 |
Reference implementation | – |
| Tail Risk | risk.capability.universal-mathematics-statistics.tail.risk.v1 |
Reference implementation | Python · tail.pot_gpd |
| Copula Dependency | risk.capability.universal-mathematics-statistics.copula.dependency.v1 |
Adapter required | – |
| Tail Dependence | risk.capability.universal-mathematics-statistics.tail.dependence.v1 |
Adapter required | Python · dependence.tail_empirical |
| Monte Carlo | risk.capability.universal-mathematics-statistics.monte.carlo.v1 |
Reference implementation | Python · simulation.monte_carlo |
| Latin Hypercube | risk.capability.universal-mathematics-statistics.latin.hypercube.v1 |
Reference implementation | Python · sampling.latin_hypercube |
| Importance Sampling | risk.capability.universal-mathematics-statistics.importance.sampling.v1 |
Reference implementation | Python · sampling.importance |
| Sequential Monte Carlo | risk.capability.universal-mathematics-statistics.sequential.monte.carlo.v1 |
Adapter required | – |
| Kalman Filter | risk.capability.universal-mathematics-statistics.kalman.filter.v1 |
Adapter required | – |
| Extended Kalman | risk.capability.universal-mathematics-statistics.extended.kalman.v1 |
Adapter required | – |
| Unscented Kalman | risk.capability.universal-mathematics-statistics.unscented.kalman.v1 |
Adapter required | – |
| Particle Filter | risk.capability.universal-mathematics-statistics.particle.filter.v1 |
Adapter required | – |
| Markov Chain | risk.capability.universal-mathematics-statistics.markov.chain.v1 |
Adapter required | Python · markov.transition |
| Hidden Markov | risk.capability.universal-mathematics-statistics.hidden.markov.v1 |
Adapter required | – |
| Change Point | risk.capability.universal-mathematics-statistics.change.point.v1 |
Reference implementation | Python · change.cusum |
| Anomaly Detection | risk.capability.universal-mathematics-statistics.anomaly.detection.v1 |
Reference implementation | Python · anomaly.robust_mad |
| Survival Analysis | risk.capability.universal-mathematics-statistics.survival.analysis.v1 |
Adapter required | Python · survival.kaplan_meier |
| Reliability | risk.capability.universal-mathematics-statistics.reliability.v1 |
Adapter required | Python · reliability.weibull |
| Fault Tree | risk.capability.universal-mathematics-statistics.fault.tree.v1 |
Adapter required | – |
| Event Tree | risk.capability.universal-mathematics-statistics.event.tree.v1 |
Adapter required | – |
| Bayesian Network | risk.capability.universal-mathematics-statistics.bayesian.network.v1 |
Adapter required | – |
| Information Theory | risk.capability.universal-mathematics-statistics.information.theory.v1 |
Reference implementation | Python · information.mutual_information |
| Entropy and Concentration | risk.capability.universal-mathematics-statistics.entropy.and.concentration.v1 |
Reference implementation | Julia · frontier_risk_math.concentration |
| Correlation | risk.capability.universal-mathematics-statistics.correlation.v1 |
Reference implementation | Python · stats.correlation |
| Regression | risk.capability.universal-mathematics-statistics.regression.v1 |
Adapter required | Python · regression.ols |
| Gaussian Process | risk.capability.universal-mathematics-statistics.gaussian.process.v1 |
Adapter required | Python · gaussian_process.rbf |
| Spatial Statistics | risk.capability.universal-mathematics-statistics.spatial.statistics.v1 |
Adapter required | Python · spatial.morans_i |
| Geostatistics | risk.capability.universal-mathematics-statistics.geostatistics.v1 |
Adapter required | Python · geostatistics.ordinary_kriging |
| Bootstrap | risk.capability.universal-mathematics-statistics.bootstrap.v1 |
Reference implementation | Python · stats.bootstrap_mean_ci |
| Global Sensitivity | risk.capability.universal-mathematics-statistics.global.sensitivity.v1 |
Connected | Python · sensitivity.sobol_outputs |
| Shapley Sensitivity | risk.capability.universal-mathematics-statistics.shapley.sensitivity.v1 |
Adapter required | Python · sensitivity.shapley_coalitions |
| Optimisation under Uncertainty | risk.capability.universal-mathematics-statistics.optimization.under.uncertainty.v1 |
Adapter required | Python · optimization.robust_minimax |
| Multi-Criteria Decision | risk.capability.universal-mathematics-statistics.multi.criteria.decision.v1 |
Adapter required | Python · decision.weighted_mcda |
| Real Options | risk.capability.universal-mathematics-statistics.real.options.v1 |
Adapter required | Python · decision.real_option_binomial |
Methods, data and supports
- Method families
- robust statistics, Bayesian inference, extreme value, Monte Carlo, copula dependence, stochastic process, time series, change detection, survival reliability, spatial statistics, geostatistics, optimisation, decision analysis, information theory
- Domains
- cross-domain
- Compute planes
- Julia, TypeScript
- Source classes
- governed-observations, sealed-risk-data-cut
- Spatial supports
- point, object, grid, region, network
- Temporal supports
- instant, series, window, scenario
Propose a method
New methods are registered with a stable ID and a hand-derived golden test.
स्थिती
The methodology, structure and definitions of The Global Risks Index are a preparatory working draft (2026), circulated for review and comment and not for implementation. No value appears until an edition is released from a governed evidence cut; values then carry intervals, classes, sources and their correction pathway. Simulators run the published methods on numbers you choose and never show a NXS-GRX value.
What NXS-GRX is not
NXS-GRX is research and risk-analytics information. It is not a credit or ESG rating and uses no rating scale, not a benchmark for financial instruments, not official statistics, not an emergency warning or official classification, and not advice. It must not be used to evaluate natural persons. Risk classes are bands on a published scale, never rankings of countries or people.
Institutions and sources
The Nexus Consortium is stewarded by three independent not-for-profit institutions: The Global Centre for Risk and Innovation (GCRI), through GCRI US in Washington, DC and GCRI Canada in Ontario, with GCRI Canada as Lead Institution, Consortium Secretariat and lead contracting organisation; The Global Risks Forum (GRF); and The Global Risks Alliance (GRA). Technology, infrastructure and service providers work with the Consortium at arm’s length under written agreements, like every other external party in the public-private-planet model, and hold no role in its stewardship.
Every value carries the attribution of its sources, which keep their own licences. External names are cited for interoperability only. Nexus-authored text is intended for CC BY 4.0 on release.
Avis en français
La méthodologie et les définitions du NXS-GRX sont un projet de travail préparatoire (2026). Le NXS-GRX est une information de recherche et d’analyse des risques : ni notation, ni indice de référence financier, ni statistique officielle, ni alerte, ni conseil. Les classes de risque sont des bandes sur une échelle publiée, non des classements.