Universelle Mathematik und Statistik
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.
| Methode | Capability ID | Status | Läuft auf |
|---|---|---|---|
| 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
- Bereiche
- 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.
Status
Methodik, Struktur und Definitionen des Global Risks Index sind ein vorbereitender Arbeitsentwurf (2026), der zur Prüfung und Stellungnahme und nicht zur Umsetzung verbreitet wird. Kein Wert erscheint, bevor eine Ausgabe aus einem geregelten Evidenzschnitt veröffentlicht ist; die Werte tragen dann Intervalle, Klassen, Quellen und ihren Korrekturweg. Die Simulatoren wenden die veröffentlichten Methoden auf Zahlen an, die Sie wählen, und zeigen niemals einen NXS-GRX-Wert.
Was NXS-GRX nicht ist
NXS-GRX ist eine Forschungs- und Risikoanalyseinformation. Es ist kein Kredit- oder ESG-Rating und verwendet keine Ratingskala, kein Referenzwert für Finanzinstrumente, keine amtliche Statistik, keine Notfallwarnung oder amtliche Einstufung und keine Beratung. Es darf nicht zur Bewertung natürlicher Personen verwendet werden. Risikoklassen sind Bänder auf einer veröffentlichten Skala, niemals Rangfolgen von Ländern oder Personen.
Institutionen und Quellen
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.
Jeder Wert trägt die Namensnennung seiner Quellen, die ihre eigenen Lizenzen behalten. Externe Namen werden nur zur Interoperabilität zitiert. Von Nexus verfasste Texte sollen bei Veröffentlichung unter CC BY 4.0 stehen.
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.