01Capabilities
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.
| Method | Capability ID | State | 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 |
| Optimization 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 |
02Scope
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, optimization, 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
03Standards