Probability and statistics
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. They underpin estimation, testing and prediction in every risk discipline. Systems Science and Modelling stewards this page for the Nexus Consortium.
- 01InstitutionThe Global Centre for Risk and Innovation (GCRI)
- 02Service levelR0: information and enquiries
- 03In briefThe short answer
- 04The methodWhat probability and statistics covers
- 05Reference practiceStatistical practice is governed by reporting and quality standards
- 06In systemic risk workDependence is the hard part
- 07Applied inPlatforms that apply this method
GCRI · Institution · service level R0
The short answer.
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. Statistical methods quantify the likelihood and uncertainty of losses across interconnected systems. In the Nexus Consortium, Systems Science and Modelling stewards its canonical page, and 12 other platforms apply it, including Health Nexus and Nexus Labs.
Systemic exposure in the Gulf of Mexico coast.
Where people and networks concentrate, the exposure through which shocks travel between systems, shown for the Gulf of Mexico coast as an example geography for this subject.
What probability and statistics covers.
- 01
Core methods
statistical inference; Bayesian analysis; regression modelling; sampling design; hypothesis testing; resampling methods.
- 02
Data and instruments
designed surveys and experiments; observational datasets; administrative records; sensor time series; simulation outputs.
- 03
Validation
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
- 04
Limits
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
- 05
Use in risk decisions
Statistical methods quantify the likelihood and uncertainty of losses across interconnected systems. They make the evidence behind risk decisions explicit and reproducible.
Statistical practice is governed by reporting and quality standards.
| Reference | What it sets |
|---|---|
| UN Fundamental Principles of Official Statistics | Quality and independence |
| EQUATOR guidelines | Reporting of studies |
| IPCC uncertainty guidance | Calibrated language for likelihood |
Dependence is the hard part.
Systemic risk is a statement about joint probabilities. Statistics for independent events understate the chance of simultaneous failures. The work is estimating dependence structures, especially in the tails, from limited data, and communicating the resulting uncertainty honestly.
- Test independence assumptions explicitly.
- Report intervals, not only point estimates.
- Use calibrated language for likelihood.
- Applications on Systems Modelling and Nexus Reports.
Platforms that apply this method.
- Health NexusInstitutionGCRI
- Nexus LabsInstitutionGCRI
- Nexus ReportsInstitutionGCRI
- Systemic Risk ManagementInstitutionGCRI
- Artificial Intelligence and Autonomous SystemsInstitutionGCRI
- Quantum TechnologiesInstitutionGCRI
- Biotechnology and BiosecurityInstitutionGCRI
- Research NexusInstitutionGRF
- Insurance NexusInstitutionGRA
- Banking NexusInstitutionGRA
- AI and Financial Model RiskInstitutionGRA
- Systems Science and ModellingInstitutionGCRI
- Actuarial and Quantitative RiskInstitutionGRA
Who maintains this page.
Systems Science and Modelling stewards probability and statistics: it keeps this description current and reviews how the method is applied across the platforms.
Terms used on this page.
Each term as this page uses it. Where a standard-setting body defines the term, the wording follows that body.
| Term | Definition |
|---|---|
| Frequency-severity model | A model that estimates expected loss as the number of claims per unit of exposure multiplied by the average claim size. |
| Generalised linear model | A regression framework widely used in insurance pricing that links rating factors to claim frequency or severity through a chosen distribution. |
| Out-of-sample validation | Testing a model on data not used to fit it, to judge how it will perform on new business. |
| Probability of default | The likelihood that a borrower defaults within a period, usually one year. |
Where this page's references lead.
The bodies and documents this page is read against. Status and editions change; each link goes to the issuing body.
Where this page leads across the Consortium.
- Statistics for health evidenceGCRIApplied in Health Nexus.
- Statistics for research designGCRIApplied in Nexus Labs.
- Statistics for evidence synthesisGCRIApplied in Nexus Reports.
- Probability and statistics for riskGCRIApplied in Systemic Risk Management.
- Statistics for AI evaluationGCRIApplied in Artificial Intelligence and Autonomous Systems.
- Statistics for quantum technologyGCRIApplied in Quantum Technologies.
- Probability and statistics for biotechnology and biosecurityGCRIApplied in Biotechnology and Biosecurity.
- Statistics for research governanceGRFApplied in Research Nexus.
- Probability and statistics in insuranceGRAApplied in Insurance Nexus.
- Statistics for bank risk measurementGRAApplied in Banking Nexus.
- Probability and statistics for AI and financial model riskGRAApplied in AI and Financial Model Risk.
- Statistics for modellingGCRIApplied in Systems Science and Modelling.
- Probability and statistics for actuarial and quantitative riskGRAApplied in Actuarial and Quantitative Risk.
Questions and answers.
Why does one institution host every method page?
How do I suggest a correction to a method page?
Around GCRI.
Start with an enquiry.
The current service level is R0: information and enquiries. An enquiry receives a reference and names the next step; applications, payments, compute allocations and registrations open only when their team, terms and review capacity exist.