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GCRI · Mathematics, statistics and data

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.

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01Register

Probability and statistics on the record.

The Global Centre for Risk and Innovation
  1. 01InstitutionThe Global Centre for Risk and Innovation (GCRI)
  2. 02The methodWhat probability and statistics covers
  3. 03Reference practiceStatistical practice is governed by reporting and quality standards
  4. 04In systemic risk workDependence is the hard part
  5. 05Applied inPlatforms that apply this method
  6. 06StewardshipWho maintains this page
  7. 07SourcesWhere this page’s references lead
02The method

What probability and statistics covers.

  1. 01

    Core methods

    statistical inference; Bayesian analysis; regression modelling; sampling design; hypothesis testing; resampling methods.

  2. 02

    Data and instruments

    designed surveys and experiments; observational datasets; administrative records; sensor time series; simulation outputs.

  3. 03

    Validation

    Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.

  4. 04

    Limits

    Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.

  5. 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.

03Reference practice

Statistical practice is governed by reporting and quality standards.

ReferenceWhat it sets
UN fundamental principles for national statistics (resolution 68/261)Quality and independence
EQUATOR guidelinesReporting of studies
IPCC uncertainty guidanceCalibrated language for likelihood
04Process

How the process runs.

Process

Probability and statistics: Catastrophe model pipeline

Catastrophe models usually have hazard, vulnerability, exposure and financial modules, and produce loss tables, average annual loss, exceedance curves, PML and TVaR.

  1. 01 Hazard

    1. 01Event catalogueDataset · Model developerThe hazard module holds a large catalogue of simulated events that represents a wide range of plausible scenarios.
    2. 03Hazard moduleModel · Model developerFor each event the hazard module gives the local hazard intensity that the vulnerability module reads.

  2. 02 Exposure and damage

    1. 02ExposureDataset · Competent authorityThe exposure module houses the portfolio data, such as location-specific information.
    2. 04Vulnerability moduleModel · Model developerThe vulnerability module quantifies the expected damage to the exposures from an event.

  3. 03 Financial

    1. 05Financial moduleModel · Competent authorityThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
    2. 06Event loss tableDataset · Competent authorityAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
    3. 07Year loss tableDataset · Competent authoritySome models also sample simulated years from event losses. This outline does not describe their format.

  4. 04 Metrics

    1. 08Exceedance probability curvesModel · Competent authorityThe occurrence curve gives the chance that the largest loss in a year exceeds an amount. The aggregate curve does so for the sum of losses.
    2. 09AAL, PML and TVaRModel · Competent authorityAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.

  5. 05 Use of results

    1. 10Use of resultsDecision · Competent authorityThe tail metrics are used when considering a portfolio’s exposure and the level of catastrophe reinsurance an insurer requires.

Outline of an external standard or method, from its public sources. It describes what the framework says, not a record of any run. It does not show that Nexus or any partner performs, certifies or approves a step. A gate is a step of the method, never a Nexus approval.

05In systemic risk work

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 Reports.
06Applied in

Platforms that apply this method.

07Stewardship

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.

08Sources

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.

09Questions

Questions and answers.

Why does one institution host every method page?
GCRI hosts the STEM Commons so that each method has one canonical description. Platforms link to it rather than repeat it, which keeps definitions consistent.
How do I suggest a correction to a method page?
Write to the integrity concern form with the passage and the reason.
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Reports is the Consortium’s quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.

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