Bayesian calibration
Model parameters are calibrated with Bayesian methods that combine prior knowledge with data and produce posterior distributions, including a term for model discrepancy.
GCRI · Systems Science and Modelling
Statistics for modelling
Probability and statistics are the language of uncertainty in modelling. In this field they underpin calibration, inference about parameters, evaluation of model performance and the honest reporting of ranges, for every modelling platform in the network.
01Register
Statistics for modelling on the record.
Method recordSTEM method
- MethodProbability and statistics
- StewardSystems Science and Modelling
- Applied inSystems Science and Modelling
- Data3 inputs
- Checks3 validation steps
- Canonical pageSTEM Commons
02Application
What probability and statistics does here.
Probability and statistics provide the mathematical framework for describing uncertainty and learning from data. They underpin estimation, testing and prediction in every risk discipline. In methods and modelling, risk management and systemic risk and research and evidence, statistical methods quantify the likelihood and uncertainty of losses across interconnected systems. They make the evidence behind risk decisions explicit and reproducible. The canonical description is on the STEM Commons.
Proper scoring of predictions
Probabilistic model outputs are scored with proper scoring rules so that honest uncertainty is rewarded.
Ensemble statistics
Ensembles of model runs are summarised with statistical methods that account for dependence between ensemble members.
03Methods and evidence
How statistics for modelling is modelled, measured and tested.
The model, its assumptions, its data and its uncertainty, in the form a scientist or engineer would check. Structures follow published methods. The values drawn are illustrative, not findings.
Model, equations and assumptions
The model structure used for statistics for modelling, the assumptions it makes and how each is tested.
Risk of element i
Ri = f(Hi, Ei, Vi, Ci)hazard, exposure, vulnerability and coping capacityExpected annual loss
EAL = ∑k pk · Lkover events k with annual probability pkCoupled systems
xt+1 = A xt + B ut + εtA carries the couplings, u the shock, ε the error| Assumption | Why it is made | How it is tested |
|---|---|---|
| Hazard and exposure are independent within an event | Keeps the loss integral tractable | Compare with a copula fit on joint records |
| Couplings are linear near the operating point | Lets shocks propagate through A | Perturb beyond the linear range and compare |
| Vulnerability curves transfer between places | Local curves are rarely available | Validate against observed losses where they exist |
- Inputs
- versioned datasets with provenance
- Outputs
- distributions, never single numbers
- Code
- released with the model card and tests
- Reproduction
- same data, code, environment and seed
FAIR guiding principles · GO FAIR and FORCE11W3C PROV · World Wide Web ConsortiumGuidance on consistent treatment of uncertainties · IPCCCEOS Analysis Ready Data · Committee on Earth Observation Satellites
04Data
What the method consumes.
Datasets and records used by probability and statistics on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Data | Role | Label |
|---|---|---|
| Observational datasets | Calibration and evaluation | OBSERVED |
| Model ensemble outputs | Statistics | MODELLED |
| Prior information from literature | Bayesian priors | REPORTED |
05Process
How the process runs.
Process
Statistics for modelling: 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.
01 Hazard
- 01Event catalogueDataset · Model developerThe hazard module holds a large catalogue of simulated events that represents a wide range of plausible scenarios.
- 03Hazard moduleModel · Model developerFor each event the hazard module gives the local hazard intensity that the vulnerability module reads.
02 Exposure and damage
- 02ExposureDataset · Validation reviewerThe exposure module houses the portfolio data, such as location-specific information.
- 04Vulnerability moduleModel · Model developerThe vulnerability module quantifies the expected damage to the exposures from an event.
03 Financial
- 05Financial moduleModel · Validation reviewerThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Validation reviewerAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Validation reviewerSome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Validation reviewerThe 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.
- 09AAL, PML and TVaRModel · Validation reviewerAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Validation reviewerThe 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.
06Validation
How results are checked.
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
| Check | How it is done |
|---|---|
| Posterior predictive checks | Calibrated models must reproduce observed data |
| Prior sensitivity | Results are recomputed under alternative priors |
| Scoring on held-out data | Predictions are scored on data not used in calibration |
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
07Connections
Topics that rely on this method.
08Stewardship
Who maintains the method.
Systems Science and Modelling stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
09Questions
Questions and answers.
What are the limits of probability and statistics in this field?
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
How are results checked?
Results are checked through diagnostics, cross-validation and sensitivity to assumptions. Independent replication confirms findings.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
The canonical method page lists every platform that applies it.
ReportsContribute
Contribute evidence from this page.
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.
GCRISystems Science and ModellingMethods and TechnicalScenario and Stress-Test
- EmailGateway GW-GCRISend it from this pageEvidence, a correction, a case, a method, a review, a translation or profile input. It arrives tagged with this page, so the editor who owns it receives it.
- ZenodoOpen depositDeposit it and submit to the communityPublish your own record on Zenodo with your ORCID iD, then submit it to the Reports community there. Curators review it; the DOI stays yours.
- ReportsGCRISee every way to contributeThe contribution types, how each is reviewed, what credit you receive, the licence and what is never accepted.
Never send personal data, sensitive infrastructure detail or anything you have no right to share. A contribution is reviewed before use; sending it confers no authorship or editorial rights, and sponsorship never buys a finding.
Systems Science and Modelling
Bring a method, a dataset or a question.
Information and enquiries are open today. 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.
Legal
Legal documents.
Maps, data and figures on this site are shown for context and general information. They are not advice, forecasts or warnings; the limits of the information are set out in the Disclaimers and Data Notices.