Meta-analysis with heterogeneity stated
Effect estimates from comparable studies are pooled with random-effects models, heterogeneity is reported and explored, and pooling is withheld where studies measure different things.
GCRI · Reports
Statistics for evidence synthesis
Probability and statistics underpin evidence synthesis and statistical review. They combine results across studies, detect bias in what gets published, judge whether a report’s numbers support its claims, and measure how consistently reviewers and screeners agree, so that the weight a synthesis gives each study can be checked by others.
01Register
Statistics for evidence synthesis on the record.
Method recordSTEM method
- MethodProbability and statistics
- Applied inReports
- Data4 inputs
- Checks4 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 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.
Small-study and publication bias
Funnel plots, selection models and comparison with trial and protocol registries test whether the published studies are a biased subset of those conducted.
Statistical review and screening agreement
A statistical reviewer checks designs, models and reported uncertainty in a report, and agreement between independent screeners in a systematic review is measured before screening proceeds.
03Monitor
Tail fit.
The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.
Tail fit
Reports · Statistics for evidence synthesis · Run R-3361
Shape parameter uncertainGCRI · Reports
Return level curve
Method card
- Method
- Probability and statistics
- Approach
- peaks over threshold
- Threshold
- 97th percentile
- Label
- MODELLED
Parameters
generalised Pareto fit
| Shape ξ | 0.17 | −0.04 | 0.56 | heavy tail if above zero |
| Scale σ | 3.4 | 1.0 | 5.6 | units of the variable |
| Exceedances | 86 | declustered |
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 |
|---|---|---|
| Study-level effect estimates and variances | Inputs to pooling and heterogeneity analysis | REPORTED |
| Cochrane and Campbell systematic reviews | Reference syntheses and their data tables | REPORTED |
| PROSPERO and OSF registrations | Comparison of planned and published analyses | DECLARED |
| Screening decisions from independent reviewers | Inter-rater agreement | OBSERVED |
05Methods and evidence
How statistics for evidence synthesis 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 evidence synthesis, 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
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 |
|---|---|
| Reporting against PRISMA | Each synthesis is checked against the PRISMA items, including the flow of records through screening |
| Sensitivity to inclusion | Results are recomputed excluding high risk-of-bias studies and influential studies |
| Outcome reporting | Published outcomes are compared with registered protocols and differences explained |
| Independent statistical review | A reviewer not involved in the analysis checks the models and the stated uncertainty |
Inference depends on assumptions about independence, distribution and sampling that may not hold. Small or biased samples limit reliability.
07Process
How the process runs.
Process
Statistics for evidence synthesis: 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 · Series editorThe 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 · Series editorThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Series editorAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Series editorSome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Series editorThe 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 · Series editorAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Series editorThe 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.
09Stewardship
Who maintains the method.
Systems Science and Modelling stewards probability and statistics for the Consortium and reviews how it is applied across platforms.
10Connected
Where this page leads across the Consortium.
11Questions
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.
GCRIReportsGlobal Systems Risk and ResilienceCountry Systems Risk and ResilienceCountry Quarterly
- 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.
Reports
Bring a method, a dataset or a question.
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Legal documents.
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