Uncertainty on benchmark scores
Bootstrap and analytical intervals are reported with every score, and differences between models are tested before rankings are stated.
GCRI · Artificial Intelligence and Autonomous Systems
Statistics for AI evaluation
Probability and statistics make AI evaluation trustworthy: confidence intervals on scores, significance of differences between models, calibration of predicted probabilities and sampling designs for audits. In this field they stop small test sets and noisy metrics from being over-read.
01Register
Statistics for AI evaluation on the record.
Method recordSTEM method
- MethodProbability and statistics
- Applied inArtificial Intelligence and Autonomous Systems
- 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 artificial intelligence and data and compute, 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.
Calibration assessment
Predicted probabilities are compared with observed outcomes to check whether a model’s confidence matches its accuracy.
Audit sampling
Samples of decisions are drawn with stated designs so that error rates for subgroups can be estimated with known precision.
03Methods and evidence
How Statistics for AI evaluation 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 AI evaluation, 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 |
|---|---|---|
| Evaluation outputs | Score estimation | OBSERVED |
| Labelled audit samples | Error estimation | OBSERVED |
| Prediction logs | Calibration | OBSERVED |
05Process
How the process runs.
Process
Statistics for AI evaluation: 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 · Incident responderThe 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 · Incident responderThe financial module calculates losses from all event scenarios. Ground-up, gross and net losses differ as shown below.
- 06Event loss tableDataset · Incident responderAn event loss table lists each event with its annual occurrence probability and its loss for the portfolio.
- 07Year loss tableDataset · Incident responderSome models also sample simulated years from event losses. This outline does not describe their format.
04 Metrics
- 08Exceedance probability curvesModel · Incident responderThe 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 · Incident responderAverage annual loss sums event probability times loss. PML is one point on the occurrence curve.
05 Use of results
- 10Use of resultsDecision · Incident responderThe 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 |
|---|---|
| Interval reporting | Every metric is reported with its uncertainty |
| Multiple comparisons | Comparisons across many tasks are corrected for multiple testing |
| Sample size planning | Audit samples are sized to detect differences of stated magnitude |
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.
09Connected
Where this page leads across the Consortium.
10Questions
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.
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