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Managing uncertainty in probabilistic risk analysis (PRA) means showing what the model represents, testing how well it supports its intended decision, and preserving enough evidence for another analyst to review and rerun the work. A model does not eliminate uncertainty: it distinguishes variability in events from uncertainty about the model and its inputs, then makes clear how each could affect the decision.
Separate randomness from uncertainty about the model
PRA uncertainty is not one thing. The U.S. Nuclear Regulatory Commission (NRC), in NUREG-1855 Revision 1, distinguishes aleatory uncertainty—randomness associated with events—from epistemic uncertainty, which reflects limits in what is known about the PRA formulation.
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- Aleatory uncertainty: variability in the events or processes represented by the model. It is part of the modeled risk, not simply a lack of knowledge that can be removed by collecting more data.
- Parameter uncertainty: uncertainty about the values assigned to model parameters.
- Model uncertainty: uncertainty about the selected model or formulation.
- Completeness uncertainty: uncertainty about whether the PRA has included all relevant contributors to risk.
The latter three are epistemic categories in the NRC guidance. Naming which kind of uncertainty is being represented prevents a probability distribution from obscuring whether it describes event variability, uncertain inputs, or a modeling choice.
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Uncertainty analysis is useful when it helps a decision-maker understand whether a conclusion is robust enough for the application. Interpret results in the context of the specific decision and its acceptance guidelines; do not treat a model output as a stand-alone verdict. The NRC guidance emphasizes considering whether PRA incompleteness could change the result and using monitoring, feedback, and corrective action where relevant.
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- State the decision and intended use. Identify what action the analysis informs, the applicable decision criteria, and the population, system, or conditions to which the result applies.
- Identify uncertainty sources that could matter. Record relevant variability, parameter uncertainty, model choices, and possible omissions. Explain why each is included or excluded.
- Test the decision’s sensitivity. Examine whether plausible changes in inputs or assumptions alter the risk estimate, its ranking, or whether the result meets the applicable criterion.
- Set a response to material uncertainty. If an uncertainty could change the decision, identify what further evidence, conservatism, monitoring, or corrective action is appropriate for the application.
- Revisit the analysis as evidence changes. Where the decision depends on continuing model performance, define how new observations or feedback will be assessed and when the model or decision should be reconsidered.
These steps are a practical synthesis of the NRC guidance, not a universal acceptance test. Criteria and required controls depend on the decision and the rules that govern it.
Keep verification, validation, and uncertainty quantification distinct
These checks answer different questions. ASME’s overview of verification, validation, and uncertainty quantification (VVUQ) describes the distinctions as follows:
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| Activity | Question it answers | What to retain |
|---|---|---|
| Verification | Does the computational implementation fit its mathematical description? | Evidence that the code and calculations implement the specified model as intended. |
| Validation | How well does the model represent the real-world application for which it is intended? | Evidence supporting the model’s fitness for that application, including relevant comparisons or limitations. |
| Uncertainty quantification | How do variations in parameters affect the outcomes? | The parameter ranges or distributions used, the methods applied, and their effect on results. |
Passing one check does not establish the others: correct implementation does not prove real-world suitability, and a validation argument does not quantify how uncertain parameters affect a particular result. ASME’s overview lists standards relevant to computational modeling and simulation; it is not, by itself, a complete PRA audit-trail framework.
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Monte Carlo analysis can represent variability and uncertainty by repeatedly sampling from specified inputs and calculating outcomes. Its usefulness depends on the supporting data, assumptions, and implementation—not on the number of simulated runs alone. The U.S. Environmental Protection Agency (EPA) says that probabilistic techniques can be viable statistical tools when supported by adequate data and credible assumptions. Its Guiding Principles for Monte Carlo Analysis (EPA/630/R-97/001, March 1997) identifies clarity, consistency, transparency, reproducibility, and sound methods as good scientific practices.
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For a Monte Carlo analysis, make the run interpretable by recording the input distributions and their rationale, dependencies or relationships among inputs, sampling and calculation methods, software and run configuration, and how results were summarized. Preserve any intermediate outputs from nondeterministic steps that cannot reliably be regenerated. Explain what the simulation does and does not establish in relation to the decision.
Build an audit trail that supports review and rerunning
An audit trail should let a reviewer trace the decision from its question and evidence through the model, computation, uncertainty analysis, and interpretation. The National Academies’ Recommendation 4-1 in Reproducibility and Replicability in Science calls for clear, specific, and complete information about computational methods and data products so others can repeat an analysis, subject to restrictions such as nonpublic data policies. Its examples include input data, intermediate results for nondeterministic steps, methods and parameters, and the original computational environment, including operating system, hardware architecture, and dependencies.
A practical record, tailored to the application rather than treated as a universal schema, should include:
- Decision context: the decision supported, intended use, scope, applicable criteria, and limitations.
- Data and assumptions: source and version of input data, transformations, parameter values or distributions, assumptions, and their rationale.
- Model and methods: formulation, computational methods, code version, dependencies, parameters, and run configuration.
- Execution evidence: the computational environment and outputs needed to reproduce the run, including intermediate or nondeterministic results that cannot be regenerated.
- Credibility evidence: verification and validation work, uncertainty analysis, and any known limitations relevant to the application.
- Decision interpretation: how uncertainty affects conclusions against the applicable criteria, including whether potential incompleteness could alter the outcome.
- Ongoing governance: monitoring results, feedback, model or data changes, and corrective actions over time.
Reproducibility is not just retaining a headline estimate or a random seed. A seed can help reproduce a stochastic run, but it cannot substitute for the code, inputs, methods, dependencies, environment, and records of results that cannot be regenerated.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Compare analyses and model versions on decision-relevant dimensions
When reviewing two analyses or deciding whether a model revision changes a conclusion, compare the evidence on the same dimensions rather than comparing final estimates alone.
| Comparison dimension | What to examine |
|---|---|
| Uncertainty scope | Which event variability and epistemic sources are represented, and whether relevant sources or potential omissions changed. |
| Data and assumptions | Input provenance, parameter choices, assumptions, and any changes between versions. |
| Verification | Evidence that the revised implementation conforms to its mathematical description. |
| Validation | Whether evidence supports use in the intended application and whether that application has changed. |
| Reproducibility | Whether methods, environment, dependencies, configuration, and necessary intermediate outputs are available to rerun or review the analysis. |
| Decision sensitivity | Whether uncertainty changes estimates, rankings, or conclusions against the applicable criteria. |
| Monitoring and response | Whether performance is monitored and changes or problems lead to feedback and corrective action. |
Govern the model within its intended use
Credibility is not permanent. New data, changed operating conditions, a revised model, or a different application can affect whether an earlier analysis remains suitable. The Federal Reserve’s supervisory guidance, published April 17, 2026, says that using a model beyond its intended purpose introduces additional uncertainty and risk, and calls for understanding limitations and assessing performance on an ongoing basis. That guidance concerns banking organizations; it should not be read as a universal legal requirement for every PRA application.
For any sector, document the model’s intended use and limitations, and make review responsive to changes that could affect its suitability. Apply the governance requirements of the relevant organization and jurisdiction rather than assuming one supervisory framework applies everywhere.
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Tailor the record to the sector and decision
There is no single audit-trail format established by these sources for every regulated and unregulated industry. The NRC material focuses on PRA uncertainty in risk-informed decision-making; the EPA principles address Monte Carlo analysis; ASME’s VVUQ overview concerns computational modeling and simulation; and the National Academies addresses reproducibility of computational results. Use the guidance that fits the analysis, alongside applicable sector-specific rules and organizational controls. NIST’s information-quality standards page references measurement-uncertainty guidance and discusses reproducibility in an analytic-results context; it is not a substitute for sector-specific PRA guidance.
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