Home / Courses / VVUQ / Uncertainty Sources

VVUQ · Module 6 of 10

Sources and Classification of Uncertainty

Not all uncertainty is the same. Some is the natural scatter of the world, which no amount of study removes; some is our own lack of knowledge, which more data can reduce. Telling them apart decides what to do next.

01

Readiness check

This module classifies uncertainty. Tick only what you can do closed-notes.

  • Combine independent uncertainties in quadrature.
  • Recall that measured properties vary from sample to sample.
  • Distinguish random scatter from a lack of knowledge.
  • Recall a percentage reduction between two values.
  • Recall that a model itself is an approximation.
0 or 1 weak itemsContinue with this module.
2 weak itemsRevisit the validation uncertainty in Module 5.
3 or more weak itemsRevisit probability and statistics in Mathematics, Module 15.
02

The core idea

Aleatory uncertainty is the inherent randomness of the world, irreducible by more knowledge; epistemic uncertainty is our lack of knowledge, reducible by more data or better models. Classifying each source tells you whether to gather data or accept the scatter.

aleatory: inherent variability, irreducibleepistemic: lack of knowledge, reducibleutotal = √(ualeatory2 + uepistemic2)

Uncertainty quantification begins by naming where the uncertainty comes from and what kind it is. Aleatory uncertainty is the intrinsic variability of a system, the scatter in material strength between nominally identical parts, the turbulence in a flow, the roughness of a surface. It is a property of the world and cannot be reduced by learning more; it can only be characterised, usually as a probability distribution. Epistemic uncertainty is a lack of knowledge on the analyst's part: a poorly known parameter, an untested boundary condition, or model-form uncertainty from approximations in the equations themselves. It is reducible, more experiments, finer models, or better data can shrink it. The distinction is practical, not academic: if a dominant uncertainty is epistemic, the right response is to invest in reducing it; if it is aleatory, no study will help and the design must simply accommodate the scatter. Independent sources combine in quadrature into a total, and knowing the split tells you how much of that total could, in principle, be removed.

The skill works when: you label each source aleatory or epistemic and act on the reducible ones.
The skill breaks down when: effort is spent trying to reduce irreducible aleatory scatter, or reducible epistemic gaps are accepted as fixed.
The concept. Aleatory uncertainty is characterised but not reduced; epistemic uncertainty is reduced by more knowledge. The split tells the analyst where effort will actually help.
03

The skills, taught in order

Five skills build the classification and its consequences.

6.1 Aleatory uncertainty

Aleatory uncertainty is inherent, irreducible variability, the natural scatter in loads, material properties, geometry, and environment. It is characterised by a probability distribution measured from data, not eliminated. A design must be robust to it.

6.2 Epistemic uncertainty

Epistemic uncertainty is reducible ignorance: an imprecisely known parameter, an assumed boundary condition, or a missing physical effect. More or better information shrinks it, so it flags where investment in data or modeling pays off.

TypeOriginReducible?Response
Aleatoryinherent variabilitynocharacterise, design for it
Epistemic (parameter)poorly known inputyesmeasure it better
Epistemic (model form)approximate equationsyesimprove the model

The two kinds of uncertainty and what each calls for. The response depends entirely on which kind dominates.

6.3 Model-form uncertainty

Model-form uncertainty is the epistemic error from the approximations in the governing equations themselves, a turbulence closure, a constitutive law, a neglected effect. It is often the hardest to quantify and is estimated through validation against data, as the earlier modules showed.

6.4 Reducible versus irreducible

Classifying a source as reducible or not sets the strategy: reducible epistemic uncertainty justifies more testing or modeling; irreducible aleatory uncertainty must be accepted and designed around. Spending effort on the wrong kind wastes it.

6.5 Combining sources

Independent uncertainties, whatever their type, combine in quadrature into a total. Keeping the aleatory and epistemic parts separate within that total shows how much of the uncertainty could be removed with more knowledge, and how much is permanent.

Engineering connection: deciding whether to run more tests or to add design margin turns on whether the dominant uncertainty is epistemic (reducible) or aleatory (not).

04

Worked example 1: combining aleatory and epistemic uncertainty

A predicted quantity has an aleatory uncertainty ua = 0.04 (inherent material scatter) and an epistemic uncertainty ue = 0.03 (a poorly known boundary condition). Find the total uncertainty.

Figure 1. The aleatory and epistemic uncertainties combine in quadrature into a total of 0.05, a clean 3-4-5 combination. Both contribute, but only one can be reduced.
  1. ProblemFind the total uncertainty from the sources in Figure 1.
  2. Given / findua = 0.04, ue = 0.03. Find utotal.
  3. AssumptionsThe two sources are independent, so they combine in quadrature.
  4. Modelutotal = √(ua2 + ue2).
  5. Equationsutotal = √(0.042 + 0.032)
  6. Solveutotal = √(0.0016 + 0.0009) = √0.0025 = 0.05.
  7. CheckThe 3-4-5 combination gives exactly 0.05. The aleatory part (0.04) is the larger contributor, so most of the total is irreducible.
  8. ConclusionThe total uncertainty is 0.05, of which the aleatory 0.04 cannot be reduced. Knowing the split is the point of the classification.
Result. utotal = 0.05, dominated by the irreducible aleatory part.
05

Worked example 2: how much can be reduced

For that result (utotal = 0.05, with ua = 0.04 aleatory and ue = 0.03 epistemic), suppose enough data are gathered to eliminate the epistemic part. Find the remaining uncertainty and the percentage reduction.

Figure 2. Removing the epistemic part leaves only the aleatory uncertainty. Because quadrature weights the larger source more, eliminating the 0.03 epistemic term cuts the total by just 20%.
  1. ProblemFind the remaining uncertainty and reduction after removing the epistemic part, as in Figure 2.
  2. Given / findutotal = 0.05, ua = 0.04, ue = 0.03. Find the new total and the percentage reduction.
  3. AssumptionsThe epistemic source is fully removed by additional data; the aleatory part is unchanged.
  4. ModelWith ue = 0, the remaining uncertainty is ua; reduction = (utotal − ua)/utotal.
  5. Equationsunew = ua = 0.04reduction = (0.05 − 0.04)/0.05
  6. Solveunew = 0.04. Reduction = (0.05 − 0.04)/0.05 = 0.20 = 20%.
  7. CheckEven though the epistemic source was 0.03 (60% of the aleatory), removing it cut the total by only 20%, because quadrature down-weights the smaller contributor.
  8. ConclusionEliminating the epistemic uncertainty leaves 0.04 and cuts the total by 20%. The classification quantifies exactly how much data collection could gain.
Result. Remaining u = 0.04, a 20% reduction from removing the epistemic part.
06

Misconceptions and diagnostics

MistakeSymptomDiagnostic questionCorrection
Trying to reduce aleatory scatterTesting that never shrinks the spread"Is this inherent variability?"Characterise aleatory uncertainty; do not try to remove it.
Accepting epistemic gapsA reducible source left unaddressed"Could more data shrink this?"Invest to reduce dominant epistemic uncertainty.
Ignoring model-form uncertaintyOnly inputs counted"Are the equations themselves approximate?"Include model-form error from validation.
Linear combinationTotal too large"Did I use quadrature?"Combine independent sources in quadrature.
07

Practice ladder

Level 1 · Direct skill

Classify each: (a) scatter in yield strength, (b) an unknown friction coefficient, (c) a turbulence-model approximation.

Show answer

(a) aleatory, (b) epistemic (parameter), (c) epistemic (model form).

Level 2 · Mixed concept

Combine ua = 0.06 and ue = 0.08 in quadrature.

Show answer

utotal = √(0.062 + 0.082) = √0.01 = 0.10.

Level 3 · Independent problem

For that case, how much does removing the epistemic 0.08 reduce the total?

Show answer

Remaining = ua = 0.06. Reduction = (0.10 − 0.06)/0.10 = 40%. The epistemic part was dominant, so reducing it helps a lot.

Transfer task | Real engineering

A prediction's uncertainty is dominated by a poorly known material parameter. Argue for the next action and why.

What good work looks like

The dominant source is epistemic and reducible, so the next action is to measure the parameter more precisely; this shrinks the total, whereas adding design margin would waste effort on an uncertainty that testing could largely remove.

08

Working with AI, and proving it yourself

Use AI as an examiner, not a solver

"Check that I classified each source as aleatory or epistemic correctly."
"Give me three uncertainty sources; I will say if each is reducible."
"Reduce my uncertainty for me." Deciding what is reducible is the skill.
"What is the total uncertainty?" Combining and splitting it yourself is the point.

Portfolio task

For a real prediction, list the uncertainty sources, classify each as aleatory or epistemic, combine them, and identify the largest reducible one to target.

Must include: a classified source list, a combined total, and a targeted reducible source.
09

Retrieval and spaced review

Closed notes. Answer out loud, then reveal.

1. What is aleatory uncertainty?

Inherent, irreducible variability of the world.

2. What is epistemic uncertainty?

Reducible lack of knowledge, in parameters or model form.

3. What is model-form uncertainty?

Epistemic error from approximations in the governing equations.

4. How do the two combine?

In quadrature, if independent, into a total uncertainty.

5. Why does the classification matter?

It decides whether to gather data (epistemic) or design around scatter (aleatory).

TodayFinish this quiz and Levels 1 and 2 of the ladder.
+1 dayRe-derive the combination and reduction from a blank page.
+3 daysClassify the sources of three new predictions.
+7 daysPropagate these uncertainties through a model, Module 7.
+30 daysReuse the aleatory-epistemic split to plan test versus margin.
10

Standards mapping

This module follows the ASME Verification, Validation, and Uncertainty Quantification standards. Use these references to read further.

Topic in this moduleWhere to read more
Role of uncertainty quantificationASME VVUQ 10.2, UQ in Solid Mechanics
Aleatory and epistemic uncertaintyASME V&V 20, CFD and Heat Transfer
Model-form uncertaintyOberkampf and Roy, Verification and Validation in Scientific Computing

Standard designations refer to the ASME V&V series; the aleatory-epistemic distinction is standard across the VVUQ literature.