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### Uncertainty & Variability

Charles Yoe, Ph.D.

A Simple Model

- Suppose we want to forecast the high temperature for a random day in February in Honolulu
- What do we need to do that?
- What is the mean high temperature?
- With uncertainty
- Estimate mean, say 70-88
- Estimate standard deviation, say 10% of mean

Mean is 81

SD is 2.3

Which is easier to pack for?

Variability

Uncertainty &

Variability

Mean is 70-88

SD is 10% of mean

Learning Objectives

- At the end of this session participants will be able to:
- Explain the differences between variability and uncertainty.
- Identify reasons for separating the two.
- Categorize uncertainty by type and cause.

The Point

- There are lots of things we don’t know in an analysis
- Do we not know because things are
- Uncertain?
- Variable?
- Be able to distinguish the two

There are facts in this world…

- …we just don’t always know them
- Mean daily flow on a stream
- Amount of rock in a channel bottom
- Average value of a house
- Mean lock time
- Mean strength of materials

Uncertainty

- Uncertainty-lack or incompleteness of information
- When there exists a constant or knowable fact unknown by us, this is uncertainty
- Sometimes called epistemic uncertainty
- Knowledge uncertainty is preferred

Variability

- Variability refers to true differences in attributes due to heterogeneity or diversity
- Variability in system, a natural characteristic of system
- Effect of chance
- Sometimes called aleatory uncertainty
- Natural variability is preferred
- Can’t be reduced through study or measurement
- Sometimes you can change the system to reduce the variability

When we’re not sure, we’re uncertain

Uncertainty represented by probability distributions

Can often be reduced by throwing money at it

Differences inherent in the system—chance

Variability represented by probability distributions

Cannot be reduced by throwing money at it

Uncertainty and VariabilityQuantity Uncertainty

- Different kinds of quantities
- Some have a “true” parameter value
- It may be known or uncertain
- Some have a “best” or “appropriate” value
- Different sources of uncertainty for each
- Treatment of uncertainty depends on the quantity and cause of uncertainty

Quantity Uncertainty

- Empirical quantities
- Only quantity with true parameter value, uncertainty and true value possible here
- Mean daily flow, mean strength of materials, value of a house, time
- Full range of treatments
- Defined constants
- Certain by definition, no reason for uncertainty, look it up
- Sq. ft./acre, gallons in an acre-foot of water, π

Quantity Uncertainty

- Decision variables
- Decision makers exercise direct control over these kinds of values
- No true value
- Can be uncertain over best value
- Reasonable incremental cost, mitigation goals, factors of safety
- Parametric variation

Quantity Uncertainty

- Value parameters
- Represent aspects of decision makers’ preferences
- No true value
- Discount rate, value of statistical life
- Parametric variation
- Index Variables
- Identify a location or cell in time or space
- A particular year in multi-year model, a geographic grid in a spatial model
- Parametric variation
- No true value

Quantity Uncertainty

- Model Domain Parameters
- Specify & define scope of system modeled
- Study area, industry segment, planning horizon
- Parametric variation
- No true value
- Outcome Criteria
- Measure or rank desirability of model outcomes
- HUs, costs, probability, reliability index, BCR
- Depends on inputs

Techniques for Addressing U&V

- Narratives
- Parametric variation
- Sensitivity analysis
- Bounding values
- Probabilistic risk assessment
- Deterministic scenario analysis
- Probabilistic scenario analysis

- Scenario planning
- Clarification
- Negotiation
- Adaptive management
- Premise sets
- Advanced analysis

Sources of Uncertainty in Empirical Quantities

- Random Error & Statistical Variation
- Sample error
- Systematic Error & Subjective Judgment
- Calibration of equipment, feels like an 8
- Linguistic Imprecision (ambiguity)
- Fill to -1
- Variability
- Chance-some fish die

Sources of Uncertainty in Empirical Quantities

- Randomness & Unpredictability
- Natural events, outbreaks
- Disagreement or Ambiguity
- Partners, experts
- Approximation
- Past conditions

Practical Approach

- Lists are your friend—make them
- Uncertain scenarios, models and quantities
- Identify those that can be easily addressed
- Address them
- Identify the most important ones not easily addressed
- Develop plan for addressing them

Variation

- Variation = Variability+Uncertainty
- Both are sometimes present
- The two are not always distinguished
- They are sometimes confused
- Would like to keep them separate when possible
- Can it be done?
- Can you do it?

Context

- There are 2 components contributing to variation in outputs
- Uncertainty is reducible
- Variability is not reducible, it is an objective characteristic of system

More Money Means

- Variability
- Better description of chance
- Better understanding of its nature
- No reduction in variability
- Uncertainty
- Better description of uncertainty
- Reduction of uncertainty
- Handling uncertainty

Take Away Points

- Variability is chance and can’t be reduced.
- Uncertainty is ignorance and often can be reduced.
- Better risk assessments separate the two but it is not always easy.
- Separating the two is becoming more important for risk management.

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