1. Sources of Uncertainty (from Morgan and Henrion) Jake Blanchard Spring 2010 Uncertainty Analysis for Engineers1

2. Types of events Subjective probability distributions are only suitable for certain types of events Empirical Quantities – measurable properties of real-world systems Constants – fundamental physical constants (certain by definition) Decision Variables – quantities over which the decision maker exercises direct control Value Parameters – aspects of the preferences of decision makers (eg. risk tolerance or value of life) Uncertainty Analysis for Engineers2

3. Event Types (cont.) Index Variables – identify a location or cell in the spatial or temporal domain (eg. a particular year or geographical grid) Model Domain Parameters – specify domain or scope of system (eg. Last year modeled, spatial extent of model, etc.) State Variables – minimal subset of all variables from which all other variables can be calculated Outcome Criteria – variables used to rank outcomes Uncertainty Analysis for Engineers3

4. Sources of Uncertainty – Empirical Quantities Statistical variation – random error in direct measurement Systematic error – difference between true value of a measured quantity and mean of measured values Linguistic imprecision – (“Pat is tall” vs. “Pat is over 6 feet tall”) Variability – (eg retail price of gasoline or flow rate of a river) Randomness – variation that cannot be attributed to a pattern or model (function of available knowledge) Uncertainty Analysis for Engineers4

5. Uncertainty About Model Form If we pick wrong model (eg normal vs. beta distribution), errors will result Uncertainty Analysis for Engineers5