Class 13.1

Uncertainty analysis: Monte-Carlo simulation, sources of uncertainty.

Oreskes, et al. (1994) paper: Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences.

  • Verification and validation of numerical models of natural systems in imposiible.
  • Verify - assertion or establishment of truth
  • Impossible to demonstrate truth in an open system
    p -> q
    If p then q
    If p is true then q is true

    If it rains tomorrow I will stay home and work

  • Closed mathematical components may be verified
    But models are not closed systems
  • Unknown inputs, parameters, processes. Scaling. Measurement errors. Assumptions.
  • Principal and auxiliary hypotheses
  • Nonuniqueness - more than one model can produce the same output.
    Undetermination
  • How to choose between two theories (models) that are empirically equivalent?
  • Validation - establishment of legitamacy.
    A valid model does not contain detectable flaws.
    Validation means consistency within a system or between systems.
  • Comparison of numerical output to analytical solution
  • Inverse problems. We know the dependent variable, and do not know the independent one.
  • Calibration.
  • Verification as comparison to the independent data set not used for calibration.
  • The goal of scientific theories is not truth but empirical adequacy.
  • Past performance is no guarantee of future performance.
  • Confirmation. If I am at home working, doesn't mean it rains.
  • We can never verify a hypothesis of any kind!
  • Confirmation is a matter of degree.
  • Why model then?

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