In Models We Trust—But First, Validate

Scientists use mathematical descriptions and simulations to make forecasts and provide recommendations to decision makers, but how reliable are these models?

Mathematics

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January-February 2023

Volume 111, Number 1
Page 42

DOI: 10.1511/2023.111.1.42

All models are beautiful—even mathematical ones. They provide insights to scientists and to the general public about a vast array of phenomena in the real world, and we have come to rely on them much more than you may realize.

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  • Mathematical models inform our understanding of the world. With varying degrees of success, they predict storm tracks, election results, and the motion of falling objects.
  • No model is perfect. Researchers who use mathematical models should question how they were validated, and what assumptions lie behind them.
  • Common validation methods include commonsense reality checks, comparison to experimental data, updating of parameters, confidence intervals, and sensitivity analysis.
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