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Models with higher effective dimensions tend to produce more uncertain estimates
Arnald Puy1,2,3, Pierfrancesco Beneventano4, Simon A Levin2
1School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham B15 2TT, UK.
Science Advances
|October 19, 2022
Summary
Adding detail to mathematical models, even without data, can lead to less accurate predictions by increasing complexity. Monitoring effective dimensions and uncertainty helps determine if added model detail is beneficial.
Area of Science:
- Mathematical modeling
- Statistical theory
- Systems dynamics
Background:
- Mathematical models are increasingly complex to improve predictions and insights.
- Model development often occurs without validation or training data.
Purpose of the Study:
- To investigate how increasing model detail affects estimation accuracy.
- To provide guidance on when model complexity is appropriate.
Main Methods:
- Analysis of Variance (ANOVA) and statistical theory were employed.
- The evolution of effective model dimensions and output uncertainty was tracked during model upgrades.
Main Results:
- Increased model detail generally leads to "fuzzier" estimates.
- This occurs due to an increase in effective dimensions and higher-order interactions.
Conclusions:
- Modelers should carefully consider the trade-offs between model detail and data quality.
- Tracking effective dimensions and uncertainty aids in making informed decisions about model complexity.
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