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Simplification of Mechanistic Models Neil Crout School of Bioscience University of Nottingham

Simplification of Mechanistic Models Neil Crout School of Bioscience University of Nottingham. Context. Interests in the prediction of contaminant transfer in the environment Originally followed rather ‘mechanistic’ approaches Drifted gradually to increasingly empirical models.

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Simplification of Mechanistic Models Neil Crout School of Bioscience University of Nottingham

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  1. Simplification of Mechanistic ModelsNeil CroutSchool of BioscienceUniversity of Nottingham

  2. Context • Interests in the prediction of contaminant transfer in the environment • Originally followed rather ‘mechanistic’ approaches • Drifted gradually to increasingly empirical models • ‘The proposers seem to believe that they will improve predictions if they remove all understanding of processes...’ • - anonymous grant reviewer

  3. Mechanistic Models - Model Complexity • Environmental systems are complex • Many interacting processes • Data is often limited • Even detailed process based models are simplifications of the real systems • Judgements are being made about the appropriate level of detail in models • Often this is done in a rather ad hoc fashion • Not much use of model selection methods etc

  4. Model Selection/Model Averaging etc • Methods exist for choosing the most predictively reliable model • Or averaging over a family of models • Why aren’t they applied much? • They require a family of alternative models for a system • These are not easy to create for mechanistic models (unlike linear models) • Can we find ways to automatically simplify mechanistic models?

  5. Example: Radiocaesium Contamination

  6. Radiocaesium Plant Uptake Model mcamg mK pH CEChumus Ex-K Kexhumus TF CECclay %clay Kdclay Kdl RIPclay %OM Kdhumus mNH4

  7. Starting from this ‘mechanistic’ model create ‘simpler’ models and compare performance Recipe: Identify model variables to be removed Replace them (one at a time) with the mean value they attain over an un-simplified run The variable whose replacement gives the best performance is then permanently replaced (Refit any adjustable parameters) Repeat with the remaining variables until they are all replaced by constants ‘Automatic Simplification’

  8. Example Results for MDL

  9. Simplification sequences for various selection criteria red = plausible models (subjectively) bold = lowest criteria value

  10. 1:1 Comparison for Model 0

  11. 1:1 Comparison for Model 0 and Model E

  12. 1:1 Graph for Transfer Factor (Model 0)

  13. 1:1 Graph for Transfer Factor (Model 0 & E)

  14. Spatial Application: TF over England & Wales • Principal application is for spatial prediction of uptake to crops • This example using the geochemical atlas of E&W • Data from c. 6000 soil samples (5x5km resolution)

  15. Distribution of TF across England & Wales

  16. Summary • Want to start with some mechanistic credibility • Recognise the risk of over-fitting • Automatically work back to simpler models iteratively (quick, easy) and compare their performance • Obviously could be made more sophisticated • Is it ‘just an abuse of statistical measures’? - paraphrasing an anonymous grant reviewer

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