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Sensitivity Analysis in GEM-SA

Sensitivity Analysis in GEM-SA. Example. ForestETP vegetation model 7 input parameters 120 model runs Objective: conduct a variance-based sensitivity analysis to identify which uncertain inputs are driving the output uncertainty. Exploratory scatter plots. Sensitivity analysis walkthrough.

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Sensitivity Analysis in GEM-SA

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  1. Sensitivity Analysis in GEM-SA

  2. Example • ForestETP vegetation model • 7 input parameters • 120 model runs • Objective: conduct a variance-based sensitivity analysis to identify which uncertain inputs are driving the output uncertainty. GEM-SA course - session 6

  3. Exploratory scatter plots GEM-SA course - session 6

  4. Sensitivity analysis walkthrough •  Project  New • In the Files tab, click on Browse on the Inputs File row • GEM-SA Demo Data / Model1 / emulator7x120inputs.txt • Click on Browse on the Outputs File row • GEM-SA Demo Data / Model1 / out11.txt • Select the Options tab GEM-SA course - session 6

  5. Sensitivity analysis walkthrough • Change the Number of Inputs to 7. • Tick the calculate main effects and sum effects boxes only • Leave the other options unchanged • Input uncertainty options: All unknown, uniform • Prior mean options: Linear term for each input • Generate predictions as: function realisations (correlated points) GEM-SA course - session 6

  6. Sensitivity analysis walkthrough GEM-SA course - session 6

  7. Sensitivity analysis walkthrough • Click OK • An Inputs Parameter Ranges window will appear. Click Defaults from input ranges, then OK •  Project  Run or use GEM-SA course - session 6

  8. Main effect plots GEM-SA course - session 6

  9. Main effect plots Fixing X6 = 18, this point shows the expected value of the output (obtained by averaging over all other inputs). Simply fixing all the other inputs at their central values and comparing X6=10 with X6=40 would underestimate the influence of this input (The thickness of the band shows emulator uncertainty) GEM-SA course - session 6

  10. Variance of main effects Main effects for each input. Input 6 has the greatest individual contribution to the variance Main effects sum to 66% of the total variance GEM-SA course - session 6

  11. Interactions and total effects • Main effects explain 2/3 of the variance • Model must contain interactions • Any input can have small main effect, but large interaction effect, so overall still an ‘important’ input • Can ask GEM-SA to compute all pair-wise interaction effects • 435 in total for a 30 input model – can take some time! • Useful to know what to look for GEM-SA course - session 6

  12. Interactions and total effects • For each input Xi Total effect = main effect for Xi + all interactions involving Xi • Main effects and total effects normalised by variance • Total effect >> main effect implies interactions in the model • Look for inputs with large total effects relative to main effects • Investigate possible interactions involving those inputs GEM-SA course - session 6

  13. Interactions and total effects Total effects for inputs 4 and 7 much larger than its main effect. Implies presence of interactions GEM-SA course - session 6

  14. Interaction effects •  Project  Edit or • In Options tab, tick calculate joint effects • De-select all inputs under inputs to include in joint effects, select X4, X5, X6, X7 GEM-SA course - session 6

  15. Interaction effects • Click OK •  Project  Run or GEM-SA course - session 6

  16. Interaction effects Note interactions involving inputs 4 and 7 Main effects and selected interactions now sum to almost 92% of the total variance GEM-SA course - session 6

  17. Exercise • Set up a new project using SAex1_inputs.txt for the inputs and SAex1_outputs.txt for the output • 8 input parameters (uniform on [0,1]) • 100 model runs • Estimate the main effects only for this model and identify the influential input variables • By comparing main effects with total effects, can you spot any interactions? • Estimate any suspected interactions to test your intuition! GEM-SA course - session 6

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