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Sensitivity Analysis in GEM-SA Jeremy Oakley

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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.

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Exploratory scatter plots

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Sensitivity Analysis Walkthrough 1. Project New 2.Select the Files tab. Click on Browse on the Inputs File row – GEM-SA Demo Data / Model1 / emulator7x120inputs.txt 3.Click on Browse on the Outputs File row – GEM-SA Demo Data / Model1 / out11.txt 4.Return to the Options tab

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Sensitivity Analysis Walkthrough 5.Change the Number of Inputs to 7. 6.Tick the calculate main effects and sum effects boxes only 7.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) 8.Click OK 9. Project Run

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Sensitivity Analysis Walkthrough

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Main effect plots

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Fixing X 6 = 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 X 6 =10 with X 6 =40 would underestimate the influence of this input (The thickness of the band shows emulator uncertainty)

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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

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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

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Interactions and total effects For each input X i Total effect = main effect for X i + all interactions involving X i Total effect >> main effect implies interactions in the model – NB main effects normalised by variance, total effects normalised by sum of total effects Look for large total effects relative to main effects

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Interactions and total effects Total effects for inputs 4 and 7 much larger than its main effect. Implies presence of interactions

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Interaction effects 10. Project Edit 11.Tick calculate joint effects 12.De-select all inputs under inputs to include in joint effects, select 4,5,6,7 13.Click OK 14. Project Run

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Interaction effects

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Note interactions involving inputs 4 and 7 Main effects and selected interactions now sum to 91% of the total variance

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Exercise 1.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 2.Estimate the main effects only for this model and identify the influential input variables 3.By comparing main effects with total effects, can you spot any interactions? 4.Estimate any suspected interactions to test your intuition!

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