Sensitivity Analysis in GEM-SA Jeremy Oakley
Mar 31, 2015
Sensitivity Analysis in GEM-SA
Jeremy Oakley
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
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
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
Sensitivity Analysis Walkthrough
Main effect plots
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)
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
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
Interactions and total effects
For each input Xi
Total effect = main effect for Xi + all interactions involving Xi
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
Interactions and total effects
Total effects for inputs 4 and 7 much larger than its main effect. Implies presence of interactions
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
Interaction effects
Interaction effects
Note interactions involving inputs 4 and 7
Main effects and selected interactions now sum to 91% of the total variance
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!