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!