Lec: Global SA
13 important questions on Lec: Global SA
Why do we have uncertainty in the input of a model?
- Scaling problems
- Measurement problems
- Model structure errors
What are the 3 main characteristics of LSA?
- Local method: results depend on base-run
- Results depend on assumed scale of variation (st dev) of parameters
- Computationally cheap, only one extra run per parameter
What is a risk with LSA?
Worst case: when you think there is no slope (your model is not sensitive to your parameter at all) when actually this is not true
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Other behaviour in models that give issues for LSA?
In case of snow parameter, it only shows sensitivity based on the temperature, meaning sensitivity can change based on situation > blocky structures.
GSA: SOBOL' methods
What is the definition of the explained variance in GSA?
Note: total variance - conditional expectation = basically the residuals
How does GSA work in steps?
- Sample parameter based on chosen distribution
- Run model many many times
- Determine conditional expectation for each parameter
- Calculate residuals
- Check which part of the model variance we can explain for this particular parameter
- Compare to total model variance to determine which parameter explains most of the variance, bc this is the parameter our model is most sensitive to
- Determine the portion of model variance explained by interaction of parameters
When would you do local and when global SA?
- Start with GSA: sample full range of parameters
- Look at which parameters influence your model most
- Calibrate these parameters
- After calibration, you do LSA; find best guess parameters
- Look in near vicinity of best guess parameters, to see what the uncertianty in your projections is
Model runtime: problem with GSA
But GSA can be done on a small range of a parameter; or we can sample full parameter space and determine which influence model results most and select these for calibration
What are the main take aways for variation analysis through sampling/GSA/SOBOL' (all same thing)?
- Global method
- Parameter space is sampled
- For identification of calibration parameters: take wide par space
- For sensitivity only: take smaller space
- Also works for highly non-linear functions
- Results depend on assumed distribution of parameters
- Computationally expensive; many model runs required
How will we sample our parameters?
What is Monte Carlo sampling?
- Pick distribution
- Randomly sample within distribution - Sample more in regions with high probability
- Run model
Issue: if your MC sample is not big enough and does not capture your distribution well, it will lead to different results each time
Thus MC is least efficient sampling strategy
2D Monte Carlo sampling vs 2D Quantile sampling
Q: we do capture full distribution of parameter; but it is not efficient for many parameters!
10 samples per par
6 pars in our model
run time: 1 sec
10^6 sec = 11 days
Give a summary of when to choose which sampling technique and give arguments why!
MC: too much insecurity due to random sampling, while we want to capture distribution correctly
Quantile: more efficient and more stable in representing distribution
2D or higher:
MC: even more expensive
Random quantile sampling: also gets too expensive
>> Latin Hypercube sampling! Kind of a mix between MC and quantile, which saves a lot of computational power. But we do have to assume the parameters are independent/do not interact
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