Add support for emulator UQ to be included in sensitivity analysis #877
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Closes #720.
This PR adds support for including emulator uncertainty in the confidence intervals for sensitivity analysis.
Approach
See description in #720 and end of section 3.2 for decomposing variance into SA sampling uncertainty and emulator uncertainty.
The approach extends the confidence intervals provided by SALib by adding an additional orthogonal variance as a result of bootstrap samples of the predictive distriibution from the emulator with the SA run and output recorded for each bootstrap sample to generate a distribution of SA outputs with respect to the emulator uncertainty.
An alternative could be to directly build the predictive sampling of outputs into a single bootstrap sampling approach that is currently within SALib for capturing the uncertainty of the SA estimates due to the input sampling.
API design choice
A design choice that might be good to consider here: currently this impl leaves the including emulator uncertainty as optional and when set to
True
with a non-UQ emulator, raises an error. This is motivated by:False
and opting in to additional expensive bootstraps