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TOPIC: Asymmetric uncertainty intervals

Asymmetric uncertainty intervals 4 years 8 months ago #72

  • ahaar
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Hi,

I am using STAN for my Master thesis (MSc. Industrial Ecology at TU Delft/Leiden University) and I was wondering if it is possible to use the asymmetric uncertainty intervals '×÷' instead of the default '±' intervals. If that is not possible, then I suggest to incorporate it in the next version :)

Regards,
Arthur
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Asymmetric uncertainty intervals 4 years 8 months ago #73

  • adminST
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Dear Arthur,
thanks for your feedback!

In STAN we assume uncertain input data to be normally distributed. The reason for this assumption is simple: if linear transformations (like in data reconciliation and error propagation) are applied to these input data the results are again normally distributed. Because of the symmetry of the normal distribution input and output data can be described with '±' intervals.
Unfortunately the story is completely different when using asymmetric distributions. Lets use the lognormal distribution (LND) as an example. The LND can be described by its geometric mean (equal to its median) */ an uncertainty. The LND does not allow values below zero. If you subtract a LND from another LND the result distribution will also cover negative values, thus cannot described anymore with a LND. This can easily be prooved by a Monte Carlo simulation.
So you see introducing */ intervals alone won't do the thing. But I have also good news: we are already working on a numerical procedure that allows to reconcile arbitrary distributed data. Maybe one day in the not so near future it will also be implemented in STAN.

Regards,
Oliver
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Asymmetric uncertainty intervals 4 years 8 months ago #74

  • ahaar
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Thank you Oliver for the clear explanations and good luck for developing the numerical procedure!
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