Choosing threshold in ExtremeValues

[torbenschmith]

Choosing threshold in ExtremeValues

In xsdba, the ExtremeValues correction procedure involves fitting of GPD distributions, which are then blended with empirical distributions to get a mixture distribution. These mixture distributions are then combined to get the bias-correction mapping. The procedure is as follows (as I understand it):
· For ref and hist datasets, define clusters as exceeding 1 mm (or a user defined threshold ’cluster_thresh’) surrounded by value below the threshold
· For ref and hist datasets, take the q_thresh (default = 0.95 ) quantile of the above, giving a threshold for ref and one for hist
· Define a final threshold as the mean of the two above thresholds
thresh = (np.nanquantile(ref[ref >= cluster_thresh], q_thresh) + np.nanquantile(hist[hist >= cluster_thresh], q_thresh)) / 2

Typically the range, i.e also peak values, will differ between hist and ref data. The above procedure of defining the threshold for the GPD fits can be inconvenient because it may select a different number of data points for ref and hist, respectively. In the extreme case, no data may be selected for one of the datasets.

A more flexible setup

A more flexible setup would be:
· possibility to specify individual thresholds for ref, hist (and sim)
· possibility tor specify individual number of peaks for ref, hist (and sim)
Such an implementation would allow for most practical applications. I would therefore like to the community’s opinion about that.

Additional context

No response

Contribution

• I would be willing/able to open a Pull Request to contribute this feature.

[coxipi]

Hi! Yes I could see the use of having a fixed specified threshold . We could add a thresh argument. Then, q_thresh and thresh would both be optional, with one of them needing to be given. cluster_thresh would remain as-is

Could you explain what you mean by 'specify individual number of peaks'? You would accept a maximum number of peaks?

[torbenschmith]

I think it is important to have a 'thresh' argument for each of the datasets (ref, hist and sim). This is needed because the different datasets may have different statistics, and therefore different level of extremes. For that reason it would also be nice to have the option to supply 'tresh' both as a global value and as a spatial field.

By the term 'specify individual number of peaks' i refer to the 'peak over threshold' approach from extreme value analysis. This means that, instead of a threshold, you would select the N largest (for instance 3/year, so if you have 30 years you select the 90 largest peak values and fit your GPD to these). Again, large flexibility would be nice: possibility of different N for ref, hist and sim, as well as option of global value or field.