Definition of edges for RPS score

[judithberner]

pangeo-data/climpred#562

[judithberner]

@abjaye
@aaronspring

[judithberner]

And here a reference:
https://journals.ametsoc.org/view/journals/mwre/135/1/mwr3280.1.xml
"Here, Yk and Ok denote the kth component of the cumulative forecast and observation vectors Y and O, respectively. That is, Yk = Σki=1 yi, with yi being the probabilistic forecast for the event to happen in category i, and Ok = Σki=1 oi with oi = 1 if the observation is in category i and oi = 0 if the observation falls into a category j ≠ i. Note that the RPS is zero for a perfect forecast and positive otherwise."

[aaronspring]

The question in pangeo-data/climpred#562 is whether bins in xhistogram can also be multidimensional for lon and lat. Docs only specify array like.
The use case is calculating an RPS (mostly using xhistogram) based on climatological terciles, which are lon, lat dependent.

@dougiesquire ideas?

[aaronspring]

One bad and slow but working solution would be looping over the grid. Searching for better ones.

[aaronspring]

Without using xhist, I think we could take N, here 3 or 4, threshold xarray.DataArrays or even xr.Datasets with lon and lat, and do the counting how many members are in between two thresholds by hand.

[aaronspring]

I think I will need to rework rps.

Here a prototype for xs.rps and also climpred: https://gist.github.com/aaronspring/3c3db6b7d5f39c08643e818b0964ee6c
which allows xarray.Dataset or xr.DataArray as category_edges

Examples for terciles:

[aaronspring]

this is how the new API would look like https://xskillscore--277.org.readthedocs.build/en/277/api/xskillscore.rps.html#xskillscore.rps