Add capability for recalibrating output of probability blending

[btrotta-bom]

Ranjan and Gneiting (https://stat.uw.edu/sites/default/files/files/reports/2008/tr543.pdf) have shown that blending well-calibrated probability forecasts does not in general produce a well-calibrated output. They demonstrate that recalibrating the blend using the beta distribution CDF improves reliability, sharpness, and score on proper metrics.

This PR adds a CLI to apply the beta CDF transformation to probability forecasts. It allows the parameters to vary with forecast period.

An experiment recalibrating the blended output of rainfall forecasts (where each forecast is already individually calibrated with Rainforests) showed clear improvement in reliability and sharpness.

Description

Testing:

• Ran tests and they passed OK
• Added new tests for the new feature(s)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.41%. Comparing base (84a8944) to head (6a66daa).
Report is 69 commits behind head on master.

Additional details and impacted files

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+ Hits        12016    13087    +1071     
- Misses        196      211      +15     

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[rachaelesler]

Great work implementing this plugin Belinda. The description in the documentation was very clear and I like the straightforward implementation. The comments from me are mostly minor suggestions and a couple of questions to help get my head around the code. Feel free to ignore ones that you think don't apply.

[rachaelesler]

Looks great Belinda 👏 You will have to show me how to run the unit tests soon too

[bayliffe]

Thanks for this application code. Do you imagine there will be specific code for estimating the coefficients at some point, or are you intending to document your approach to this estimation somewhere?

I've asked one potentially daft question, and added a few comments that are hopefully useful.

[btrotta-bom]

Thanks for reviewing @bayliffe. I don't intend to add code in Improver for estimating the coefficients. Similarly to choosing the blending weights, we'd do this via ad-hoc analysis, e.g. using scipy.optimize.

[bayliffe]

Thanks for the changes @btrotta-bom and the answers to my questions. Happy to approve.

It would be great to see how you approach the alpha/beta estimation, and ideally that work might make it into the IMPROVER docs at some point, or be included as a reference to a paper, so that other users of IMPROVER can create the necessary inputs to benefit from this new functionality.