Decide on nomenclature

[tommyod]

We should decide what we call parameters.

• response_ensemble vs. Y vs. responses
• observation_errors vs. C_dd
• param_ensemble vs. X vs. parameters
• etc

Shapes

• num_obs vs. num_observations vs. num_outputs
• ensemble_size vs. num_ensemble vs. N_e vs. N
• etc

We can use different names for the public API and the internals.

If we decide on this now, it will save us time and headache in the future.

[tommyod]

I propose:

• The public API should be consistent across all algorithms. I think parameters, responses, covariance, observations is quite good, instead of the ensemble-suffix and the shortenings param instead of parameters. However, the similarity between a response and an observation might confusing.
• The internal variable names. I propose that we rename all input arguments immediately to mathematical notation that corresponds with the paper, and follow that in all the internals (non-public facing API).
• For shapes, I propose num_parameters, num_responses and num_ensemble, using the num_ prefix for all shapes.

We could add some checks in the CI/CD pipeline that fail if any common misspellings are used, so we do not regress in the future.