De-register ES-MDA with full/subspace/subspace2 (wrong posterior)? LM-EnRML/subspace stops early #192

tests/assimilation/test_statistical_consistency.py (#191) compares every scheme and analysis with the exact posterior of a linear-Gaussian problem. Known deviations are marked as expected failures, so CI passes. (LM-/GN-EnRML with approx are not tested, being approximations by design.)

I'm of the opinion that the following combos should be de-registered, since none of these analyses is meant for ES-MDA. Its correct analysis is approx, which should perhaps go under a different name: for ES-MDA it is not an approximation, since the term it drops is zero there. The causes below are confirmed.

• ES-MDA, full: always adds the RML pull towards the prior, (enX - prior_enX), which does not belong in ES-MDA. Without it, exact.
• ES-MDA, subspace/subspace2: rebuild the state from the prior ensemble (propose_state), so the result is the posterior for noise α R: too wide by about α.

With 4 steps of α = 4 and one unknown, the variance is 1.7–2.9 x too large and the mean 0.6–0.8 posterior sd off. It gets worse with larger α.

In addition the combo LM-EnRML, subspace fails at the default λ = 100 because the first step is ~1 % of a full one, which the 1 % misfit rule reads as convergence. It stops after one iteration, at about the prior, and reports that it converged. Exact with λ = 1. Can we adjust the rules somehow?