[patnr]

Adds a README to tests/, and a new test module, test_statistical_consistency.py.

The README describes the cases the methods are run on end to end (Van der Pol, the linear 1D field, MiniRes, Rosenbrock and the quadratic), and which scheme and analysis is checked on which case, and how: pinned numbers, property tests, the benchmark, or the new checks. The unit and regression tests are left to their docstrings.

The new checks are a linear sanity check. With a linear model and a Gaussian prior and noise, the posterior is known exactly, so every registered scheme and analysis is compared with the correct answer, on its mean and its spread, rather than with previously pinned numbers. The cases are multivariate but not spatial: 1, 2 and 10 unknowns, with a random prior correlation, a dense random G, and noise variances spanning three orders of magnitude. The reference is the exact update of the prior ensemble's own mean and covariance, so prior sampling error does not count against a method; the rest is averaged over 5 seeds of 100 members.

Combinations left out are listed in EXCLUDED, each with its reason, and expected deviations in DEVIATIONS, as strict xfails, so that a fix shows up as a failure until its entry is removed. The tolerances were set from repeated runs with independent seeds.

The module runs in about 20 s.

Checked locally: the new module, and ruff.

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