fips.Posterior.summary

Posterior.summary()

Return the diagnostics of the solve as a table of one row.

Nothing is printed: the numbers are returned, and the row of one posterior stacks with those of others (pd.concat), as in a sweep over the regularization factor.

Returns:

One row: gamma (the regularization factor), n_state and n_obs (the sizes of the state and of the observations), then dofs, information_content, chi2, reduced_chi2, r2, rmse and uncertainty_reduction.

Return type:

DataFrame

See also

chi2_tests

The chi-squared tests, with their p-values.

desroziers

The observation error variances the residuals diagnose.

with_gamma

The posterior with another regularization factor.

Examples

>>> import numpy as np
>>> import pandas as pd
>>> import fips
>>> cells = pd.Index(["a", "b"], name="cell")
>>> obs_id = pd.Index(["o1", "o2", "o3"], name="obs_id")
>>> prior = fips.Vector.from_series(pd.Series(0.0, index=cells), block="flux")
>>> obs = fips.Vector.from_series(
...     pd.Series([1.0, 2.0, 3.0], index=obs_id), block="co2"
... )
>>> problem = fips.Problem(
...     prior=prior,
...     prior_cov=fips.Independent().with_std(1.0),
...     obs=obs,
...     obs_cov=fips.Independent().with_std(np.sqrt(0.1)),
...     forward=fips.Operator(
...         np.array([[1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]),
...         obs.space,
...         prior.space,
...     ),
... )
>>> post = fips.solve(problem)
>>> table = pd.concat(
...     [post.with_gamma(g).summary() for g in (0.1, 1.0, 10.0)],
...     ignore_index=True,
... )
>>> table[["gamma", "dofs", "reduced_chi2"]].round(3)
   gamma   dofs  reduced_chi2
0    0.1  1.250         1.208
1    1.0  1.877         1.603
2   10.0  1.987         1.660