[remislp]

What this adds

ApproximateSD has always sized one relative increment, chosen so that moving every parameter together changes the function by 0.5% of its own value.

Colquhoun, Hatton & Hawkes (2003) J Physiol 547:699–728, p. 702, describe a different rule, and it is the one their Tables 2 and 3 were made with: find the increment for each parameter separately that changes the log likelihood by a specified absolute amount, and where no such increment exists, omit that parameter's row and column from the Hessian before inverting it.

delta_L selects that rule.

Why the per-parameter part matters

Sizing one step by moving every parameter at once walks along the diagonal ridge that an anisotropic likelihood has — the direction in which the function barely changes. The step that comes out is therefore far too large for the directions across the ridge, which are the ones the curvature is wanted for.

The interface

kept and dropped say which parameters survived.

• hessian and covariance cover the survivors only;
• sd and correlations stay the full size of theta, with nan in the dropped places.

So sd[i] always refers to theta[i], and a table of results cannot silently misalign — which is the failure mode worth designing against here, because it produces a plausible table rather than an error.

A function that raises where it cannot be evaluated is treated as too large a step rather than propagating the error.

The default path is untouched

Verified rather than asserted: the existing pinned Hessian, covariance, SD and correlation values in test_errors.py are unchanged, and that file still passes.

Tests

10 new, on quadratics whose Hessian is known exactly, so a failure means the estimator is wrong rather than that a reference value drifted:

test_both_rules_recover_a_known_hessian
test_absolute_rule_gives_the_right_correlation
test_each_increment_produces_the_requested_change
test_increments_differ_between_parameters
test_insensitive_parameter_is_dropped
test_dropping_leaves_the_others_exact
test_dropped_entries_are_nan_and_indexed_by_parameter
test_the_flat_case_is_what_the_default_rule_cannot_do
test_a_function_that_raises_is_treated_as_too_large_a_step
test_zero_valued_parameter_does_not_give_a_zero_increment

test_the_flat_case_is_what_the_default_rule_cannot_do records the case that motivated the whole thing.

Suite goes from 48 to 60 passed.

Provenance

Written on 2 September during the reproduction of CHH 2003, committed to a local master and never pushed. This is that work rebased onto origin/master as a single commit, with the merge commit flattened out. Nothing in the module or its tests references the reproduction; it needs no new dependency.

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