Filtering statistics

TL;DR

Filtering asks whether an observed node-pair occupation is surprising under a fitted independent null model. The output is an edge classification, not a new network model.

Tail choices

Tail	Test
upper	observed occupation is larger than expected
lower	positive observed occupation is smaller than expected
two-sided	split alpha across upper and lower tests

For observed positive pairs, MENoBiS uses conditional p-values under the positive support where appropriate. This avoids treating “pair exists” as random after selecting only existing observed pairs.

Two-sided tests

A two-sided filter with alpha=0.05 tests each tail at 0.025. Report the tail and correction whenever you report filtered edges.

Multiple testing

Correction	Meaning
none	compare each p-value directly with alpha
bonferroni	conservative family-wise correction
fdr	false-discovery-rate style threshold

Start with none for exploration and report the correction used in scientific work.

Absent edges

Absent-edge filtering is optional because it scans candidate pairs with observed occupation zero. Enable it when missing edges are scientifically meaningful:

result = filter_model(
    edges,
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH,
    fit=fit,
    detect_absent=True,
    min_occupation=0.5,
    max_absent=1000,
)

Option	Meaning
detect_absent	scan zero-occupation candidate pairs
min_occupation	only report pairs likely to be occupied
min_expected	require a minimum expected occupation
max_absent	cap output size

Interpretation

A significant pair is significant relative to the chosen null constraints. If a signal disappears after adding cost or degree constraints, it may be explained by those constraints rather than by higher-order structure.