methodeutics

Anytime-valid evidence as a running bet. The e-value bankroll, in three lines:

from methodeutics import Bankroll, bernoulli

b = Bankroll(bernoulli(p0=0.5, p1=0.6), alpha=0.05).extend(observations)
b.plot()  # pip install methodeutics[plot]

Start with one dollar. Each observation multiplies your bankroll by the likelihood ratio the alternative assigns against the null. If the null is true, no strategy grows the dollar on average, and the bankroll crosses 1/alpha with probability at most alpha, no matter when or how often you look (Ville's inequality). If the null is false, the bankroll compounds. Look every day. Stop whenever you want. The guarantee holds.

b.e           # current e-value
b.trajectory  # e-value after each observation
b.threshold   # 1/alpha, pre-committed
b.decided     # crossed the threshold? (remembered even if it later falls)
b.compose(b2) # evidence from an independent bankroll: multiply, no correction

Models: normal(null_mean, alt_mean, sd), bernoulli(p0, p1), categorical(null, alt), or any callable lr(x) returning a likelihood ratio.

This is the companion package to chapters 9-10 of the Methodeutics textbook, where the bankroll is derived from scratch and the three guarantees (anytime validity, optional stopping, composition) are stated with their lineage: Ville 1939, Doob 1953, Shafer 2021, Ramdas 2023, Grünwald 2024.

Not the epidemiology E-value (VanderWeele & Ding's sensitivity-analysis quantity). Same letter, unrelated concept.

See also: confseq (confidence sequences, the reference implementation), expectation (a fuller e-process library), savvi (anytime-valid inference for specific models).

AGPL-3.0-or-later license.