`grid_shape` asked for 12 nodes across the narrowest feature and then
clamped to MAX_GRID_POINTS with no detection that the request was not
met. Past `step/sigma ~ 1.7` the trapezoid rule stops resolving the
density, and the result is unbounded:
sigma_a step/sig_a P(a first) exact total
2.0e-3 0.86 0.515953 0.515953 1.000000
1.0e-3 1.72 0.517185 0.515953 1.002388
1.0e-4 17.17 2.791336 0.515953 5.410065
A probability of 2.79. Reachable through `predict_outcome` with a pinned
reference competitor — a documented pattern — where `predict_outcome` and
`predict_win_probabilities` disagreed 44x and `predict_outcome` was the
wrong one.
There is no useful answer on the far side of that cliff, so this reports
`GridTooCoarse` rather than guessing, and the message points at
`predict_win_probabilities`, which answers the same matchup through
adaptive quadrature and is accurate there to 1e-13. The floor is 4 nodes
per feature rather than the 12 requested, because the request carries
margin: measured accurate to 2.2e-12 at 1.4 nodes per sigma and wrong by
1.2e-3 at 0.7.
This also fixes the `ln k` ceiling violation. `expected_information_gain`
weights `probability * divergence`, so probabilities of 3.97 and 2.62
made it return 3.237828 nats against `ln 2 = 0.693147` — 4.67x over. The
crate's docs call that ceiling its sharpest test and record a prototype
once returning 4.77 nats; it was live again by a different route.
The new sweep then caught a second, independent defect: `kl_divergence`
returned NEGATIVE values, worst -5.55e-17, exactly one ULP of its
`- 1.0`. Rewritten as `0.5*(u - ln1p(u)) + gap^2/(2*var_p)` with
`u = var_q/var_p - 1`, so both terms are non-negative by construction.
It is also more accurate where it matters: at `u = 1e-9` the old form
returned 0.0 where the true value is 2.5e-19, and well-conditioned cases
are unchanged.
tests/prediction_bounds.rs sweeps rather than spot-checks, because a
single fixture cannot defend a bound like this — the previous check
passed throughout. It asserts the sweep still reaches the coarse-grid
regime, so it cannot quietly stop testing the case it was written for.
BREAKING CHANGE: `predict_outcome`, `predict_ranking` and
`expected_information_gain` return `GridTooCoarse` for matchups whose
performance sigmas are too far apart to integrate on one grid. They
previously returned wrong answers, including probabilities above 1.
Closes#55, closes#56
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
logaritmiskandClaude Opus 5
bbc7705c75