#48: every predict_* answers "who wins", and a consumer recording scores
never asks that. It wants the interval on the result, and having none it
hand-fitted a noise law whose fitted node weight came out at 0.0 — so
the quoted sigma was 5.83 whether the competitor had forty rounds or
none, against real residual spreads of 5.8 and 12.44.
`predict_margin` composes the three things that make a scored result
uncertain: the joint posterior over the competitors, their per-event
performance noise, and the observation noise on the score. It widens as
the model knows less — measured, sigma 2.48 against an opponent with
forty rounds, 3.38 against one seen once, wider still against one never
seen — which is the property the hand-fitted law lost.
It is a margin, not a score, and that is not a shortcut. Scored
ingestion reduces every event to `score_a - score_b` before inference,
so the absolute level is discarded: shifting every score in a history by
+100 or -1000 produces a bit-identical fit, verified. There is no
information from which to predict what a competitor will *score*.
Returning one would be a number derived entirely from the prior, which
is exactly the plausible constant this crate keeps finding and removing.
`posterior_of` now honours `UnknownKeys::Prior`, which gives #48 its
second requirement — "I have never seen this competitor, here is the
prior-informed answer". An unseen competitor shares no event with the
slice, so it is independent by construction and its variance is additive
rather than part of the solve.
Worth recording for expectations: for a *margin* the joint buys little
over adding marginals (2.4798 against 2.5112 here), because a margin is
a difference and differences are where the loopy underestimate and the
ignored correlation cancel. The gain here is having a predictive
distribution at all. `posterior_of`'s correlation handling earns its
keep on sums and single nodes instead — see tests/additive_model.rs.
Closes#48
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
