#46: every accessor returns a per-competitor marginal, and almost
nothing a consumer publishes is one competitor. Combining marginals
assumes independence, and competitors are correlated through every event
they share.
`posterior_of(&[(a, 1.0), (b, -1.0)])` returns the posterior of that
combination with the correlation intact. Validated against the exact
linear-Gaussian posterior on both a tree and a loopy fixture, for
differences and for single competitors: agreement to 1e-9 relative in
every case.
The investigation that preceded this is why it is not a covariance
accessor. Marginals from loopy message passing are about half the true
width, and ignoring correlation overstates a difference — the two errors
partially cancel, leaving 1.327x rather than 2.646x. Bolting true
correlations onto the existing marginals would have given 0.765 against
a true 1.524, which is overconfident: the direction the reporter
specifically called unsafe. Rebuilding the joint from the factor
structure fixes both at once, and a single-competitor query now returns
the exact marginal rather than the narrow one.
The precision matrix depends only on structure — who played whom, with
what weights and what noise — not on the observed outcomes, and the
means were already exact. So only the second moment is reconstructed.
Known limits, all deliberate and documented on the method:
- Latest slice only. A functional spanning times, such as "current
versus career", needs the time-expanded joint and is not covered.
- Scored events only. A ranked outcome's truncation is EP-approximated
and its converged factors are not retained after inference, so ranked
slices return `JointUnavailable` rather than a plausible wrong number.
- Dense Cholesky, O(n^3) per query in the slice's competitor count:
38.8us at 50, 5.66ms at 400, 49.1ms at 800. Fine for the sizes this
serves today; caching the factorization per slice would make repeat
queries O(n^2), and sparsity is the next step after that.
Refs #46, #47, #48
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
logaritmiskandClaude Opus 5
c52e2550af