#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
clippy::useless_vec. Pushed broken because the verification chain used
`if ... then echo` blocks that report status without gating the `&&`
that follows — the same shape of mistake as e1bddf2, where a grep
succeeded on the error text. Both times the check printed FAIL and the
push went ahead.
The reliable form is a single fail-fast chain:
just lint && just test && just determinism && cargo test --doc
so nothing runs after the first failure.
Investigation for #46 and #47, before touching either.
A scored history is linear-Gaussian, so its true joint posterior has a
closed form and the crate can be checked against ground truth. Measured
on five competitors:
means marginal sd (crate / exact)
tree (star) exact 1.000
loopy (robin) exact 0.502
On a tree the crate is exact in both. With cycles the means stay exact —
the standard Gaussian-BP result, and the property ratings rely on —
while marginal variances come out about half the true width.
That is the opposite direction from what #47 reports, so whatever is
happening in that consumer's model, the crate being conservative is not
it.
It also means #46 cannot be implemented as an added covariance accessor.
The exact correlation between two nodes here is +0.857, so ignoring it
overstates the width of a difference — but the too-narrow marginals
partially cancel that, leaving 1.327x rather than 2.646x. Adding true
correlations to these marginals without correcting them would give 0.765
against a true 1.524: overconfident, which is the direction the reporter
specifically called unsafe.
Pins the two real invariants (exactness on a tree, exact means with
cycles) and deliberately only records the variance gap, since closing it
is what #46 proposes.
Also records the working rules this project has converged on: investigate
before implementing, fix the root issue, and scout crates.io on measured
accuracy rather than adoption.
Refs #46, #47
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
logaritmiskandClaude Opus 5