feat: add History::posterior_of for a linear combination of competitors
#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
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@@ -123,6 +123,7 @@ mod game;
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pub mod gaussian;
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pub mod graph;
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mod history;
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mod joint;
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mod key_table;
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mod matrix;
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mod observer;
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