Investigating #47 needed a reproduction of the reporter's structure: a
joint player/layout model where every observation measures a sum of
nodes against a reference, so the data pins differences and leaves the
overall level to the prior.
The result corrects #46's framing as well as answering #47. Combining
marginals is wrong in opposite directions depending on the combination,
and the unsafe direction is not the one either issue assumed:
combination exact adding marginals
p0 + h0 (a round) 4.0850 0.8041 0.20x OVERconfident
p0 - p1 (rank two) 0.8741 0.8592 0.98x about right
h0 - h1 0.7119 0.7057 0.99x about right
#46 assumed every published figure was too wide and that this was "at
least the safe direction". That holds for differences. For sums it
reverses: adding marginals is five times too narrow, which publishes a
claim the data does not support.
For a single node the exact marginal is ~5x wider than message passing
reports, because the level it shares with its partners is pinned only by
the prior. That is the honest posterior for a weakly identified
parameter, not a defect — and it is why #47's node "should be
publishable" intuition and its posterior sigma disagree.
Refs #46, #47
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
