Inference for joint historical fits with disconnected human comparisons

Develop inference for joint historical fits when the human comparison graph among historical models is disconnected.

Background

The paper’s main estimation and inference theory assumes a connected human-comparison graph for the historical models. It notes that Supplementary Section C.3 provides conditions under which the historical parameters and the new-model score can nevertheless be jointly identified when the graph is disconnected, including settings where humans compare only one pair of historical models with distinct scores.

The unresolved extension is to develop valid inference—not merely identification—for joint historical fits under such disconnected human-comparison designs. This would extend the ANCHOR framework to settings where the human data do not connect all historical models directly.