Focused Correlation, Confirmation, and the Jigsaw Puzzle of Variable Evidence

Abstract

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. Wheeler and Scheines have shown that a difference in incremental confirmation of two evidence sets is robustly tracked by a difference in their focus correlation. In this essay, we generalize that tracking result by allowing for evidence having unequal relevance to the hypothesis. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation.

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