Focused Correlation and Confirmation

This essay presents results about a deviation from independencemeasure called focused correlation. This measure explicatesthe formal relationship between probabilistic dependence ofan evidence set and the incremental confirmation of a hypothesis,resolves a basic question underlying Peter Klein and Ted Warfield's‘truth-conduciveness’ problem for Bayesian coherentism,and provides a qualified rebuttal to Erik Olsson's claim thatthere is no informative link between correlation and confirmation.The generality of the result is compared to recent programsin Bayesian epistemology that attempt to link correlation andconfirmation by utilizing a conditional evidential independencecondition. Several properties of focused correlation are alsohighlighted.

1. Introduction
2. Correlation Measures

   2.1 Standard covarianceand correlation measures

   2.2 The Wayne–Shogenjimeasure

   2.3 Interpreting correlation measures

   2.4 Correlationandevidential independence

3. Focused Correlation
4. Conclusion

Appendix