Focused Correlation and Confirmation

This essay presents results about a deviation from independence measure called focused correlation. This measure explicates the formal relationship between probabilistic dependence of an 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 that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. 1. Introduction2. Correlation Measures2.1. Standard covariance and correlation measures2.2. The Wayne–Shogenji measure2.3. Interpreting correlation measures2.4. Correlation and evidential independence3. Focused Correlation4. Conclusion Introduction Correlation Measures Standard covariance and correlation measures The Wayne–Shogenji measure Interpreting correlation measures Correlation and evidential independence Focused Correlation Conclusion Appendix