Learning Conditional Evidence

Learning indicative conditionals and learning relative frequencies have one thing in common: they are examples of conditional evidence, that is, evidence that includes a suppositional element. Standard Bayesian theory does not describe how such evidence affects rational degrees of belief, and natural solutions run into major problems. We propose that conditional evidence is best modeled by a combination of two strategies: First, by generalizing Bayesian Conditionalization to minimizing an appropriate divergence between prior and posterior probability distribution. Second, by representing the relevant causal relations and the implied conditional independence relations in a Bayesian network that constrains both prior and posterior. We show that this approach solves several well-known puzzles about learning conditional evidence (e.g., the notorious Judy Benjamin problem) and that learning an indicative conditional can often be described adequately by conditionalizing on the associated material conditional.

Athleticism in NCAA D-III: It Ain’t Only Football That Matters

Most D-III universities field a football team, yet little is known about how a football program can influence the quality of the student body or rate at which students graduate. To evaluate these advertising and effectiveness effects of football, we build balanced panel data sets using available private D-III universities (80–90% of all D-III universities) from 2003 through 2010. We also account for overall athletic participation. Using generalized linear model (GLM) and linear-in-means estimation procedures, we find conditional evidence of the advertising and effectiveness hypotheses of football. We find that female athletes are successful as advertising and effectiveness, while male athletes are negative advertising and of neutral to negative effectiveness.