Statistical and metastatistical considerations in analysing the desirability of human Bayesian conservatism

Abstract

Goldstein (1979) showed that interdependence of Bernoulli data can lead to either overestimation or underestimation of odds depending on the type of interdependence, and inferred that conservative behaviour is not a necessary outcome of interdependence. It is argued here that the effect of data interdependence on posterior odds in the real world cannot be determined by pure statistical reasoning. Logical arguments suggest that interdependence which requires conservative revisions is most typical. Thus, a Bayesian processor acting on the assumption that data are conditionally independent is likely to end up with inflated posterior odds.