Bayesianism from a philosophical perspective and its application to medicine

Bayesian philosophy and Bayesian statistics have diverged in recent years, because Bayesian philosophers have become more interested in philosophical problems other than the foundations of statistics and Bayesian statisticians have become less concerned with philosophical foundations. One way in which this divergence manifests itself is through the use of direct inference principles: Bayesian philosophers routinely advocate principles that require calibration of degrees of belief to available non-epistemic probabilities, while Bayesian statisticians rarely invoke such principles. As I explain, however, the standard Bayesian framework cannot coherently employ direct inference principles. Direct inference requires a shift towards a non-standard Bayesian framework, which further increases the gap between Bayesian philosophy and Bayesian statistics. This divergence does not preclude the application of Bayesian philosophical methods to real-world problems. Data consolidation is a key challenge for present-day systems medicine and other systems sciences. I show that data consolidation requires direct inference and that the non-standard Bayesian methods outlined here are well suited to this task.