Shimin Zhao

This paper proposes a new Bayesian confirmation theory, according to which confirmational relations are causal relations between credences. The idea is that proposition E is evidentially relevant to proposition H relative to a credence distribution cr just in case cr(E) is a cause of cr(H), which is understood from an interventionist perspective as intervening on cr(E) would make a difference to the value of cr(H). E confirms H means that under an intervention on cr(E), cr(H) and cr(E) would covary in the same direction; disconfirmation means that they would covary in the opposite direction. I argue that this causal theory explains how orthodox Bayesian theory succeeds in non-extreme credences and fails in extreme credences, the latter known as “the old evidence problem”. Furthermore, the causal theory provides a solution to the old evidence problem that avoids serious problems faced by some other solutions. Ultimately, the causal theory of confirmation subsumes orthodox Bayesian theory as a special-case application to non-extreme credences.

Simpson’s paradox (SP) is a statistical phenomenon where the association between two variables reverses, disappears, or emerges, after conditioning on a third variable. It has been proposed (by, e.g., Judea Pearl) that SP should be analyzed using the framework of graphical causal models (i.e., causal DAGs) in which SP is diagnosed as a symptom of confounding bias. This paper contends that this confounding-based analysis cannot fully capture SP: there are cases of SP that cannot be explained away in terms of confounding. Previous works have argued that some cases of SP do not require causal analysis at all. Despite being a logically valid counterexample, we argue that this type of cases poses only a limited challenge to Pearl’s analysis of SP. In our view, a more powerful challenge to Pearl comes from cases of SP that do require causal analysis but can arise without confounding. We demonstrate with examples that accidental associations due to genetic drift, the use of inappropriate aggregate variables as causes, and interactions between units (i.e., inter-unit causation) can all give rise to SP of this type. The discussion is also extended to the amalgamation paradox (of which SP is a special form) which can occur due to the use of non-collapsible association measures, in the absence of confounding.