Towards a Bayesian Decision Theoretic Analysis of Contextual Effect Modifiers

Relevance measures based on parametric and structural properties of Bayesian networks can be utilized to characterize predictors and their interactions. The advantage of the Bayesian framework is that it allows a detailed view of parametric and structural aspects of relevance for domain experts. We discuss two particularly challenging scenarios from psycho-genetic studies, (1) the analysis of weak effects, and (2) the analysis of contextual relevance, where a factor has a negligible main effect and it modifies an effect of another factor only in a given subpopulation. To cope with this challenge, we investigate the formalization of expert intuitions and preferences from the exploratory data analysis phase. We propose formal losses for these two scenarios. We introduce and evaluate a Bayesian effect size measure using an artificial data set related to a genetic association study, and real data from a psycho-genetic study.

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