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Complex stochastic models represented by directed acyclic graphs (DAGs) areincreasingly employed to synthesise multiple, imperfect and disparate sourcesof evidence, to estimate quantities that are difficult to measure directly. Thevarious data sources are dependent on shared parameters and hence have thepotential to conflict with each other, as well as with the model. In a Bayesianframework, the model consists of three components: the prior distribution, theassumed form of the likelihood and structural assumptions. Any of thesecomponents may be incompatible with the observed data. The detection andquantification of such conflict and of data sources that are inconsistent witheach other is therefore a crucial component of the model criticism process. Wefirst review Bayesian model criticism, with a focus on conflict detection,before describing a general diagnostic for detecting and quantifying conflictbetween the evidence in different partitions of a DAG. The diagnostic is ap-value based on splitting the information contributing to inference about a"separator" node or group of nodes into two independent groups and testingwhether the two groups result in the same inference about the separatornode(s). We illustrate the method with three comprehensive examples: anevidence synthesis to estimate HIV prevalence; an evidence synthesis toestimate influenza case-severity; and a hierarchical growth model for ratweights.

Conflict Diagnostics in Directed Acyclic Graphs, with Applications in Bayesian Evidence Synthesis