Bayesian measures of leverage and influence

Local sensitivity diagnostics for Bayesian models are described that are analogues of frequentist measures of leverage and influence. The diagnostics are simple to calculate using MCMC. A comparison between leverage and influence allows a general purpose definition of an outlier based on local perturbations. These outliers may indicate areas where the model does not fit well even if they do not influence model fit. The sensitivity diagnostics are closely related to predictive information criteria that are commonly used for Bayesian model choice. A diagnostic for prior-data conflict is proposed that may also be used to measure cross-conflict between different parts of the data.