This paper describes an approach to Bayesian sensitivity analysis that uses an influence statistic and an outlier statistic to assess the sensitivity of a model to perturbations. The basic outlier statistic is a Bayes factor, whereas the influence statistic depends strongly on the purpose of the analysis. The task of influence analysis is aided by having an interpretable influence statistic. Two alternative divergences, an L  ₁-distance and a χ²-divergence, are proposed and shown to be interpretable. The Bayes factor and the proposed influence measures are shown to be summaries of the posterior of a perturbation function.