Detecting and diagnosing prior and likelihood sensitivity with power-scaling

Determining the sensitivity of the posterior to perturbations of the prior and likelihood is an important part of the Bayesian workflow. We introduce a practical and computationally efficient sensitivity analysis approach using importance sampling to estimate properties of posteriors resulting from power-scaling the prior or likelihood. On this basis, we suggest a diagnostic that can indicate the presence of prior-data conflict or likelihood noninformativity and discuss limitations to the power-scaling approach. The approach can be easily included in Bayesian workflows with minimal effort by the model builder and we present an implementation in our new R package \texttt{priorsense}. We further demonstrate the workflow on case studies of real data using models varying in complexity from simple linear models to Gaussian process models.