Detecting and diagnosing prior and likelihood sensitivity with power-scaling
Noa Kallioinen, Topi Paananen, Paul‐Christian Bürkner, Aki Vehtari
Abstract
Abstract 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 this 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 . We further demonstrate the workflow on case studies of real data using models varying in complexity from simple linear models to Gaussian process models.