  Prior sensitivity examination plays an important role in applied Bayesian
analyses. This is especially true for Bayesian hierarchical models, where
interpretability of the parameters within deeper layers in the hierarchy
becomes challenging. In addition, lack of information together with
identifiability issues may imply that the prior distributions for such models
have an undesired influence on the posterior inference. Despite its relevance,
informal approaches to prior sensitivity analysis are currently used. They
require repetitive re-runs of the model with ad-hoc modified base prior
parameter values. Other formal approaches to prior sensitivity analysis suffer
from a lack of popularity in practice, mainly due to their high computational
cost and absence of software implementation. We propose a novel formal approach
to prior sensitivity analysis which is fast and accurate. It quantifies
sensitivity without the need for a model re-run. We develop a ready-to-use
priorSens package in R for routine prior sensitivity investigation by R-INLA.
Throughout a series of examples we show how our approach can be used to detect
high prior sensitivities of some parameters as well as identifiability issues
in possibly over-parametrized Bayesian hierarchical models.
