  The use of flat or weakly informative priors is popular due to the objective
a priori belief in the absence of strong prior information. In the case of the
Weibull model the improper uniform, equal parameter gamma and joint Jeffrey's
priors for the shape parameter are popular choices. The effects and behaviors
of these priors have yet to be established from a modeling viewpoint,
especially their ability to reduce to the simpler exponential model. In this
work we propose a new principled prior for the shape parameter of the Weibull
model, originating from a prior on the distance function, and advocate this new
prior as a principled choice in the absence of strong prior information. This
new prior can then be used in models with a Weibull modeling component, like
competing risks, joint and spatial models, to mention a few. This prior is
available in the R-INLA for use, and is applied in a joint
longitudinal-survival model framework using the INLA method.
