Ricerc@Sapienza

We study the penalised complexity priors and their applications in a Bayesian framework. For instance, some of the applications we are working on are related to the elicitation of the prior distribution for the shape parameter of univariate skew symmetric models; other applications concern copula modelling. In our project, we make use of a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. These proper penalising complexity priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisation, have a natural connection to Jeffreys' prior, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable.