Extension of the univariate PC Prior

In the present paper, we describe and explore new methods for constructing joint penalised complexity prior distributions, PC priors hereafter, on the additive model components that build up a more flexible model starting from a base model which would not include those components. Although, an extension to the multivariate case has been already proposed, it is difficult to handle, especially in high-dimensional problems. So, we need something more manageable, particularly for computational purposes. We propose two different constructions of the multivariate PC prior, one based on the conditional PC prior distributions via the Hammersley-Clifford theorem, the other one based on the marginal PC prior distributions by means of a copula approach.