Specification of Informative Prior Distributions for Multinomial Models Using Vine Copulas

Abstract

We consider the specification of an informative prior distribution for the probabilities in a multinomial model. We utilise vine copulas: flexible multivariate distributions built using bivariate copulas stacked in a tree structure. We take advantage of a specific vine structure, called a D-vine, to separate the specification of the multivariate prior distribution into that of marginal distributions for the probabilities and parameter values for the bivariate copulas in the vine. We provide guidance on each of the choices to be made in the prior specification and each of the questions to ask the expert to specify the model parameters within the context of an engineering application. We then give full details of the approach for the general problem.