  A recommender system based on ranks is proposed, where an expert's ranking of
a set of objects and a user's ranking of a subset of those objects are combined
to make a prediction of the user's ranking of all objects. The rankings are
assumed to be induced by latent continuous variables corresponding to the
grades assigned by the expert and the user to the objects. The dependence
between the expert and user grades is modelled by a copula in some parametric
family. Given a prior distribution on the copula parameter, the user's complete
ranking is predicted by the mode of the posterior predictive distribution of
the user's complete ranking conditional on the expert's complete and the user's
incomplete rankings. Various Markov chain Monte-Carlo algorithms are proposed
to approximate the predictive distribution or only its mode. The predictive
distribution can be obtained exactly for the Farlie-Gumbel-Morgenstern copula
family, providing a benchmark for the approximation accuracy of the algorithms.
The method is applied to the MovieLens 100k dataset with a Gaussian copula
modelling dependence between the expert's and user's grades.
