Nonparametric priors with full-range borrowing of information

Modelling of the dependence structure across heterogeneous data is crucial for Bayesian inference, since it directly impacts the borrowing of information. Despite extensive advances over the past two decades, most available methods only allow for nonnegative correlations. We derive a new class of dependent nonparametric priors that can induce correlations of any sign, thus introducing a new and more flexible idea of borrowing of information. This is achieved thanks to a novel concept, which we term hyper-tie, and represents a direct and simple measure of dependence.We investigate prior and posterior distributional properties of the model and develop algorithms to perform posterior inference. Illustrative examples on simulated and real data showthat the proposed method outperforms alternatives in terms of prediction and clustering.