  Modeling of the dependence structure across heterogeneous data is crucial for
Bayesian inference since it directly impacts the borrowing of information.
Despite the extensive advances over the last two decades, most available
proposals allow only for non-negative 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 show that
our proposal outperforms alternatives in terms of prediction and clustering.
