Nonparametric priors with full-range borrowing of information

TL;DR

This paper introduces a new class of nonparametric priors that allow for flexible dependence modeling with correlations of any sign, enhancing Bayesian inference by enabling more nuanced borrowing of information.

Contribution

The authors develop a novel hyper-tie concept to induce arbitrary correlation signs in nonparametric priors, expanding the flexibility of dependence modeling in Bayesian analysis.

Findings

Outperforms existing methods in prediction accuracy.

Provides effective clustering on simulated and real data.

Ensures desirable prior and posterior properties.

Abstract

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.