A Nearest Neighbors Quadrature for Posterior Approximation via Adaptive Sequential Design

We introduce a novel adaptive quadrature scheme based on a Nearest Neighbors (NN) approach and a sequential design procedure. The nodes of the quadrature are adaptively chosen by maximizing a suitable acquisition function. The proposed method is a powerful tool for the integration and emulation of complex posterior distributions. Numerical results show the advantage of the proposed approach with respect to Markov Chain Monte Carlo (MCMC) and importance sampling algorithms.