A sensitivity analysis for Bayesian nonparametric density estimators

Bayesian nonparametric methods have recently gained popularity in the context of density estimation. In particular, the density estimator arising from the mixture of Dirichlet process is now commonly exploited in practice. In this paper we perform a sensitivity analysis for a wide class of Bayesian nonparametric density estimators including the mixture of Dirichlet process and the recently proposed mixture of normalized inverse Gaussian process. Whereas previous studies focused only on the tuning of prior parameters, our approach consists of perturbing the prior itself by means of a suitable function. In order to carry out the sensitivity analysis we derive representations for posterior quantities and develop an algorithm for drawing samples from mixtures with a perturbed nonparametric component. Our results bring out some clear evidence for Bayesian nonparametric density estimators, and we provide an heuristic explanation for the neutralization of the perturbation in the posterior distribution.