  We propose a geometric framework to assess global sensitivity in Bayesian
nonparametric models for density estimation. We study sensitivity of
nonparametric Bayesian models for density estimation, based on Dirichlet-type
priors, to perturbations of either the precision parameter or the base
probability measure. To quantify the different effects of the perturbations of
the parameters and hyperparameters in these models on the posterior, we define
three geometrically-motivated global sensitivity measures based on geodesic
paths and distances computed under the nonparametric Fisher-Rao Riemannian
metric on the space of densities, applied to posterior samples of densities:
(1) the Fisher-Rao distance between density averages of posterior samples, (2)
the log-ratio of Karcher variances of posterior samples, and (3) the norm of
the difference of scaled cumulative eigenvalues of empirical covariance
operators obtained from posterior samples. We validate our approach using
multiple simulation studies, and consider the problem of sensitivity analysis
for Bayesian density estimation models in the context of three real datasets
that have previously been studied.
