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We propose a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this article is restricted to metric-based diagnosis under two settings: assessing local and global robustness in Bayesian procedures to perturbations of the likelihood and prior, and identification of influential observations. The approach is based on the square-root representation of densitiesarXiv:1403.5150v2 fatcat:uzslpsdjy5cuni5gug4foz6sbu