A tool for assessing weak identifiability of statistical models

The notion of identifiability has a long history in the statistical literature, with econo- metrics providing the first theoretical contributions. On the one hand, within the frequentist paradigm, identifiability represents a critical issue to tackle, closely tied to the feasibility of the model estimation. On the other hand, identifiability issues in the Bayesian frame- work could be overcome by complementing the non-identifiable likelihood with additional prior beliefs summarized via an informative prior distribution. Unfortunately, since esti- mation is still feasible, unidentifiabily may remain unnoticed and silently hinder posterior consistency. This contribution provides a tool to inspect whether the model specification is weakly identified. Our procedure is based on estimating the intrinsic dimension of posterior samples. The methodology is illustrated with a simulated example.