  Probabilistic modeling is cyclical: we specify a model, infer its posterior,
and evaluate its performance. Evaluation drives the cycle, as we revise our
model based on how it performs. This requires a metric. Traditionally,
predictive accuracy prevails. Yet, predictive accuracy does not tell the whole
story. We propose to evaluate a model through posterior dispersion. The idea is
to analyze how each datapoint fares in relation to posterior uncertainty around
the hidden structure. We propose a family of posterior dispersion indices (PDI)
that capture this idea. A PDI identifies rich patterns of model mismatch in
three real data examples: voting preferences, supermarket shopping, and
population genetics.
