UCLA

We introduce the relative distribution as a tool in Bayesian analysis to compare the posteriorto the prior distribution. Two interpretations are given: one as a density ratio, and another as a reparametrized likelihood. Several important properties are reviewed, as well as notes on usage and connections to information theory and relative surprise inference. Explicit examples and derivations for several common models are given. The relative distribution focuses on the effect of the data and the resulting differences between the posterior and prior, emphasizing the role of the likelihood in connecting the two.