A Generalized Savage-Dickey Ratio

Abstract

In this brief research note I present a generalized version of the Savage-Dickey Density Ratio for representation of the Bayes factor (or marginal likelihood ratio) of nested statistical models; the new version takes the form of a Radon-Nikodym derivative and is thus applicable to a wider family of probability spaces than the original (restricted to those admitting an ordinary Lebesgue density). A derivation is given following the measure-theoretic construction of Marin & Robert (2010), and the equivalent estimator is demonstrated in application to a distributional modeling problem.