The Savage-Dickey ratio is known as a specialised representation of the Bayes factor (O'Hagan and Forster, 2004) that allows for a functional plugging approximation of this quantity. We demonstrate here that the Savage-Dickey representation is in fact a generic representation of the Bayes factor that relies on specific measure-theoretic versions of the densities involved in the ratio, instead of a special identity imposing the above constraints on the prior distributions. We completely clarify the measure-theoretic foundations of the representation as well as the generalisation of Verdinelli and Wasserman (1995) and propose a comparison of this new approximation with their version, as well as with bridge sampling and Chib's approaches.
- Pub Date:
- October 2009
- Mathematics - Statistics Theory;
- Mathematics - Probability;
- Statistics - Computation
- Accepted version of the paper to appear in the Electronic Journal of Statistics, 9 pages, one figure