On resolving the SavageDickey paradox
Abstract
The SavageDickey 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 SavageDickey representation is in fact a generic representation of the Bayes factor that relies on specific measuretheoretic 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 measuretheoretic 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2009
 DOI:
 10.48550/arXiv.0910.1452
 arXiv:
 arXiv:0910.1452
 Bibcode:
 2009arXiv0910.1452M
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability;
 Statistics  Computation
 EPrint:
 Accepted version of the paper to appear in the Electronic Journal of Statistics, 9 pages, one figure