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arXiv · 0910.1452

On resolving the Savage-Dickey paradox

Jean-Michel Marin·Christian Robert
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Abstract

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.

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Jean-Michel Marin, Christian Robert. 2009-10-08. On resolving the Savage-Dickey paradox. https://doi.org/10.1214/10-ejs564

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