## On the Savage-Dickey paradox

Following several posts on this topic, we eventually managed to write down a short note with Jean-Michel Marin, which is now posted on arXiv, waiting for a last round of polishing before being submitted to the Annals. My conclusion on this topic is that Dickey’s (1971) condition on the conditional prior under the alternative has no measure-theoretic meaning unless additional continuity conditions are imposed upon those priors, while the other choices of versions found in the derivation can be seen as imposing a representation of

$\dfrac{\pi(\theta|x)}{\pi(\theta)} \quad\text{and of}\quad\dfrac{\pi(\theta|x,\psi)}{\pi(\theta|\psi)}$

that holds everywhere instead of almost everywhere.

### 3 Responses to “On the Savage-Dickey paradox”

1. […] well-covered by Chen, Shao and Ibrahim. The Savage-Dickey approach unsurprisingly misses the difficulty with the representation (as well as the spelling for Isabella Verdinelli’s last name). The description of Carlin and […]

2. […] and Wasserman (1995). we have now completed (and rearXived) our rewriting of the paper on the Savage-Dickey paradox. And we eventually made the submission to the Annals of Statistics, with the hope that the mix of […]

3. […] of the posterior by the normal asymptotic approximation to the likelihood, as already shown in the entry on Savage-Dickey posted a few days […]

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