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 […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 706 other followers