While browsing this paper on astro ph today I noticed an amusing trend for gravitational wave astronomers (or particularly Neil Cornish’s group) to refer to the Savage-Dickey density ratio estimator as Savage-**Dicke** or Savage-**Dickie**, even while citing James Dickey’s original paper. I tried googling “Savage-Dicke” to see if it was in fact a common alternative spelling, but all I could find were German pornos (‘dicke’ = thick/fat) and the gravitational wave uses. Curious.

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I assume they* just have Robert Dicke, of Brans-Dicke fame, in their heads and are automatically associating any hyphenated theorem/method involving “Dicke”, “Dickie” or “Dickey” with that.

*as in those GW astronomers that have referred to Savage-Dickey, rather than GW astronomers as a whole of which I am one!

Interesting; that probably explains it! Thanks, Matt

I am always confused by the Savage-Dickey ratio. Some people say it is not a valid operation, but others use it without problems.

This is an interesting point: the standard derivation of the Savage-Dickey density ratio places an invalid restriction on the priors of the more complex model from a measure-theoretic perspective, but as Jean-Michael and Xian show in their paper ( http://arxiv.org/pdf/0910.1452.pdf ) it is easy enough to find appropriate constraints to re-derive the SDDR consistently from measure-theoretic perspective. At the end of the day it gives the same formula, but the value the derivation is that it reveals a sensible estimator for the SDDR to use in posterior sampling (e.g. from MCMC output). Importantly, this estimator avoids the first-order approximations used in astronomical implementations of the SDDR where some parametric density (like a Gaussian) is fit to the posterior samples.

FYI, I also have written down some thoughts on generalizing the SDDR for priors induced by stochastic processes: http://arxiv.org/pdf/1311.1292.pdf