Scope of Jaynes analysis/Bayesian formalism

[jscargle]

Your reference to Jaynes (1987) implies that he discussed the Lomb-Scargle periodogram. I don't think he knew about this particular algorithm, but was remarking more generally on least-squares fits to sinusoids.

Also, I wonder if you considered and rejected a fully Bayesian formalism for the problem you address in this paper? In http://arxiv.org/abs/math/0111127 I tried to demonstrate a generic link between frequentist statistics such as the periodogram and the Bayesian posterior for a corresponding quantity (in the spirit of Larry Bretthorst's power spectrum analysis: Bretthorst, G. Larry, 1988, Bayesian Spectrum Analysis and Parameter Estimation, Lecture Notes in Statistics, Springer-Verlag, No. 48; http://bayes.wustl.edu/). I don't know how universal it is, but a connection of the form

                       P( a ) ~ exp[ - C(a) / error variance ]  

seems to pop up a lot. C(a) can be an auto- or cross-correlation function; or a power spectrum or a cross-power spectrum, corresponding to a being a time lag or the frequency of a sinusoidal component. Then the expedient of simply multiplying posteriors (for independent quantities) might be useful in the multi band context. If nothing else this might lead to a more rigorous "Occam factor" regularization.