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[rodluger]

It is the nature of modern theoretical work to re-discover known results in different contexts. In this case, you may see that marginalizing the likelihood over a linear model with Gaussian prior is discussed in Sec. 2.7 of Rasmussen and Williams, which you cite for the basic GP likelihood. Indeed, according to that section, the idea originated in the 70s with Blight, Ott, and O'Hagan. For once, statisticians had a result ready made for astronomers, so they will be happy if you acknowledge them.

We have been ourselves using this marginalization to great profit in pulsar-timing-array GW searches (see 2014PhRvD..90j4012V for a review of Gaussian-process techniques for pulsar timing), precisely because it allows significant numerical optimizations in describing time-correlated noise processes as low-rank sums over small bases. You may also enjoy 2015MNRAS.446.1170V for related tricks.

[dfm]

Also: from Yuri Levin:

http://adsabs.harvard.edu/abs/2013MNRAS.428.1147V Section 3.2 and Appendix B http://adsabs.harvard.edu/abs/2009MNRAS.395.1005V also section 3.2

[davidwhogg]

Also ack the people who wrote us.