I discussed with Perez-Giz and with Foreman-Mackey the creation of quasi-periodic oscillator Gaussian Process models for stars. We want to start by fitting with a damped simple harmonic oscillator kicked by a white-noise source (this has an exact solution as a Gaussian Process, worked out by Goodman and I am sure many others before him). We then want to evolve to non-harmonic oscillators that are better at modeling pulsating stars, but still with tunable incoherence. Applications include: Making the study of quasi-periodic oscillations in compact objects more probabilistic, and more faithful and complete searches for RR Lyrae stars. One problem is that you can't arbitrarily modify your covariance function (kernel function) and obey the rule that it must construct only positive definite variance tensors. I don't really see how to deal with that problem in a simple way, since there is no simple test one can apply to a kernel function that tells you whether or not it is permitted.
Sometimes it helps to look at the problem as one of choosing an SPDE that does what you want, then figuring out what Gaussian process it corresponds to afterwards. https://www.birs.ca/events/2012/5-day-workshops/12w5023
ReplyDeletehttp://www.math.ntnu.no/inla/r-inla.org/papers/spde-jrssb-revised.pdf
Here is a paper on a similar subject, recently submitted: http://lanl.arxiv.org/abs/1402.5978
ReplyDeleteBrandon Kelly knows what's up, you should talk to him.
ReplyDeleteNeil Lawrence's group has been doing stuff that sounds related for several years:
ReplyDeletehttp://ml.sheffield.ac.uk/~neil/cgi-bin/publications/bibpage.cgi?keyName=Alvarez:llfm13&printAbstract=1
http://ml.sheffield.ac.uk/~neil/cgi-bin/publications/bibpage.cgi?keyName=Alvarez:lfm09&printAbstract=1