WIP: More correct low-rank expansion of powerlaw noise #1877
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The existing low-rank expansions for red noise and related processes are based on the Lentati et al. (2014) expansion which uses a diagonal prior for frequency modes at 1/T. This is only approximately correct when fitting for quadratic spindown. For DM variations, which use the same model, contemporary analyses now consequently also include a DM2 term to "make the analysis work". DM2 is not necessarily physical when doing a fully unconstrained fit, so it is more correct to let this term be modeled by the stochastic process.
A low-rank expansion with frequencies below 1/T can improve the expansion while keeping the prior matrix diagonal. This is explored in van Haasteren & Vallisneri (2014): https://doi.org/10.1093/mnras/stu2157
This PR implements that model. Note that newer and more accurate expansions are in development that have a nondiagonal prior matrix. The design idea is that the models in this PR will also be implemented as part of the Classes in this PR: they represent the same model, namely a correct powerlaw. The Lentati expansion is a physically different model with spectral leakage explicitly not present, so that is different.