More correct low-rank expansion of powerlaw noise #1877
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I will merge in changes from #1762 , as those changes overlap with this one. I will get rid of the low-frequency cut-off, and instead use the corner frequency as in #1762 by @abhisrkckl |
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Hi... can you please merge #1896 again? I just figured out that my fix was not general enough. I have updated the PR to address this. |
I thought I had already just a few minutes ago. I did get an updated Changelog though, so it should be current now |
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Please add a test that simulates TOAs using the newly added parameters. |
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@abhisrkckl , in EDIT: There is one test I can think of that makes sense. To compare the covariance matrix you get from the red noise process. In principle we can compare it to an analytical powerlaw. However, the low-frequency cut-off is hard to assign to log-spaced frequency bins. My recommendation is to not do this test for powerlaw signals. For other types of kernels it's more doable. Here, I think the above tests are good enough |
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Hold off on this until we verify with Mike |
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Mike and I agreed to do this the same in PINT and Tempo2. The tempo2 PR is here: https://bitbucket.org/psrsoft/tempo2/pull-requests/93 So they are consistent. I think it's good to go like this @abhisrkckl |
Has a dependency on #1896
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.
We have coordinated with the tempo2 devs, and the additional parameters are:
The FLOG parameters dictate how many log-frequency-spaced extra bins we need below 1/T. The _FACTOR parameters dictate by what fraction the frequency needs to shrink every frequency bin. So setting both to 2 will lead to two new frequency bins: 1/(2T) and 1/(4T)