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implement a new sampling parameters: mu_2

This MR implements a new sampling parameter \mu_2, a combination of Post-Newtonian coefficients introduced by This can be used instead of \chi_1.

In this implementation, the prior is decomposed as \pi(\mathcal{M}, q, \mu_2, \chi_2) = \pi (\mu_2|\mathcal{M}, q, \chi_2) \pi(\mathcal{M}, q, \chi_2), and \pi (\mu_2|\mathcal{M}, q, \chi_2) is implemented by using ConditionalPrior. Since \mu_2 is a linear combination of \chi_1, it is reduced to \chi_1 prior with linear transformation from \mu_2 to \chi_1.

This MR does the following:

  • bilby/gw/ implement conversion function from \mu_2 to \chi_1
  • bilby/gw/ implement conditional prior of \mu_2, and conditional prior of \chi_{1,\perp} conditioned on \mu_2

Here are auto-correlation plots from bilby-mcmc: without mu_2 and with mu_2, which were generated by this script.

This will be prototype of !1162, as this does not implement \mu_1.

Edited by Soichiro Morisaki

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