# implement a new sampling parameters: mu_2

This MR implements a new sampling parameter `\mu_2`

, a combination of Post-Newtonian coefficients introduced by https://arxiv.org/abs/2203.05216. 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/conversion.py: implement conversion function from
`\mu_2`

to`\chi_1`

- bilby/gw/prior.py: 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`

.