A possible first step is to use the chirp mass, but we can do better: Roulet+2022 describe a full parametrization for the waveform, starting from $\mathcal{M}$ and $\log q$ but also including distance and angles, such that the posterior is way more Gaussian. Their parametrization is publically available here.
We could perform derivatives according to these new parameters, get a Fisher-based covariance matrix in these variables, sample from it, perform the inverse transformation, and finally apply priors.
A possible first step is to use the chirp mass, but we can do better: Roulet+2022 describe a full parametrization for the waveform, starting from $\mathcal{M}$ and $\log q$ but also including distance and angles, such that the posterior is way more Gaussian. Their parametrization is publically available here.
We could perform derivatives according to these new parameters, get a Fisher-based covariance matrix in these variables, sample from it, perform the inverse transformation, and finally apply priors.