gwinferno.preprocess.priors.chi_p_prior_given_chi_eff_q#

chi_p_prior_given_chi_eff_q(chi_p, chi_eff, q, a_max=1.0, ndraws=10000, bw_method='scott')[source]#

Calculate the prior density for effective precession conditioned on effective spin and mass ratio, \(p(\chi_\mathrm{p}\mid \chi_\mathrm{eff}, q)\), corresponding to uniform and isotropic component spin priors.

The prior density is computed numerically by:

  1. drawing random component spins and tilts,

  2. computing the corresponding effective precession values,

  3. training a kernel density estimate (KDE),

  4. building an interpolant using the KDE’s density evaluated over a grid.

Parameters:
chi_pfloat, array-like

Effective precession value at which to compute the prior density.

chi_efffloat

Effective spin value to condition on.

qfloat

Mass ratio value to condition on. Expected convention \(q<1\).

a_maxfloat, default=1.0

Maximum allowed dimensionless component spin magnitude.

ndrawsint, default=10000

Number of draws from the component spin priors used to train KDE.

**kwargs: dict, optional

Keyword arguments to pass to chi_p_prior_given_chi_eff_q().

Returns:
array-like

Prior density at given effective precession value.

See also

joint_prior_from_isotropic_spins

Notes

This can be `np.vectorize`ed for convenience, but it can become _painfully_ slow, especially when operating near boundaries where monte-carlo sampling of tilts results in frequent unphysical spins (e.g., extremal effective spins).