Description
We have implemented priors to sample in the aligned and planar components of spins rather than magnitude and tilt using the usual uniform in magnitude and tilt prior distribution. This can be beneficial as the likelihood is closer to orthogonal in these parameters.
See the attached pdf for a demonstration of equivalence.
Reviewer statement
The notebook above tests the implementation of a conditional prior for the in-plane component of the spins. It does this is two ways--firstly, samples are drawn directly from the prior, testing the inverse sampling from the CDF, and secondly drawn sampling a ZeroLikelihood, testing the PDF. In both cases, the samples drawn from this new prior are statistically identical to those drawn from the 'usual' uniform in magnitude and tilt prior distribution (as determined by a KS-test).
Simon Stevenson 29/03/23