gravpop 0.1.1

Package to perform astrophysical population modelling using gravitational waves,

gravpop

This library allows one to perform a gravitational wave population analysis, (Hussain et al., Thrane et al.) that allows exploration of population features even in narrow regions near the edges of a bounded domain.

Feel free to jump to the tutorial here

The approach splits parameter space into two sectors:

• An analytic sector ($\theta^a$), where the population model is represented as a weighted sum of multivariate truncated normal distributions, allowing for an analytical computation of the population likelihood.
• A sampled sector ($\theta^s$), which accommodates more general population models and utilizes Monte Carlo estimates of the population likelihood.

This technique represents posterior samples using a truncated Gaussian mixture model (TGMM), where the population likelihood, $p(x)$, is expressed as a sum of truncated multivariate Gaussian components:

$$ p(x) = \sum_k w_k , \phi_{[a,b]}(x \mid \mu_k, \Sigma_k). $$

This form of the posterior allows analytic evaluation in the analytic sector, and falls back to using Monte-Carlo based estimation in the sampled sector.

For implementing the Truncated Gaussian Mixture Model fit, see truncatedgaussianmixtures, a package designed to fit data to mixtures of truncated Gaussians.