Astrophysical population modelling for gravitational waves with the ability to probe narrow population features over bounded domains.

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.

To use this package you can use pip:

pip install gravpop