Normal Approximate Likelihoods for Gravitational Wave Events*

Gravitational-Wave population inference depends upon accurate and fast evaluations of the likelihood function for each detected observation. Typical likelihood interpolation and kernel density estimation relies upon cumbersome accounting with the many posterior samples available publicly from the Gravitational-Wave Transient Catalog. The Multivariate Normal approximation has been shown to meet those needs, but inferring μ and Σ directly from the mean and covariance of the samples introduces a bias in symmetric mass ratio on the order of a standard deviation away from equal mass. We provide a method for obtaining these fit parameters in a way which avoids introducing bias caused by edge effects. Our publicly available results offer an efficient and unbiased set of likelihood functions for each gravitational-wave detection. We demonstrate the utility of our approach with selected applications.