Varaha: A promising sampler for obtaining gravitational wave posteriors

Nested sampling is often used in Bayesian statistics problems in astronomy. It operates with a set of live points, iteratively replacing the point with the lowest likelihood with a new point of higher likelihood. Each iteration reduces the enclosed volume by a known factor. The estimated sampling density and the likelihood values of both new and old live points quantify the enclosed probability mass. Although robust, nested sampling often discards a majority of the sampled points ($\sim 99.9\%$) at which likelihood was calculated. Here, we present an efficient method to explicitly calculate the sampling density for small dimensional problems~(ten or less), thereby removing the need to discard samples. The points' sampling density and likelihood values constitute the posterior distribution. We build on the existing version of the sampler Varaha and present an alternate version that is significantly more efficient for expensive likelihoods. These samplers specifically focus on obtaining compact binary parameters from their gravitational wave signals. They provide a viable alternative to nested sampling when the full fifteen-dimensional space is sampled separately for observer-dependent parameters and parameters intrinsic to the binary.