Making Bayesian gravitational-wave inference faster
Bayesian parameter estimation for gravitational-wave signals repeatedly evaluates a likelihood over a high-dimensional parameter space. For compact binaries, the expensive part is usually not the statistical formalism itself but the repeated evaluation of waveform-dependent frequency-domain inner products.
A large fraction of this work is redundant.
Nearby waveforms are strongly correlated, and the quantities entering the likelihood vary much more smoothly across frequency than the raw waveform phase might suggest. Fast inference methods exploit this structure rather than evaluating every likelihood on the full native frequency grid.
Several complementary strategies are possible. Relative binning represents the ratio between nearby waveforms using a much coarser frequency grid. Meshfree methods interpolate quantities entering the likelihood across intrinsic parameter space. Adaptive grids place frequency samples according to the local variation of the waveform rather than at every Fourier frequency.
These methods are particularly important for next-generation detectors. Lowering the starting frequency from tens of hertz to a few hertz greatly increases the signal duration and the number of Fourier samples. A method that is inexpensive for a current-detector binary-neutron-star signal can otherwise become prohibitively costly.
The aim is therefore not to approximate the posterior after the fact, but to reorganize the likelihood calculation so that the expensive information is computed once and reused efficiently throughout the inference.
Papers from our work on fast inference
L. Pathak, A. Reza and A. S. Sengupta, Fast likelihood evaluation using meshfree approximations for reconstructing compact binary sources.
The original meshfree likelihood construction.L. Pathak, S. Munishwar, A. Reza and A. S. Sengupta, Prompt sky localization of compact binary sources using a meshfree approximation.
Extension to coherent network inference and rapid sky localization.A. Sharma, A. S. Sengupta and S. Mukherjee, Accelerated parameter estimation of supermassive black hole binaries in LISA using a meshfree approximation.
Extension of the meshfree approach to LISA.A. Sharma, L. Pathak, S. Roy and A. S. Sengupta, Rapid parameter estimation with the full symphony of compact binary mergers using meshfree approximation.
Extension to richer compact-binary waveform structure, including higher modes.