ILE

As noted below about lalinference, gravitational wave astronomy begins with inference : figuring out what kind of astrophysical source was responsible for the implausible event in our data. One conventional, robust, and easily generalized approach is Markov Chain Monte Carlo, where detector data is serially compared with a sequence of proposed model waveforms. For any ``reasonable” way of choosing these sequences (i.e., for any reasonable “jump proposal”), due to detailed balance, random samples from Markov Chain Monte Carlo asymptotically converge in distribution to the posterior parameter distribution. Like any Markov Chain Monte Carlo analysis, the challenge for gravitational wave parameter estimation is efficiency, scalability, and confidence in one’s results, particularly given systematic errors and multiple secondary posterior maxima. Rapid and highly accurate parameter estimation is particularly important for:

• EM followup: Anyone wanting to point a telescope at a LIGO event immediately wants to know where to point and what to expect (e.g., binary black hole).

• Waveform systematics: When estimating source parameters of detected gravitational waves, the most accurate and comprehensive multimodal gravitational wave signal models are expensive to simulate and include.

In a recent work with colleagues from UWM, we proposed an alternative: the ILE architecture, short for integrate_likelihood_extrinsic. For each set of intrinsic parameters – the parameters which specify a physically distinct binary, like component masses and spins – our algorithm fully explores and properly weights all extrinsic parameters – the parameters like distance, source orientation, and sky locations, which only influence how the binary appears in our instruments. Critically, our approach employs brute-force Monte Carlo integration of a low-cost likelihood function, enabling rapid processing with controlled statistical errors, even for expensive-to-compute waveforms.

For experts : By carefully reorganizing and caching waveform calculations that are used to compute the likelihood, we can efficiently marginalize over all extrinsic parameters by brute-force Monte Carlo. To further accelerate convergence, we use an adaptive Monte Carlo scheme that exploits information from the search (for sky location) and explicitly marginalize in time. With extremely low cost per likelihood, our method provides a useful complement to reduced-order methods for nonprecessing systems. However, further investigations are needed to extend this approach to explore more intrinsic dimensions, notably spin precession.

For more information, see

• Pankow et al, A novel scheme for rapid parallel parameter estimation of gravitational waves from compact binary coalescences (PRD 92 3002; arxiv:1502.04370)