On combining information from multiple gravitational wave sources
In the coming years, advanced gravitational wave detectors will observe signals from a large number of compact binary coalescences. The majority of these signals will be relatively weak, making the precision measurement of subtle effects, such as deviations from general relativity, challenging in the individual events. However, many weak observations can be combined into precise inferences, if information from the individual signals is combined in an appropriate way. In this study we revisit common methods for combining multiple gravitational wave observations to test general relativity, namely (i) multiplying the individual likelihoods of beyond-general-relativity parameters and (ii) multiplying the Bayes factor in favor of general relativity from each event. We discuss both methods and show that they make stringent assumptions about the modified theory of gravity they test. In particular, the former assumes that all events share the same beyond-general-relativity parameter, while the latter assumes that the theory of gravity has a new unrelated parameter for each detection. We show that each method can fail to detect deviations from general relativity when the modified theory being tested violates these assumptions. We argue that these two methods are the extreme limits of a more generic framework of hierarchical inference on hyperparameters that characterize the underlying distribution of single-event parameters. We illustrate our conclusions first using a simple model of Gaussian likelihoods and also by applying parameter estimation techniques to a simulated dataset of gravitational waveforms in a model where the graviton is massive. We argue that combining information from multiple sources requires explicit assumptions that make the results inherently model dependent.
© 2019 American Physical Society. Received 1 April 2019; published 25 June 2019. We thank Will Farr, Max Isi, Walter Del Pozzo, and Salvatore Vitale for helpful discussions. We are grateful for computational resources provided by Cardiff University, and funded by an STFC grant supporting UK Involvement in the Operation of Advanced LIGO. C.-J. H. acknowledges support of the MIT physics department through the Solomon Buchsbaum Research Fund, the National Science Foundation, and the LIGO Laboratory. The Flatiron Institute is supported by the Simons Foundation. This is LIGO Document No. P1900098.
Accepted Version - 1903.11008.pdf
Published - PhysRevD.99.124044.pdf