Efficiently Parameterizing Gravitational Waveform Uncertainty for Marginalization

Gravitational waves have intrinsic uncertainties between the true waveform we detect from space and the waveform models, or waveform approximants, we use for parameter estimation. These uncertainties can be quantified in amplitude and phase, δA and δφ. We want to examine the effect they have on the posterior data of the parameter estimation: how much does waveform uncertainty matter? This can be achieved by marginalizing over a large set of potential waveform uncertainties after the parameter estimation process. To do so, we need an efficient method of generating waveform uncertainty data and accessing it. This process is typically long and inefficient, as multiple generated waveforms are needed for each possible set of source parameters. For example, for a GW170817 posterior this takes between 10 and 20 minutes to complete. We wanted a way to store this uncertainty data in a file, where it can be easily accessed to greatly reduce the amount of time it takes to generate a dataset for our needs. The solution was to parameterize the waveform uncertainty. Rather than expressing each draw of waveform uncertainty as a fixed set of hundreds of thousands of points, each one was expressed as 15 parameters. These parameters were then used to interpolate the waveform uncertainty over any number of frequency points in a matter of seconds, improving the efficiency of generating the waveform uncertainty data to be marginalized over.