Bayesian transfer function fitting for gravitational-wave detector calibration

Underpinning all gravitational-wave observations made by the LIGO-Virgo-KAGRA Scientific Collaboration is the requirement for accurate calibration of each detector’s response. This relies on in-situ measurements and accurate fitting of the different components of the feedback control loop — including the associated uncertainty. Previous methods for inferring a detector’s transfer function relied on reconstructing the transfer function in multiple steps which loses implicit correlations present in the model and obfuscates the construction of the inferred transfer functions. Here, we present a Bayesian framework for this analysis using a Gaussian process likelihood to simultaneously infer the agnostically modeled transfer function and the underlying noise process. We demonstrate its utility for gravitational-wave detector calibration for previous and upcoming observational science periods of instrument operation.