Gravitational-wave (GW) ringdown signals from black holes encode crucial information about the gravitational dynamics in the strong-field regime, which offers unique insights into the properties of black holes. Improving the sensitivity of GW detectors will enable the extraction of several quasi-normal modes from ringdown signals. However, incorporating several modes drastically enlarges the parameter space, posing computational challenges to data analysis. Inspired by the \({\mathcal{F}}\) -statistic method in the continuous GW searches, here we develop an algorithm that enhances the parameter-marginalization scheme, dubbed FIREFLY, which is tailored for accelerating the ringdown signal analysis. FIREFLY analytically marginalizes the amplitude and phase parameters of quasi-normal modes to reduce the computational cost and to speed up the standard Bayesian inference with full parameters from hours to minutes while achieving consistent posterior and evidence. The acceleration becomes more pronounced when more quasi-normal modes are considered. Rigorously based on Bayesian inference and importance sampling, our method is statistically interpretable, flexible in prior choice and compatible with various advanced sampling techniques and, thus, provides a new perspective for accelerating future GW data analysis.
