We conduct the first full Bayesian inference analysis for LISA parameter estimation incorporating the effects of subdominant harmonics and spin precession through a full time domain response. The substantial computational demands of using time domain waveforms for LISA are significantly mitigated by a novel Python implementation of the IMRPhenomT family of waveform models and the LISA response with GPU acceleration. This time domain response alleviates the theoretical necessity of developing specific transfer functions to approximate the LISA response in the Fourier domain for each specific type of systems and allows for the use of unequal-arms configurations and realistic LISA orbits. Our analysis includes a series of zero-noise injections for a massive black hole binary with aligned and precessing spins. We investigate the impact of including subdominant harmonics, compare equal and unequal-arm configurations, and analyze different time-delay-interferometry (TDI) configurations. We utilize full and uniform priors, with a lower frequency cutoff of 0.1 mHz, and a signal duration of approximately two months, sampled every 5 seconds. The sampler is initialized based on Fisher’s estimates. Our results demonstrate LISA’s capability to measure the two spin magnitudes and the primary spin tilt angle, alongside sky localization, with percent-level precision, while component masses are determined with subpercent accuracy.

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• Gravitational waves
• Astronomical black holes