Fast LISA Likelihood Approximations by Downsampling

The Laser Interferometer Space Antenna (LISA) is due to launch in the mid-2030s. A key challenge for LISA data analysis is efficient Bayesian inference with parametrised gravitational-wave models, particularly for early inspirals of low- and intermediate-mass black-hole binaries, where time series can contain $\sim 10^8$-$10^9$ samples and naive likelihood evaluations become prohibitively expensive. For purely simulated studies, we present a simple time-domain likelihood-approximation scheme for such signals. The method retains only a small subset of samples and defines a modified noise-weighted inner product on this reduced set that closely reproduces the original inner product on the waveform manifold. Because this alters the effective noise model, the scheme is intended for simulated LISA data rather than direct analysis of real LISA data. In our examples, the resulting posteriors agree to high accuracy with those obtained using much denser sampling, while retaining only $10^3$-$10^4$ samples. The computational cost then scales linearly with the number of retained samples $N_s$, so the speed-up is roughly $N/N_s$, where $N$ is the original data length; for realistic LISA-like datasets with $N\sim10^8$-$10^9$ this would correspond to gains of order $10^4$-$10^6$ over straightforward frequency-domain likelihood evaluations of the full dataset. The time-domain formulation is particularly convenient for incorporating waveform modifications from non-trivial astrophysical environments or alternative-gravity effects. The results presented here provide the theoretical basis for the software package \texttt{Dolfen}.