Accurate and efficient simulation-based inference for massive black-hole binaries with LISA

Abstract

We develop an accurate simulation-based inference framework for high-mass ($\gtrsim\!10^7 \rm{M_\odot}$) black-hole binaries observable by LISA. The method is implemented within the DINGO gravitational-wave parameter-estimation code, extending its application from ground-based detectors to the LISA band. We train a normalizing-flow model using aligned-spin higher-mode waveform models and a low-frequency approximation of the detector response. After sampling, we importance-sample to the true posterior. We validate performance on simulated signals spanning the signal-to-noise regimes relevant for LISA observations and benchmark our new DINGO implementation against standard methods. We report robust agreement in the inferred posterior distributions up to signal-to-noise ratios of $\sim\!500$. At higher signal-to-noise ratios of $\sim\!1000$, we observe a reduction in sampling efficiency, while still yielding unbiased and tightly localized posteriors that can be used as a starting point for follow-up with traditional methods.The trained flow can generate 20 thousand posterior samples in less than a minute, establishing DINGO as a promising neural inference framework for rapid full-parameter estimation of massive black-hole binaries in the LISA band. The likelihood-free nature of this approach allows for straightforward generalizations, including a time-dependent detector response, non-stationary noise artifacts such as gaps and glitches, and low-latency parameter estimations.

Figures (6)

• Figure 1: Evolution of the training (green) and validation (teal) losses as a function of epoch. The drops at epochs $\sim$160, 220, 255, 275, and 360 are due to learning rate reductions triggered by the ReduceLROnPlateau scheduler 2019arXiv191201703P.
• Figure 2: Probability-probability ($p$--$p$) plot for 1000 simulated injections obtained with Dingo-IS. Colored curves show results for each of the 11 marginal distributions. The dashed line indicates a uniform distribution, and grey shaded regions denote the expected $1\sigma,\,2\sigma,\,3\sigma$ confidence intervals. KS test $p$-values are provided in the legend.
• Figure 3: Posterior distributions for our representative source with low SNR ($\sim 87$) obtained with different sampling methods. The lower left triangle compares results from Dingo (dark-blue filled contours) and Dingo-IS (dashed black contours), while the upper right triangle compares Nessai (light-blue filled contours) and Dingo-IS. Contours indicate the 50% and 90% credible regions. The true injected values are indicated by dotted lines.
• Figure 4: Posterior distributions for our representative source with moderate SNR ($\sim 500$) obtained with different sampling methods. The lower left triangle compares results from Dingo (dark-green filled contours) and Dingo-IS (dashed black contours), while the upper right triangle compares Nessai (light-green filled contours) and Dingo-IS. Contours indicate the 50% and 90% credible regions. The true injected values are indicated by dotted lines.
• Figure 5: Posterior distributions for our representative source with high SNR ($\sim 1000$) obtained with different sampling methods. The lower left triangle compares results from Dingo (dark-orange filled contours) and Dingo-IS (dashed black contours), while the upper right triangle compares Nessai (light-orange filled contours) and Dingo-IS. Contours indicate the 50% and 90% credible regions. The true injected values are indicated by solid dotted lines.