Neural Bayesian updates to populations with growing gravitational-wave catalogs

TL;DR

This work uses variational neural posterior estimation to rapidly update the inferred population of binary black holes as data are observed in gravitational-wave detectors, finding that the robustness of updating is sensitive to the information contained in each update and that updating is most effective when performed with larger segments of data.

Abstract

As gravitational-wave catalogs grow, they will become increasingly computationally expensive to analyze in their entirety, especially when inferring astrophysical source populations with high-dimensional, flexible models. Bayesian statistics offers a natural remedy, letting us update our knowledge of physical models as new data arrive, without re-analyzing existing data. However, doing so requires the posterior probability density of model parameters for previous observations, which is typically intractable. Here, we use variational neural posterior estimation to rapidly update the inferred population of binary black holes as data are observed in gravitational-wave detectors. We apply this approach to real and simulated catalogs analyzed with both low- and high-dimensional population models, testing the reliability of three update cadences: with new catalogs of sources, month by month during an observing run, and as each new signal arrives. We investigate the success and failure modes of neural sequential updates, finding that the robustness of updating is sensitive to the information contained in each update and that updating is most effective when performed with larger segments of data. We outline one additional scientific application enabled by Bayesian updating: identification of events that are individually informative about the population. Neural Bayesian updates to astrophysical population models also provide efficient likelihood representations for joint analyses with other data, e.g., standard-siren cosmology, and similar methods can be used to perform Bayesian stochastic background searches.

Figures (11)

• Figure 1: Convergence of sequential updates starting from GWTC-3 and adding BBH observed in O4a. We show the Pareto smoothing shape parameter $\hat{k}$ as a function of update (left) when we update month-by-month (top) or as each event arrives (bottom). We compute $\hat{k}$ relative to the cumulative posterior (circles) and the target density during training (crosses). We include a dashed gray line at $\hat{k} = 0.7$, a reference threshold for convergence 2015arXiv150702646V. In the right two columns, we compare posterior distributions on log-likelihood estimator $\ln \hat{\mathcal{L}}$ and variance $\mathcal{V}$ drawn according to nested sampling (blue, filled), the variational approximant after the final update (orange), and Pareto-smoothed importance sampling (PSIS) of the variational approximant (green).
• Figure 2: PPD in primary mass (top left), mass ratio (top right), spin magnitude (bottom center), and tilt (bottom right) given all 153 BBH in GWTC-4. We also show the posterior on the source-frame merger rate density over redshift (bottom left). We compare results obtained with nested sampling (blue, filled) and sequentially updating with all of O4a (orange), month by month (green), and event by event (red). Thin lines or shading enclose the 90% credible region and thick lines denote medians; we exclude the median of the update with all of O4a as it was nearly identical to the median reported by nested sampling. In the top right, we include an inset showing $\mathrm{PPD}(q)$ at $q > 0.7$.
• Figure 3: PPD in spin magnitude after each month of O4a (top) after Pareto-smoothed importance sampling; we denote later months with warmer colors and emphasize November 2023 and December 2023 with dashed and dotted lines, respectively. Marginal importance-sampled posteriors on the width $\sigma_\chi^2$ of the spin magnitude distribution (bottom) are shown before observing GW231123 (purple), immediately after GW231123 (orange, dashed), and after all of O4a (yellow).
• Figure 4: Convergence of sequential updates under a strongly-modeled approach with a mock catalog of high SNR sources, as we decrease the number of events in each update (top to bottom). We also record the number of updates $n$ in each row. Format otherwise matches Fig. \ref{['fig:gwtc4-convergence']}
• Figure 5: PPD in cosine-spin tilts $\cos \tau_{1,2}$ returned by nested sampling (blue, filled), 54 single-event updates (orange, dashed), and PSIS of the variational approximant after all single-event updates (PSIS, green). Thick lines denote the medians; filled regions or lines enclose the 90% credible interval. A black line denotes the true distribution.