Parallel adaptive reweighting importance sampling for Bayesian astrophysics

Abstract

Efficiently sampling from high-dimensional, multi-modal posteriors is a central challenge in Bayesian inference for astrophysics, especially gravitational-wave astronomy. Popular families of methods like Markov-chain Monte Carlo, nested sampling, and importance sampling all rely on proposal distributions to guide exploration. Because prior knowledge of the target is often limited, practitioners can adopt adaptive proposals that iteratively refine themselves using information gained from previously drawn samples. Traditional adaptive strategies, however, struggle in high-dimensional multi-modal settings: complex, non-linear correlations are hard to capture, and hyperparameters typically require tedious, problem-specific tuning. To address these issues, we introduce Parallel Adaptive Reweighting Importance Sampling (PARIS). PARIS models its proposal as a Gaussian mixture whose component centers are the existing samples and whose component weights match the current importance weights. New draws from the proposal therefore concentrate around high-weight regions, while candidate points in unexplored areas receive intentionally inflated weights. As the algorithm continuously reweights all samples up to the latest proposal, any initial over-weighting self-corrects once additional neighbor samples are collected. To enable rapid reweighting, we present an efficient update scheme and evaluate PARIS on illustrative toy problems and more realistic gravitational-wave parameter estimation tasks. PARIS achieves accurate posterior reconstruction and evidence estimation with substantially fewer function evaluations than competing approaches, highlighting its promise for widespread use in astrophysical data analysis.

Figures (7)

• Figure 1: Pointwise density (blue) and radial shell probability (orange) for a 10-dimensional Gaussian. Most probability mass lies near the typical radius $\sqrt{p}$ rather than at the peak, so the self-term’s peak value overestimates local density by an exponential factor.
• Figure 2: Reconstructed posterior distributions for the 2D "NUS" toy model. The target density features a complex, disjoint geometry with sharp boundaries. Green, blue and orange contours denote results from PARIS, DNS and PTMCMC, respectively. The visual comparison confirms that PARIS accurately resolves the disconnected modes and non-Gaussian features, yielding a density profile consistent with the baseline samplers.
• Figure 3: Comparison of 1D marginalized posterior distributions for a 10-dimensional GMM with 10 equally weighted modes, whose centers are selected via LHS to ensure maximal separation. The grey curve represents the analytically computed marginalized density of the target GMM, appearing uniform in 1D projections due to the mode placement. PARIS achieves consistent sampling across all modes with fewer function evaluations, closely aligning with the analytical solution. In contrast, DNS and PTMCMC use more function evaluations, but show uneven mode recovery.
• Figure 4: Corner plot comparison of the 4D toy GW posterior, parameterized by phase ($\phi$), frequency ($f$), and its derivatives ($\dot{f}, \ddot{f}$). The reference distribution (grey) is derived from an extensive PTMCMC run. PARIS correctly reproduces the complex multi-modal structure and non-linear correlations, matching the reference. In contrast, both DNS and a shorter PTMCMC run exhibit significant sampling error.
• Figure 5: Dendrogram of the 10 surviving PARIS processes (reduced from 50 initial seeds) clustered by waveform mismatch ($1 - \text{Overlap}$). A broad mismatch threshold band of 0.6 (dashed line) to 0.8 resolves five distinct clusters, each corresponding to an injected signal.