Validating Sequential Monte Carlo for Gravitational-Wave Inference

TL;DR

The paper addresses the computational bottleneck of Bayesian gravitational-wave inference by evaluating sequential Monte Carlo with persistent sampling (PS) as an alternative to nested sampling. It introduces pocomc, a PS-based GW inference engine with normalizing-flow preconditioning and a tempering kernel, and validates it against dynesty on BBH/BNS injections and real events. The results show PS reproduces NS posteriors and evidence while offering approximately 2× efficiency and 2.74× speedups in BBH analyses, with similar gains for BNS cases; some tidal-parameter analyses exhibit larger posterior differences, underscoring the need for further convergence checks in publication-quality runs. The work demonstrates PS as a viable, scalable method suitable for low-latency and next-generation GW endeavors, with potential for online learning and gradient-based kernels for future improvements.

Abstract

Nested sampling (NS) is the preferred stochastic sampling algorithm for gravitational-wave inference for compact binary coalenscences (CBCs). It can handle the complex nature of the gravitational-wave likelihood surface and provides an estimate of the Bayesian model evidence. However, there is another class of algorithms that meets the same requirements but has not been used for gravitational-wave analyses: Sequential Monte Carlo (SMC), an extension of importance sampling that maps samples from an initial density to a target density via a series of intermediate densities. In this work, we validate a type of SMC algorithm, called persistent sampling (PS), for gravitational-wave inference. We consider a range of different scenarios including binary black holes (BBHs) and binary neutron stars (BNSs) and real and simulated data and show that PS produces results that are consistent with NS whilst being, on average, 2 times more efficient and 2.74 times faster. This demonstrates that PS is a viable alternative to NS that should be considered for future gravitational-wave analyses.

Figures (17)

• Figure 1: Annealed one- and two- dimensional posterior distributions (see \ref{['eq:intermediate_densities']}) for chirp mass ($\mathcal{M}$) and mass ratio ($q$) for a GW150914-like injection in zero-noise at four different inverse temperatures ($\beta_t$). The injection was simulated in a two-detector network using IMRPhenomPv2. The same waveform was used when computing the likelihood and all other parameters were fixed to the injected values except for the phase at coalescence, which as analytically marginalized Thrane:2018qnx. The dashed vertical and horizontal lines indicate the injection parameters.
• Figure 2: Single iteration $t$ of the algorithm demonstrating its three key operations, (i) reweighting, (ii) resampling, and (iii) moving. Particle positions are shown in 1D with particle weights represented by their relative size. Low-weight particles are discarded and high-weight ones are multiplied during resampling. The moving step diversifies the resampled population, yielding equally weighted and distinct particles.
• Figure 3: Evolution of the $\beta$ parameter, log-evidence $\log Z$ and of the particles when analysing GW150914_095045 using pocomc, this analysis includes calibration uncertainties. The $\beta$ parameter is adaptively chosen at each iteration and slowly increases until $\beta=1$, during this time, the of particles is kept constant. Once $\beta=1$ additional samples are drawn to reach the specified by the user, 10,000 in this case. The results are discussed in detail in \ref{['sec:real_data']}.
• Figure 4: Probability-probability plot obtained using pocomc to analyse 100 simulated signals in two-detector network consisting of LIGO Hanford and LIGO Livingston. The shaded regions denote the 1-, 2- and 3-$\sigma$ bounds respectively. Per-parameter $p$-values are quoted, as well as the combined $p$-value computed using Fisher's method fisher1970statistical.
• Figure 5: Per-parameter between the posterior samples obtained with pocomc and dynesty for 100 simulated binary black hole signals when analysed in two- and three-detector networks. The upper and lower histograms show the three- and two-detector results respectively, the counts have been rescaled such the bin with the most counts has the same height between different parameters. The vertical dashed line shows the threshold proposed in Ashton:2021anp. 'Max.' and 'Median' denote the maximum and median over all parameters per analysis, respectively. $t_\textrm{IFO}$ denotes the time of coalescence as measured in the detectors with highest .