Accelerated Sequential Posterior Inference via Reuse for Gravitational-Wave Analyses

Technical Summary: Accelerated Sequential Posterior Inference via Reuse (ASPIRE)

Problem Statement
Gravitational-wave astronomy faces a growing computational bottleneck as the catalog of detected compact binary mergers expands. Scientific progress increasingly relies on reanalyzing existing events under alternative waveform models, adding physical effects (such as spin precession or orbital eccentricity), or testing fundamental physics hypotheses. Traditional Bayesian inference requires repeating the full analysis from scratch for each new hypothesis, a process that can take hours to days per event using nested sampling. Naive reuse of previous posterior samples as priors for new analyses is statistically invalid, as it double-counts data and biases model comparison via Bayes factors. While methods like importance sampling exist, they fail when the initial and target distributions differ substantially. Current accelerated inference methods often do not leverage existing results, and sophisticated techniques like Parallel Tempered Markov Chain Monte Carlo (PTMCMC) can be sensitive to tuning parameters and may struggle with accurate evidence estimation.

Methodology
The paper introduces ASPIRE (Accelerated Sequential Posterior Inference via Reuse), a framework designed to transform existing posterior samples and Bayesian evidence estimates into unbiased results under a new model ($M_2$) without rerunning the original analysis. ASPIRE combines two core components:

1. Normalizing Flow Approximation: The method begins with posterior samples obtained under an initial model ($M_1$). A normalizing flow (specifically a Masked Autoregressive Flow) is trained via maximum likelihood to approximate the density of these samples, creating a flexible, invertible transformation $f_\phi$ that maps a simple base distribution to an approximation of the posterior $q_\phi(\theta) \approx p(\theta|d, M_1)$. If $M_2$ introduces new parameters, the flow is extended by drawing incompatible components from the prior, ensuring the approximation spans the parameter space of the new model.

2. Generalized Sequential Monte Carlo (SMC): Instead of starting from the prior, ASPIRE evolves the flow-based approximation $q_\phi(\theta)$ to the true posterior under $M_2$ using a generalized SMC scheme. The algorithm defines a sequence of intermediate distributions $\pi_t(\theta)$ that interpolate between the flow approximation and the target posterior using an inverse temperature parameter $\beta_t \in [0, 1]$:
   $$\pi_t(\theta) \propto q_\phi(\theta)^{1-\beta_t} [p(d|\theta, M_2)p(\theta|M_2)]^{\beta_t}$$
   The algorithm starts with samples from $q_\phi$ and iteratively increases $\beta_t$ using an adaptive schedule based on the Effective Sample Size (ESS). At each step, particles are reweighted, resampled, and diversified using a $t$-preconditioned Crank–Nicolson (t-pCN) Markov Chain Monte Carlo (MCMC) step. The process terminates at $\beta=1$, yielding unbiased posterior samples and an estimate of the Bayesian evidence.

Key Contributions

• Unbiased Reuse: ASPIRE provides a statistically rigorous method to update existing analyses, guaranteeing unbiased posterior and evidence estimates even when the target and initial posteriors occupy different regions of parameter space or when new parameters are introduced.
• Efficiency: By avoiding the need to explore the prior volume from scratch, ASPIRE significantly reduces computational costs.
• Open-Source Implementation: The authors provide the aspire Python package, along with interfaces for bilby and gravitational-wave specific workflows (aspire-gw), enabling immediate application in the field.

Results
The authors validate ASPIRE across simulated and real gravitational-wave data:

• Waveform Systematics: When switching between waveform models (e.g., from IMRPhenomXPHM to IMRPhenomXO4a), ASPIRE reproduces results consistent with full nested sampling (dynesty) baselines. The Jensen-Shannon Divergence (JSD) between ASPIRE and baseline posteriors is typically below 2.1 mbits, indicating statistical indistinguishability.
• Adding Physical Effects: The framework successfully recovers new parameters when adding spin precession (transitioning from aligned-spin to precessing models) and orbital eccentricity. In these cases, ASPIRE produces posteriors consistent with baselines while capturing the new physical degrees of freedom without bias.
• Real Data Application: Reanalyses of GW150914 and GW200129 demonstrate that ASPIRE remains effective on real data, even for events known to exhibit waveform systematics.
• Statistical Validation: A Probability-Probability (P-P) test on 100 simulated signals confirms that ASPIRE produces statistically unbiased posteriors (combined p-value = 0.574).
• Performance Gains: ASPIRE reduces total likelihood evaluations by factors of up to 5.8 and wall times by up to 5.5 compared to traditional nested sampling. When normalized by the number of posterior samples produced, efficiency gains are even larger (up to 12.3x in likelihood evaluations and 9.8x in wall time).
• Comparison to PTMCMC: In controlled tests, ASPIRE demonstrates more stable evidence estimates and greater efficiency than PTMCMC. While PTMCMC can recover correct posteriors, it showed variability in evidence estimates and required careful tuning of temperature ladders. ASPIRE failed to recover a second mode in a multimodal toy example if the initial proposal lacked support for it, but this limitation was shown to be mitigated by augmenting initial samples with a small fraction of prior draws.

Significance
The paper claims that ASPIRE transforms the repeated reanalysis of gravitational-wave events from a computationally prohibitive task into a routine, fast, and reliable update process. By enabling systematic studies of waveform systematics and scalable reanalyses across large event catalogs, ASPIRE maximizes the scientific return from the growing catalog of detections. The framework is presented as broadly applicable to other scientific domains where competing models abound and Bayesian reanalysis is common, such as particle physics and cosmology. The authors emphasize that the method's efficiency depends on the similarity between the initial and target posteriors; however, for the typical regime of sequential gravitational-wave analyses where updated models remain close to previous results, ASPIRE offers a robust and superior alternative to conventional sampling methods.