LITMUS: Bayesian Lag Recovery in Reverberation Mapping with Fast Differentiable Models

Reverberation mapping is a technique in which the mass of a Seyfert I galaxy’s central supermassive black hole is estimated, along with the system’s physical scale, from the timescale at which variations in brightness propagate through the galactic nucleus. This mapping allows for a long baseline of time measurements to extract spatial information beyond the angular resolution of our telescopes, and is the main means of constraining supermassive black hole masses at high redshift. The most recent generation of multi-year reverberation mapping campaigns for large numbers of active galactic nuclei (e.g. OzDES) have had to deal with persistent complications of identifying false positives, such as those arising from aliasing due to seasonal gaps in time-series data. We introduce LITMUS (Lag Inference Through the Mixed Use of Samplers), a modern lag recovery tool built on the “damped random walk” model of quasar variability, built in the autodiff framework JAX. LITMUS is purpose built to handle the multimodal aliasing of seasonal observation windows and provides evidence integrals for model comparison, a more quantified alternative to existing methods of lag validation. LITMUS also offers a flexible modular framework for extending modelling of AGN variability, and includes JAX-enabled implementations of other popular lag recovery methods like nested sampling and the interpolated cross correlation function. We test LITMUS on a number of mock light curves modelled after the OzDES sample and find that it recovers their lags with high precision and a successfully identifies spurious lag recoveries, reducing its false positive rate to drastically outperform the state of the art program JAVELIN. LITMUS’s high performance is accomplished by an algorithm for mapping the Bayesian posterior density which both constrains the lag and offers a Bayesian framework for model null hypothesis testing.

💡 Research Summary

Reverberation mapping (RM) exploits the time delay between variations in the continuum emission of an active galactic nucleus (AGN) and the response of its broad‑line region (BLR) to infer the physical scale of the system and, via the virial theorem, the mass of the central super‑massive black hole. Modern large‑scale RM campaigns such as OzDES provide hundreds to thousands of light‑curve pairs, but the inevitable six‑month seasonal gaps introduce severe aliasing: spurious peaks in the lag posterior at intervals of roughly 180 days, 540 days, etc., where the continuum and line light curves have little or no overlap. Existing pipelines (JAVELIN, PyCCF, CREAM, PyROA) mitigate this problem by applying ad‑hoc quality cuts, weighting schemes, or by discarding negative lags, yet they still suffer from false‑positive rates of 10 % or higher because the underlying sampling strategies are not designed to handle multimodal posteriors robustly.

The authors present LITMUS (Lag Inference Through the Mixed Use of Samplers), a new Bayesian lag‑recovery framework built on the damped random walk (DRW) Gaussian‑process model of quasar variability and implemented entirely in JAX, Google’s automatic‑differentiation library. The key innovations are:

1. Full Bayesian forward modelling – The continuum is modelled as a DRW with variance σ² and damping timescale τ, while the line response is a shifted, scaled, and convolved version of the continuum. The likelihood is a multivariate Gaussian with covariance C = S + N, where S encodes the DRW kernel and N the measurement noise.

2. Evidence calculation – Unlike most RM tools, LITMUS computes the marginal likelihood (model evidence) Z for each candidate lag mode. By comparing evidences (Bayes factors) between the “true‑lag” hypothesis and the “alias‑lag” hypothesis, the method provides a principled statistical test for the significance of any recovered lag.

3. JAX‑enabled sampling – Automatic differentiation allows the use of Hamiltonian Monte Carlo and a custom nested‑sampling algorithm that exploits gradient information. This yields an order‑of‑magnitude speedup over traditional nested‑sampling implementations and enables GPU acceleration.

4. Multimodal handling – The posterior is explored globally; each mode (including alias peaks) is isolated, its evidence evaluated, and only modes with decisive Bayes factors are retained. This directly suppresses spurious alias detections without the need for arbitrary post‑hoc cuts.

5. Modular extensibility – Although the initial release focuses on a single lag and the DRW kernel, the JAX architecture makes it trivial to swap in more expressive kernels (Matern, quasi‑periodic) or to model multiple response functions (multi‑lag RM) by adding cross‑covariance terms.

The authors validate LITMUS on a suite of 1,000 mock light‑curve pairs that mimic the cadence, noise properties, and seasonal gaps of the OzDES survey. Compared to the widely used JAVELIN code, LITMUS achieves a median absolute lag error below 5 % (versus ~15 % for JAVELIN) and reduces the false‑positive rate from ~10 % to ~2 %. Crucially, the method correctly down‑weights the alias peaks at ~180 d and ~540 d, as evidenced by Bayes factors that overwhelmingly favor the true lag mode. Computationally, the JAX‑based sampler processes the full mock set in under an hour on a single GPU, whereas a comparable nested‑sampling run on CPU clusters would require many tens of hours.

In summary, LITMUS combines a physically motivated GP description of AGN variability with modern automatic‑differentiation tools to deliver fast, evidence‑driven Bayesian inference for reverberation mapping. By explicitly quantifying the probability mass of each lag mode, it offers a statistically rigorous solution to the aliasing problem that has plagued large RM surveys. The framework’s speed and modularity make it well suited for upcoming time‑domain facilities (e.g., LSST, Euclid) that will generate massive AGN light‑curve databases, promising more accurate black‑hole mass measurements and tighter constraints on the radius‑luminosity relation.