[Paper Review] Mitigating the effect of the population model uncertainty on the strong lensing Bayes factor using nonparametric methods

Damon H. T. Cheung, S. Rinaldi+2 more|arXiv (Cornell University)|Aug 23, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy3 citations

TL;DR

This study proposes using nonparametric population modeling to reduce bias in strong gravitational lensing detection via Bayes factors, demonstrating that nonparametric methods yield significantly lower bias than parametric models when inferring lensed binary black hole events from gravitational wave data.

ABSTRACT

Strong lensing of gravitational waves can produce several detectable images as repeated events in the upcoming observing runs, which can be detected with the posterior overlap analysis (Bayes factor). The choice of the binary black hole population plays an important role in the analysis as two gravitational-wave events could be similar either because of lensing or astrophysical coincidence. In this study, we investigate the biases induced by different population models on the Bayes factor. We build up a mock catalog of gravitational-wave events following a benchmark population and reconstruct it using both nonparametric and parametric methods. Using these reconstructions, we compute the Bayes factor for lensed pair events by utilizing both models and compare the results with a benchmark model. We show that the use of a nonparametric population model gives a smaller bias than parametric population models. Therefore, our study demonstrates the importance of choosing a sufficiently agnostic population model for strong lensing analyses.

Motivation & Objective

• To investigate how uncertainty in astrophysical population models affects the Bayes factor used to identify strongly lensed gravitational wave events.
• To compare the performance of parametric versus nonparametric population modeling in reconstructing mock gravitational wave event catalogs.
• To quantify the bias introduced by incorrect population model assumptions in lensing hypothesis testing.
• To demonstrate that nonparametric methods provide a more robust and agnostic approach to population inference in strong lensing analyses.

Proposed method

• Construct a mock catalog of binary black hole gravitational wave events based on a benchmark population model.
• Reconstruct the population using both parametric (assumed functional form) and nonparametric (kernel density estimation) methods.
• Compute the Bayes factor for lensed event pairs using both reconstructed population models and compare results to the benchmark model.
• Use a hierarchical Bayesian framework to compute the evidence ratio between lensed and unlensed hypotheses, integrating over shared source parameters.
• Apply a uniform prior in parameter estimation to simplify the Bayes factor expression, isolating the impact of population prior choice.
• Derive the Bayes factor formula under both hypotheses, incorporating population priors and event-specific posteriors to assess model sensitivity.

Figure 1: A strong lens can produce multiple images of a binary black hole (BBH). Although we can not discern the images in the sky with a ground-based gravitational-wave detector due to poor angular resolution, we can detect them as ”repeated events” – two or more gravitational-wave copies that onl

Experimental results

Research questions

• RQ1 How does the choice of population model affect the Bayes factor in strong gravitational lensing detection?
• RQ2 To what extent do parametric population models introduce bias in lensing hypothesis testing compared to nonparametric alternatives?
• RQ3 Can nonparametric population modeling reduce uncertainty in the lensing Bayes factor when the true population is unknown?
• RQ4 How does the performance of the Bayes factor depend on the fidelity of the assumed population prior relative to the true underlying distribution?

Key findings

• Nonparametric population modeling results in significantly lower bias in the Bayes factor compared to parametric models when inferring lensed gravitational wave events.
• The use of a nonparametric approach reduces the systematic error introduced by incorrect assumptions about the binary black hole population distribution.
• The study confirms that parametric models can mislead lensing inference when the true population deviates from the assumed functional form.
• The Bayes factor computed with a nonparametric population model shows better agreement with the benchmark model, even under model misspecification.
• The results highlight the importance of using agnostic, nonparametric methods to minimize model-dependent biases in strong lensing analyses.
• The derived Bayes factor formula explicitly separates the impact of population priors, enabling direct comparison of model robustness.

Figure 2: Population models for observed distribution. Moving from left to right, the columns correspond to the benchmark model, the inferred (H)DPGMM model, the inferred power-law model, and the uniform model, respectively. The first row represents the marginalised distribution of redshifted primar