Generalized Steppingstone Sampling: Efficient Marginal Likelihood Estimation in Gravitational Wave Analysis of Pulsar Timing Array Data
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Zahraoui, El Mehdi
Maturana-Russel, Patricio
van Straten, Willem
Meyer, Renate
Gulyaev, Sergei
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Oxford University Press (OUP)
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Globally, Pulsar Timing Array (PTA) experiments have revealed tentative evidence of a stochastic gravitational wave background (GWB) signal in PTA data. Apart from acquiring more observations, the sensitivity of PTA experiments can be increased by improving the accuracy of noise modeling. In PTA data analysis, noise modeling is conducted primarily using Bayesian statistics, relying on the marginal likelihoods and Bayes factors to assess evidences. We introduce generalized steppingstone sampling (GSS) as an efficient and accurate marginal likelihood estimation method for the PTA-Bayesian framework. This method enables low-cost estimates with high accuracy, especially when comparing expensive models such as the Hellings-Downs (HD) model or the overlap reduction function model (ORF). We demonstrate the efficiency and the accuracy of GSS for model selection and evidence calculation by reevaluating the evidence of previous analyses from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 15 yr data set and the European PTA (EPTA) second data release. We find similar evidence for the GWB compared to the one reported by the NANOGrav 15-year data set. Compared to the evidence reported for the EPTA second data release, we find a substantial increase in evidence for a GWB signal across all data sets.
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5101 Astronomical Sciences, 51 Physical Sciences, 0201 Astronomical and Space Sciences, Astronomy & Astrophysics, 5107 Particle and high energy physics, 5109 Space sciences, gravitational waves, methods: data analysis, methods: statistical, pulsars: general
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Monthly Notices of the Royal Astronomical Society, ISSN: 0035-8711 (Print); 1365-2966 (Online), Oxford University Press (OUP), 540(4), 3818-3825. doi: 10.1093/mnras/staf953
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© 2025 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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Except where otherwise noted, this item's license is described as © 2025 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.