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Accurate characterization of the stochastic gravitational-wave background with pulsar timing arrays by likelihood reweighting

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arxiv 2212.06276 v2 pith:EJZFS5JX submitted 2022-12-12 gr-qc astro-ph.HE

Accurate characterization of the stochastic gravitational-wave background with pulsar timing arrays by likelihood reweighting

Sophie Hourihane , Patrick Meyers , Aaron Johnson , Katerina Chatziioannou , Michele Vallisneri This is my paper
classification gr-qc astro-ph.HE
keywords likelihoodposteriorsaccurateapproximatebackgroundcorrelationsexactstochastic
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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An isotropic stochastic background of nanohertz gravitational waves creates excess residual power in pulsar-timing-array datasets, with characteristic inter-pulsar correlations described by the Hellings-Downs function. These correlations appear as nondiagonal terms in the noise covariance matrix, which must be inverted to obtain the pulsar-timing-array likelihood. Searches for the stochastic background, which require many likelihood evaluations, are therefore quite computationally expensive. We propose a more efficient method: we first compute approximate posteriors by ignoring cross correlations, and then reweight them to exact posteriors via importance sampling. We show that this technique results in accurate posteriors and marginal likelihood ratios, because the approximate and exact posteriors are similar, which makes reweighting especially accurate. The Bayes ratio between the marginal likelihoods of the exact and approximate models, commonly used as a detection statistic, is also estimated reliably by our method, up to ratios of at least $10^6$.

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Cited by 4 Pith papers

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