Don’t wait, reweight: Accurate characterization of the stochastic gravitational-wave background with pulsar timing arrays by likelihood reweighting

The nanohertz gravitational-wave background modifies pulsar pulse arrival times stochastically, generating excess power in pulsar-timing-array datasets with characteristic inter-pulsar correlations that follow the Hellings-Downs function. These correlations appear as non-diagonal terms in the noise-covariance matrix which is inverted to evaluate the pulsar-timing-array likelihood. Gravitational-wave background searches, which require many such likelihood calculations, therefore become quite expensive. In this talk I present a more efficient method: first compute approximate posteriors by ignoring the inter-pulsar correlations and then obtain the exact posteriors via reweighting. I will show that this method is robust, unbiased, and able to estimate Bayes factors up to at least 10⁶.