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Pulsar-timing datasets have been analyzed with great success usingprobabilistic treatments based on Gaussian distributions, with applicationsranging from studies of neutron-star structure to tests of general relativityand searches for nanosecond gravitational waves. As for other applications ofGaussian distributions, outliers in timing measurements pose a significantchallenge to statistical inference, since they can bias the estimation oftiming and noise parameters, and affect reported parameter uncertainties. Wedescribe and demonstrate a practical end-to-end approach to perform Bayesianinference of timing and noise parameters robustly in the presence of outliers,and to identify these probabilistically. The method is fully consistent (i.e.,outlier-ness probabilities vary in tune with the posterior distributions of thetiming and noise parameters), and it relies on the efficient sampling of thehierarchical form of the pulsar-timing likelihood. Such sampling has recentlybecome possible with a "no-U-turn" Hamiltonian sampler coupled to a highlycustomized reparametrization of the likelihood; this code is describedelsewhere, but it is already available online. We recommend our method as astandard step in the preparation of pulsar-timing-array datasets: even ifstatistical inference is not affected, follow-up studies of outlier candidatescan reveal unseen problems in radio observations and timing measurements;furthermore, confidence in the results of gravitational-wave searches will onlybenefit from stringent statistical evidence that datasets are clean andoutlier-free.

Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling