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

Abstract

Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for nanosecond gravitational waves. As for other applications of Gaussian distributions, outliers in timing measurements pose a significant challenge to statistical inference, since they can bias the estimation of timing and noise parameters, and affect reported parameter uncertainties. We describe and demonstrate a practical end-to-end approach to perform Bayesian inference 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 the timing and noise parameters), and it relies on the efficient sampling of the hierarchical form of the pulsar-timing likelihood. Such sampling has recently become possible with a "no-U-turn" Hamiltonian sampler coupled to a highly customized reparametrization of the likelihood; this code is described elsewhere, but it is already available online. We recommend our method as a standard step in the preparation of pulsar-timing-array datasets: even if statistical inference is not affected, follow-up studies of outlier candidates can reveal unseen problems in radio observations and timing measurements; furthermore, confidence in the results of gravitational-wave searches will only benefit from stringent statistical evidence that datasets are clean and outlier-free.

6 pages, 2 figures, RevTeX 4.1

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• The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Noise analysis of the Indian Pulsar Timing Array data release I
• Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo
• Reducing instrumental errors in Parkes Pulsar Timing Array data
• Regularizing the Pulsar Timing Array likelihood: A path towards Fourier Space
• Controlling Outlier Contamination In Multimessenger Time-domain Searches For Supermasssive Binary Black Holes