Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Sensitivity analysis after multiple imputation under missing at random: a weighting approach.

Multiple imputation (MI) is now well established as a flexible, general, method for the analysis of data sets with missing values. Most implementations assume the missing data are ;missing at random' (MAR), that is, given the observed data, the reason for the missing data does not depend on the unseen data. However, although this is a helpful and simplifying working assumption, it is unlikely to be true in practice. Assessing the sensitivity of the analysis to the MAR assumption is therefore important. However, there is very limited MI software for this. Further, analysis of a data set with missing values that are not missing at random (NMAR) is complicated by the need to extend the MAR imputation model to include a model for the reason for dropout. Here, we propose a simple alternative. We first impute under MAR and obtain parameter estimates for each imputed data set. The overall NMAR parameter estimate is a weighted average of these parameter estimates, where the weights depend on the assumed degree of departure from MAR. In some settings, this approach gives results that closely agree with joint modelling as the number of imputations increases. In others, it provides ball-park estimates of the results of full NMAR modelling, indicating the extent to which it is necessary and providing a check on its results. We illustrate our approach with a small simulation study, and the analysis of data from a trial of interventions to improve the quality of peer review