Reliability of parameter estimates in the first observing run of Advanced LIGO

Accurate parameter estimation is key to maximizing the scientific impact of gravitational-wave astronomy. Parameters of a binary merger are typically estimated using Bayesian inference. It is necessary to make several assumptions when doing so, one of which is that the detectors output stationary Gaussian noise. We test the validity of these assumptions by performing percentile-percentile tests in both simulated Gaussian noise and real detector data in the first observing run of Advanced LIGO (O1). We add simulated signals to 512s of data centered on each of the three events detected in O1—GW150914, GW151012, and GW151226—and check that the recovered credible intervals match statistical expectations. We find that we are able to recover unbiased parameter estimates in the real detector data, indicating that the assumption of Gaussian noise does not adversely effect parameter estimates. However, we also find that both the parallel-tempered sampler emcee_pt and the nested sampler dynesty struggle to produced unbiased parameter estimates for GW151226-like signals, even in simulated Gaussian noise. The emcee_pt sampler does produce unbiased estimates for GW150914-like signals. This highlights the importance of performing percentile-percentile tests in different targeted areas of parameter space.

Figure 1

Distribution of the “optimal” SNRs of the injections used in our analysis. Here, SNR is defined as $\sqrt{{\sum }_i⟨{\tilde{s}}_i,{\tilde{s}}_i⟩}$, where the sum is over the number of detectors and $s_i$ is the simulated waveform. The bounds on the comoving volume prior are chosen so that majority of the injections have an SNR close to that of the actual event.

Figure 2

Percentile-percentile plot for simulated non-Gaussian noise. Shown are the fraction of simulated signals with parameter values recovered in a credible interval as a function of credible intervals for each parameter. If the parameters were recovered exactly, the plot would follow the line $y=x$ as indicated by the diagonal line. Simulated glitches were added to the same Gaussian noise as used in Fig 3, and the same simulated signals were used to perform the test. We perform a KS test to obtain a p value for each parameter, which is indicated by the color bar. We then perform a KS test on the set of p values to obtain a p value of p values of 0.001, indicating that the noise fails the percentile-percentile test, as expected.

Figure 3

GW150914: plot of the fraction of simulated signals with parameter values recovered in a credible interval as a function of credible intervals for each parameter. If the parameters were recovered exactly, the plot would follow the line $y=x$ as indicated by the diagonal line. For each parameter, a KS test is performed between the recovered curve and the diagonal line to obtain a two-tailed p value, which is indicated by the color bar.

Figure 4

GW151226: plot of the fraction of simulated signals with parameter values recovered in a credible interval as a function of credible intervals for each parameter. If the parameters were recovered exactly, the plot would follow the line $y=x$ as indicated by the diagonal line. For each parameter, a KS test is performed between the recovered curve and the diagonal line to obtain a two-tailed p value, which is indicated by the color bar.

Figure 5

GW150914 shifted: plot of the fraction of simulated signals with parameter values recovered in a credible interval as a function of credible intervals for each parameter. If the parameters were recovered exactly, the plot would follow the line $y=x$ as indicated by the diagonal line. For each parameter, a KS test is performed between the recovered curve and the diagonal line to obtain a two-tailed p value, which is indicated by the color bar.