# Inference¶

For CBC events, we calculate a number of quantities that are inferred from the signal. In preliminary alerts, these quantities are based on the candidate significance and the matched-filter estimates of the source parameters. Once parameter estimation has been completed, updated values will be provided based on samples drawn from the posterior probability distribution.

## Classification¶

The classification consists of four numbers, summing to unity, that give the probability that the source is either a BNS, NSBH, BBH merger, or is of Terrestrial (i.e. a background fluctuation or a glitch) origin.

Our search pipelines use independent methods to assign those source probabilities to their own triggers. These methods all start from the common assumptions that terrestrial and astrophysical events occur as independent Poisson processes, and that NSs and BHs only exist below and above \(3 M_{\odot}\) respectively (see the figure in the alert contents section for the boundaries of the source classification categories in the \((m_1,m_2)\) plane). The search pipelines then account for the rates of background and astrophysical events in ways that differ in detail, but are all based on the population of events observed during the O1, O2 and O3 runs.

For details of the GstLAL method, see [1] (especially Equation 20). For MBTA, see [2]. For PyCBC Live, see [3]. For SPIIR, see [4] and [3].

## Properties¶

The source properties consist of a set of numbers, each between zero and unity, that give the probabilities that the source satisfies certain conditions. These conditions are:

**HasNS**: At least one of the compact objects in the binary (that is, the less
massive or *secondary* compact object) has a mass that is consistent with a
neutron star. Specifically, we define this as the probability that the
secondary mass satisfies \(m_2 \leq M_{\mathrm{max}}\), where
\(M_{\mathrm{max}}\) is the maximum mass allowed by the neutron star
equation of state (EOS). Several NS EOSs are considered and the value
is marginalized by
weighting using the Bayes factors reported in [5].

**HasRemnant**: The source formed a nonzero mass outside the final remnant
compact object. Specifically, the probability is calculated using the disk mass
fitting formula from [6] (Equation 4). Several neutron star EOSs
are considered to compute the remnant mass. The value is marginalized by
weighting based on Bayes factors in reference mentioned above.

**HasMassGap**: At least one of the compact objects in the binary has a mass in
the hypothetical “mass gap” between neutron stars and black holes, defined here
as \(3 M_{\odot} \leq m \leq 5 M_{\odot}\).

The performance of these quantities across online CBC pipelines is shown below.

The ROC curves shown above were constructed using pipeline recovered injections from the O3 Mock Data Challenge (MDC). For details see [8].

The mass values mentioned in this section are source-frame mass. The value reported in the preliminary alert is calculated using a supervised machine learning classifier on a feature space consisting of the masses, spins, and SNR of the best-matching template, described in [7]. This is to account for the uncertainty in the reported template parameters compared to the true parameters. The value reported in the update alerts uses the online parameter estimation to compute the value.