\subsection{Baseline search with HEN and GW candidate lists}
\label{subsec:parallel}

Joint GW and HEN multimessenger searches provide another interesting perspective for data analysis compared to more traditional externally triggered searches, e.g., with electromagnetic (EM) GRB observations. While EM observations of GRBs allow for searches for GW or HEN signals from a precisely determined time and direction, the joint search for GW and HEN signals with no EM counterpart relies on the combination of significance and directional probability distribution from these two messengers~\cite{Baret:2011nu}. In such a case, the possibility that multiple neutrinos are detected from the same astrophysical source can also be considered, e.g. if several neutrino candidates happen to fall within a predefined space-time window.

Similarly to how multiple GW detectors are effective in rejecting ''glitches" from the non-Gaussian background noise by requiring the coincident occurrence of an astrophysical signal in spatially separated GW detectors, requiring spatial and temporal coincidence from GW and HEN signal candidates can highly reduce false alarm rate \cite{ligo_icecube}.

Due to the uncertainty of directional reconstruction, especially for GWs, one can also enhance background rejection by using the expected source distribution in the nearby universe. Such distribution can be based on the distribution of nearby galaxies and their weight. The density of at least some GW+HEN sources can be connected to the blue luminosity of galaxies \cite{blueluminositybinary1991ApJ...380L..17P,0264-9381-28-8-085016}, while source density can also depend on the type of the galaxy \cite{2006IJMPD..15..235D,2010ApJ...716..615O}.

The search for joint GW+HEN signal candidates can be aimed for detecting a single astrophysical signal with high-enough significance to claim detection. Another possibility is to aim for a set of weaker signals that could not be detected individually, but their joint distribution differentiates them from the background. Such a technique has been used in various searches for GWs; see e.g. \citet{Abbott:2009kk}.

A schematic flow diagram of a joint search algorithm is shown in Figure \ref{figure:flowchart}.

\begin{figure}
\begin{center}
\resizebox{0.6\textwidth}{!}{\includegraphics{GWHEN-FlowDiagram}}
\end{center}
\caption{Schematic flow diagram of a joint GW+HEN search pipeline. The inputs of the pipeline are, besides data from HEN and GW detectors, the astrophysical source distribution from a galaxy catalog, as well as the coincidence time window used for the search. Spatially and temporally coincident neutrinos can be clustered, that can potentially greatly increase a significance, and decrease the false alarm rate, of a coincident GW+HEN signal. Combining these information in a joint test statistic, one can evaluate the results to look for individual or statistical detection of signal candidates. Upon non-detection, the results can be used to determine an upper limit on the source population.} \label{figure:flowchart}
\end{figure}