  We compare two strategies of multi-detector detection of compact binary
inspiral signals, namely, the coincidence and the coherent. For simplicity we
consider here two identical detectors having the same power spectral density of
noise, that of initial LIGO, located in the same place and having the same
orientation. We consider the cases of independent noise as well as that of
correlated noise. The coincident strategy involves separately making two
candidate event lists, one for each detector, and from these choosing those
pairs of events from the two lists which lie within a suitable parameter
window, which then are called as coincidence detections. The coherent strategy
on the other hand involves combining the data phase coherently, so as to obtain
a single network statistic which is then compared with a single threshold. Here
we attempt to shed light on the question as to which strategy is better. We
compare the performances of the two methods by plotting the Receiver Operating
Characteristics (ROC) for the two strategies. Several of the results are
obtained analytically in order to gain insight. Further we perform numerical
simulations in order to determine certain parameters in the analytic formulae
and thus obtain the final complete results. We consider here several cases from
the relatively simple to the astrophysically more relevant in order to
establish our results. The bottom line is that the coherent strategy although
more computationally expensive in general than the coincidence strategy, is
superior to the coincidence strategy - considerably less false dismissal
probability for the same false alarm probability in the viable false alarm
regime.
