  Global network of advanced Interferometric gravitational wave (GW) detectors
are expected to be on-line soon. Coherent observation of GW from a distant
compact binary coalescence (CBC) with a network of interferometers located in
different continents give crucial information about the source such as source
location and polarization information. In this paper we compare different
multi-detector network detection statistics for CBC search. In maximum
likelihood ratio (MLR) based detection approaches, the likelihood ratio is
optimized to obtain the best model parameters and the best likelihood ratio
value is used as statistic to make decision on the presence of signal. However,
an alternative Bayesian approach involves marginalization of the likelihood
ratio over the parameters to obtain the average likelihood ratio. We obtain an
analytical expression for the Bayesian statistic using the two effective
synthetic data streams for targeted search of non-spinning compact binary
systems with an uninformative prior on the parameters. Simulations are carried
out for testing the validity of the approximation and comparing the detection
performance with the maximum likelihood ratio based statistics. We observe that
the MLR {\it hybrid} statistic gives comparable or better performance with
respect to the Bayesian statistic.
