Estimates of the Galactic coalescence rate (R) of close binaries with twoneutron stars (NS-NS) are known to be uncertain by large factors (about twoorders of magnitude) mainly due to the small number of systems detected asbinary radio pulsars. We present an analysis method that allows us to estimatethe Galactic NS-NS coalescence rate using the current observed sample and,importantly, to assign a statistical significance to these estimates and tocalculate the allowed ranges of values at various confidence levels. The methodinvolves the simulation of selection effects inherent in all relevant radiopulsar surveys and a Bayesian statistical analysis for the probabilitydistribution of the rate. The most likely values for the total Galacticcoalescence rate (R_peak) lie in the range 2-60 per Myr depending on differentpulsar population models. For our reference model 1, where the most likelyestimates of pulsar population properties are adopted, we obtain R_tot =8_{-5}^{+9} per Myr at a 68% statistical confidence level. The correspondingrange of expected detection rates of NS-NS inspiral are 3_{-2}^{+4}x10^{-3} peryr for the initial LIGO and 18_{-11}^{+21} per yr for the advanced LIGO.
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