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