Abstract: In the paper it is assumed that the underwater acoustic noise, of a noisy vessel, is a sum of a zero mean Gaussian stochastic process with a finite variance due to propeller(s) cavitation and of a finite number of sine waves with extremely small amplitudes. These two processes are mutually statistically independent. The deep-sea underwater ambient acoustic noise is supposed to be a zero mean Gaussian stochastic process with a finite variance as well. In the paper are considered the probability density function of the instantaneous values of the underwater acoustic noise of the noisy vessel and of the deep-sea underwater ambient acoustic noise. The likelihood ratio and the detection algorithm of the optimal statistical detection are given. The statistical indirect evaluation of the noisy vessel passive detection is considered. The indirect evaluation measure of the detection algorithm is so-called deflection coefficient, which is the function of the difference between statistical expectations of the two possible probability density functions of the received acoustic signals.