In pulse Doppler radars, the pulse compressed signal intensity belongs to Gamma distributions, so that the evaluation of indices, such as signal-to-noise ratio and signal to interference plus noise ratio, is indeed the statistical inference of Gamma means ratio. The classical inference method for Gamma means ratio is maximum likelihood estimation; whereas, it not only neglects the use of prior information, but also results in unexplained confidence levels from probability views. To overcome these shortcomings,the posterior distribution of the Gamma parameters follows log-concave distribution is proved by deriving the relationship between the ratio′s distribution of Gamma means and the Beta distribution. Thus, the Bayesian statistical inference for Gamma means ratio based on Gibbs sampling methods is proposed, and posterior point estimation methods as well as interval estimation ones are proved. The effectiveness of the method has been verified by the measured data process.