The article illustrates the results of an exploratory study on the effectiveness of maximum likelihood Bayesian estimation in the identification of cavitation instabilities in axial inducers using the blade-to-blade pressure measured by a single transducer flush-mounted on the impeller casing. The typical azimuthal distribution of the pressure in the blade channels is parameterized and modulated in space and time for theoretically reproducing the expected pressure generated by known forms of cavitation instabilities (cavitation surge auto-oscillations, n-lobed synchronous/asynchronous rotating cavitation, and higher-order surge/rotating cavitation modes). The power spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame, corrected for frequency broadening effects, and parametrically fitted by maximum likelihood estimation to the measurements of the pressure on the inducer casing just downstream of the blade leading edges. In addition to its fundamental frequency, each form of instability generates a characteristic spectral distribution of sidebands. The identification uses this information for successfully discriminating flow oscillation modes occurring simultaneously with intensities differing by up to one order of magnitude. The method returns the estimates of the model parameters and their standard errors, allowing one to assess the accuracy and statistical significance of the identification. The results first demonstrate that elementary maximum likelihood Bayesian identification is indeed capable to effectively detect and characterize the occurrence of flow instabilities in cavitating inducers at a fraction of the experimental and postprocessing costs and complexities of traditional cross-correlation methods.