A method of estimating vibration characteristics of moving rotor blades in a turbomachine comprising a housing and rotor including a shaft with the rotor blades attached thereto includes measuring, by at least one proximity sensor, a Time-of-Arrival (ToA) of a proximate tip of a moving rotor blade. The method includes manipulating, by a control module, timing data to determine a corresponding blade tip deflection at each measured ToA, expressing blade tip vibration behaviour as a Bayesian statistical model consisting of intermediate model parameters, wherein model coefficients in the statistical model are probabilistic quantities as opposed to conventional, deterministic quantities, and expressing, by the control module, the determined blade tip deflections as observed values in the statistical model. The method includes manipulating the intermediate model parameters in the statistical model using Bayesian linear regression or inference to estimate the intermediate model parameters and consequently the vibration behaviour of the rotor blade.