Sinusoidal parameter estimation is an important problem in a wide range of signal processing applications such as audio coding, compression, signal enhancement and restoration. In this thesis, sinusoidal parameter estimation is treated from a Bayesian perspective which is an emerging signal processing field. In this connection, we give in the first part of the thesis an introduction to the fundamentals of Bayesian thinking and compare it against traditional signal processing methods. In the second part of the thesis, we propose and develop a new Bayesian inference scheme for the sinusoidal model parameters of the dynamic sinusoidal model. This model can be used for modelling non-stationary signals and it is thus more flexible than the more popular static sinusoidal model. The developed inference scheme is evaluated through simulations on synthetic signals as well as on a real audio signal. These simulations show that the developed inference scheme works very well for making inference about unknown model parameters as well as for restoration. The major drawback of the inference scheme is that it suffers from a high computational complexity which renders it infeasible for most real-time applications.