A new probabilistic model identification methodology is proposed using measured response time histories only. The proposed approach requires that the number of independent measurements is larger than the number of independent excitations. Under this condition, no input measurements or any information regarding the stochastic model of the input is required. Specifically, the method does not require the response to be stationary and does not assume any knowledge of the parametric form of the spectral density of the input. Therefore, the method has very wide applicability. The proposed approach allows one to obtain not only the most probable values of the updated model parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centered at the most probable values of the parameters. Examples are presented to illustrate the proposed method.