Paul T. Troughton and Simon J. Godsill. Bayesian model selection for linear and non-linear time series using the Gibbs sampler. In Mathematics in Signal Processing IV, pp. 249-261. Oxford University Press, 1998.

We present a stochastic simulation technique for model selection in time series, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset AR models, in which only significant lags are included. The same approach is then used to identify the structure of a non-linear time series. We discuss the possibility of model mixing where the model is not well determined by the data.