Bayesian model discrimination and Bayes factorsfor linear Gaussian state space models

It is shown how to discriminate between different linear Gaussian state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. A practical implementation of this procedure requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters and is carried out by Markov chain Monte Carlo methods. An application to some non-standard situations such as testing hypothesis on the boundary of the parameter space, discriminating non-nested models and discrimination of more than two models is discussed in detail.