A Bayesian state-space model treats the linear state-space model parameters Θ as random variables, rather than fixed but unknown quantities, with joint prior distribution Π(Θ). This treatment leads to a more flexible model and intuitive inferences. Bayesian models also allow you to specify non-Gaussian state disturbances and observation innovations.

Bayesian state-space model analyses involve drawing samples from the joint posterior distribution Π(θ|D_t), which is composed of the joint prior and data likelihood computed by the standard Kalman filter, where D_t is the response and predictor data set. Econometrics Toolbox™ uses a Markov chain Monte Carlo algorithm, such as the Metropolis-Hastings sampler, to sample from the posterior.

To start a Bayesian state-space model analysis, create a model object that best describes the structure of the state-space (from which the likelihood is inferred) and your prior assumptions on the joint distribution of the parameters by using bssm. Then, using the model and data, you can estimate characteristics of the posterior distributions or draw samples from the posterior distribution.