Sequential parameter learning and filtering in structured autoregressive state-space models

We present particle-based algorithms for sequential filtering and parameter learning in state-space autoregressive (AR) models with structured priors. Non-conjugate priors are specified on the AR coefficients at the system level by imposing uniform or truncated normal priors on the moduli and wavelengths of the reciprocal roots of the AR characteristic polynomial. Sequential Monte Carlo algorithms are considered and implemented for on-line filtering and parameter learning within this modeling framework. More specifically, three SMC approaches are considered and compared by applying them to data simulated from different state-space AR models. An analysis of a human electroencephalogram signal is also presented to illustrate the use of the structured state-space AR models in describing biomedical signals.