Parameter estimation for non-Gaussian autoregressive processes

It is proposed to jointly estimate the parameters of non-Gaussian autoregressive (AR) processes in a Bayesian context using the Gibbs sampler. Using the Markov chains produced by the sampler an approximation to the vector MAP estimator is implemented. The results reported here used AR(4) models driven by noise sequences where each sample is iid as a two component Gaussian sum mixture. The results indicate that using the Gibbs sampler to approximate the vector MAP estimator provides estimates with precision that compares favorably with the CRLBs. Also briefly discussed are issues regarding the implementation of the Gibbs sampler for AR mixture models.